An Interval Efficiency Measurement without Sign Restrictions in Data

Mostly, all conventional DEA models assume that input-output data are precise and nonnegative, but in real-life application, this condition is mostly not applicable. .rough progressive development in the methodology of DEA, some models separately deal with imprecise and negative data. In this study, the IMSBMmodel is proposed to evaluate the performance of a set of homogenous DMUs with imprecise and negative input-output data..e IMSBMmodel is far superior to models with similar capability because it considers the inefficiency caused by both radial and nonradial slacks. .e lower and upper bounds of interval efficiency calculated by the IMSBMmodel reflect the performance of observed DMU in most unfavourable and most favourable situations. Further, it is proved that the IMSBM model is units invariant, monotone, and translation invariant. Moreover, we elaborate both bounds of the interval efficiency are in the range of [0,1]. .e degree of preference approach is introduced to rank the DMUs. In addition, we compare the interval efficiency scores calculated by the IMSBMmodel and the interval SORMmodel and explain the reason for the difference between the scores. By adjusting the weights of inputs and outputs, it is found that only inefficiency scores fluctuate with slack weights.

Introduction
Due to limited production resources, efficiency is a key factor for both public and private sector organisations. ere are numerous techniques to measure the efficiency of a particular decision making unit (DMU), and one of the popular mathematical tools is known as data envelopment analysis (DEA). DEA is widely used to compare the performances of a set of homogenous DMUs by calculating the relative efficiency. With multiple-inputs and multiple-outputs, DEA can measure the relative efficiency of DMUs by using a ratio of the weighted sum of outputs to the weighted sum of inputs, and an efficient DMU always uses less inputs to produce a specific amount of outputs or produce more outputs using equal amount of inputs, as compared to other observed DMUs. However, two priori assumptions limit the application of conventional DEA models: (1) precise inputoutput data and (2) nonnegative input-output data. e conventional DEA models assume that input-output data should be precise. However, in real-life situations, it is not always possible. So, we often see bounded (interval), ordinal, and ratio bounded data in applications [1,2]. erefore, the assumption of precise data limits the application of conventional DEA models. To deal with this concern, Cooper et al. [3] firstly introduced imprecise DEA (IDEA) to cope with imprecise data, and there were several papers presented on the theoretical development of this method. Despotis and Smirlis [4] transformed classical CCR (Charnes et al. [5]) model into the case of interval data straightforwardly, and the proposed model gave the natural outcome of lower and upper bounds of efficiency scores. However, the transformation was applied only to variables. Wang et al. [6] developed a pair of interval models, and it was addressed in this work that ordinal preference information and fuzzy data could be converted into interval data through scale transformation and α-level sets, respectively. Jahanshahloo et al. [7] suggested the interval generalised DEA (IGDEA) model which treated the basic DEA models, specifically CCR model, BCC model (Banker et al. [8]), and free disposal hull (FDH) model [9], with interval data in a unified way. Aghayi et al. [10] presented a robust DEA model with a common set of weights (CSWs) under varying degrees of conservatism, and the interval data were used to represent data uncertainty. Azizi and Amirteimoori [11] and Toloo et al. [12] proposed DEA models to measure the relative efficiency of DMUs with flexible measures (also called dual-role factors) using interval inputoutput data. Shabani et al. [13] also proposed a common set of weights imprecise DEA (CSW-IDEA) to handle imprecise data. e models mentioned above were not slacks-based, indicating they could only measure the radial efficiency, but nonradial slacks were not accounted for. Tone [14] proposed a slacks-based measure (SBM) of efficiency. One of the advantages of the SBM model was that it put aside the assumption of proportionate changes in inputs and outputs and dealt with slacks directly. Lotfi et al. [15] developed an interval DEA model based upon the SBM model, and the DMUs were classified into three subsets according to the lower and upper bounds of the interval efficiency. Azizi et al. [16] generalised the SBM model into imprecise data to measure the performance of the DMUs, and the same constraint sets were used for maintaining the comparability.
Apart from the assumption of precise data, conventional DEA models assume that all inputs and outputs of DMUs are nonnegative. However, in real-life problems, this is not possible all the time, for example, when net profit acts as an output variable while loss happens. Traditionally, negative values are transformed into positive through data transformation [17], but somehow, such transformation impacts the solution of the objective function. Pastor and Ruiz [18] pointed out that the translation invariance property allowed a DEA model to deal with negative data. Cheng et al. [19] developed a variant of radial measure (VRM) to deal with variables that could be negative or nonnegative for different DMUs. Although the VRM input-oriented model was output translation invariant and the output-oriented model was input translation invariant, there were still some limitations while measuring the relative efficiency. e efficiencies given by the input-oriented VRM model might be negative [20] and the efficiencies given by the output-oriented VRM model could be in the range of [0.5,1] [21]. To avoid these drawbacks, Tung et al. [21] further defined two efficiency measures for input-oriented and output-oriented VRM models. Although the models mentioned above can deal with negative data and some of them are translation invariant, they are not slacks-based models and ignore the inefficiency caused by nonradial slacks. Sharp et al. [22] introduced the idea of the range of possible improvement [23] into the SBM model. ey developed a modified slacks-based measure (MSBM) model to evaluate DMUs with negative data. e MSBM model took into account input and output slacks and possessed the property of translation invariant.
Most existing works addressed only imprecise data or only negative data, and hardly any models considered these two characters simultaneously. Hatami-Marbini et al. [24] developed the interval semioriented radial measure (interval SORM) model to evaluate efficiency in the presence of interval data without sign restrictions. Although the interval SORM model was able to evaluate the efficiency with negative data, it only revealed the radial efficiency and failed in considering the inefficiency caused by nonradial slacks.
is study extended the MSBM model into an imprecise framework to evaluate the efficiency of particular DMUs with interval data. Compared with existing interval DEA models, the interval modified slacks-based measure (IMSBM) model considers both radial and nonradial efficiency from the perspective of slacks and is translation invariant to cope with the existence of negative data. ere are existing studies that illustrate that ordinal preference and fuzzy data can be converted into interval data [6,25,26].
erefore, the IMSBM model focuses on interval data in this paper. e rest of this paper is organised as follows. In Section 2, the IMSBM model is presented and proved to possess basic properties as an efficiency measurement. Section 3 classifies DMUs into three subsets, and the degree of preference approach is introduced to rank interval efficiencies. A numerical illustration is exemplified in Section 4. Moreover, in the last section, the findings of our study are concluded.

IMSBM Model
As Färe et al. [27] pointed out that there was an assumption of the constant returns to scale (CRS) that any DMU could be radially expanded or contracted to form other feasible ones, which caused inconsistency when negative data exist. However, it is not the case under variable returns to scale (VRS). erefore, the models mentioned below are assigned under the VRS.

MSBM Model with Precise
Data. Firstly, we illustrate the MSBM model constructed by Sharp et al. [22].
Consider a set of n homogenous units under analysis, and each of them consumes varying amounts of m different inputs to produce varying amounts of s different outputs. Specifically, DMU j (j � 1, 2, . . . , n) consumes x ij (i � 1, 2, . . . , m) of each input to produce y rj (r � 1, 2, . . . , s) of each output.
Generalising the SBM model to the case of nonpositive input-output data is not straightforward. Firstly, the translation invariant is not consistent when zero exists. Secondly, the optimal value can become negative with the existence of negative data [22]. Introducing the ideal point into the SBM model is fruitful in overcoming the drawbacks. For a given dataset, the ideal point is considered as I � (min j x ij (i � 1, 2, . . . , m), max j y rj (r � 1, 2, . . . , s)).
erefore, for DMU k , the range of possible improvement is defined as where s − ik and s + rk are slacks in the i th input and r th output of DMU k , respectively. e weights of each input w i and of each output v r are determined subjectively by decision makers and subject to m i�1 w i � 1, s r�1 v r � 1, w i ≥ 0, and v r ≥ 0.
Note that when R − ik � 0 or R + rk � 0, it is assumed that the corresponding (w i s − ik )/R − ik or (v r s + rk )/R + rk is dropped from the numerator or denominator.

MSBM Model with Interval Data.
Due to the lack of sufficient information in some complex systems, imprecise mathematics seems more appropriate to reality. e inputs and outputs are assumed to be interval variables denoted as x ij ∈ [x ij , x ij ] and y rj ∈ [y rj , y rj ], where x ij is the lower bound of x ij , x ij is the upper bound of x ij , y rj is the lower bound of y rj , and y rj is the upper bound of y rj . In this case, the ideal point in IMSBM model is considered as I � (min j x ij (i � 1, 2, . . . , m), max j y rj (r � 1, 2, . . . , s)). Consequently, for DMU k , the range of possible improvement is defined as erefore, the MSBM model for evaluating DMU k with interval data is subject to is zero, the corresponding term is assumed to be dropped from the numerator or denominator. e lower bound of the interval efficiency ρ k is the efficiency under the most unfavourable situation for DMU k . In this manner, DMU k consumes x ik to produce y rk while the DMU j consumes x ij to produce y rj (j ≠ k). Symmetrically, the upper bound of the efficiency ρ k is the most favourable situation for DMU k . In this manner, DMU k consumes x ik to produce y rk while DMU j consumes x ij to produce y rj (j ≠ k). erefore, model (5) can be replaced by a pair of precise models as follows: subject to subject to e IMSBM model can be transformed into a linear programming form by Charnes-Cooper transformation [28]. Considering multiplying a scalar variable t(t > 0) to both the numerator and the denominator of the objective function of (8), it does not impact ρ k . Adjust t and equal the denominator to 1; then, the denominator can be regarded as a constraint and the objective function is minimizing the corresponding numerator. e lower bound of the IMSBM model is subject to (11) is a nonlinear programming problem due to the nonlinear terms, and some definitions are needed to transform it into a linear programming problem. Assume subject to Assuming the optimal solution of (14) is Symmetrically, the transformed problem of (10) is subject to Assuming the optimal solution of (17) is (τ * k , t * , Λ * , S − * ik , S + * rk ), then the optimal solution of (10) is If the lower bound of DMU k is inefficient, it can be improved to be efficient by Symmetrically, if the upper bound of DMU k is inefficient, it can be improved to be efficient by 2.3. Properties of IMSBM. e following properties are considered as basic in designing an efficiency measure: P1: Units Invariant. It is considered to be an important property in DEA, and the term in general mathematical properties is known as dimensionless. P2: Monotone. e measure is monotone decreasing with the increasing of inputs or the decreasing of outputs. P3: Translation Invariant. It is critical, especially when input-output data contain zero or negative values.
IMSBM model is demonstrated to possess these properties in the following.

Theorem 1. IMSBM model is units invariant.
Proof. Considering the g th input and h th output in the model (8), rescale both bounds of the g th input by multiplying it a scalar α > 0 and rescale both bounds of the h th output by multiplying it a scalar β > 0. e ideal point is

slacks of inputs and outputs change into s
,j≠k λ j y rj + λ k (y rk − Δy rk ) − (y rk − Δy rk ). Proving ρ k is monotone can be converted into two problems: (1) the numerator of the objective function is a decreasing function of Δx ik and (2) the denominator of the objective function is an increasing function of Δy rk .
Firstly, we prove that the numerator of the objective function is a decreasing function of Δx ik . ere are two cases for R − ik ′ : )) ≤ 0. erefore, in this case, the numerator is a decreasing function of erefore, in this case, the numerator is a decreasing function of Δx ik ; In conclusion, the numerator of the objective function is a decreasing function of Δx ik . en, we prove that the denominator of the objective function is an increasing function of Δy rk . ere are two cases for R + rk ′ : (1) If ∀j ≠ k such that y rj ≤ y rk − Δy rk , then R +′ rk � y rk − Δy rk − (y rk − Δy rk ) � y rk − y rk . It can be proved that ′ )))/(d(Δy rk ))) ≥ 0. erefore, in this case, the denominator is an increasing function of Δy rk .
In conclusion, the denominator of the objective function is an increasing function of Δy rk .
In conclusion, model (8) is monotone decreasing with the increasing of inputs or the decreasing of outputs.
Likewise, model (10) can also be verified to be monotone decreasing with the increasing of inputs or the decreasing of outputs. erefore, the IMSBM model is monotone. is proof is complete. Proof. A measure is translation invariant if and only if the model is equivalent before and after the translation [29].
Transform the input data x ij and x ij (i � 1, 2, . . . , m) by the real number z i (i � 1, 2, . . . , m) and transform the output data y rj and y rj (r � 1, 2, . . . , s) by the real number t r (r � 1, 2, . . . , s), where z i subjects to x ij + z i ≥ 0 (∀j � 1, 2, . . . , n) and t r subjects to y rj + t r ≥ 0 (∀j � 1, 2, . . . , n) (without loss of generality, z i and t r are assumed to be nonnegative). e model of translated data is subject to Model (10) can be proved to be translation invariant likewise.
erefore, the IMSBM model is translation invariant. is proof is complete.
In the following part, let us demonstrate that the efficiency score of the IMSBM model is in the range of [0, 1].
Note, since n j�1 λ j � 1, With m i�1 w i ≤ 1 and s r�1 v r ≤ 1 (it is not greater than 1 because the corresponding terms are dropped when R − ik (R − ik ) and R + rk (R + rk ) are zero), the lower bound and upper bound of the efficiency score can be verified to be 0 ≤ ρ k ≤ 1 and 0 ≤ ρ k ≤ 1 (even if the input-output data are negative).
Since ρ k is obtained in the most unfavourable situation of DMU k and ρ k is obtained in the most favourable situation, the interval efficiency score satisfies 0 ≤ ρ k ≤ ρ k ≤ 1.
Mathematical Problems in Engineering

Advantages and Benefits of IMSBM.
To demonstrate the advantages over the existing models, we compared the IMSBM model with the IGDEA model [7], the interval SBM model [16] (Azizi et al. [16] did not specifically name their proposed model; for our convenience, we mentioned it as the interval SBM model in the comparison), the VRM model and its variants [19,21] (for our convenience, we mentioned them as the VRMs in the comparison), the MSBM model [22], and the interval SORM model [24]. Table 1 shows that the IMSBM model, as an interval model, can easily tackle the imprecise data without losing the information besides the situation complexity. Further, it has the advantage of handling the negative values in the data without any data transformation. At last, due to the slacksbased characteristics, the IMSBM model has the ability to reveal the inefficiency caused by both radial and nonradial slacks.
Applicability of DEA models on imprecise data extends its effectiveness for real-life situations. As imprecise data contain more information, IMSBM could be applied directly to measure the relative efficiency. It is important to mention that the IMSBM model is constructed without any prior assumption of nonnegative data. As an efficiency measure, the IMSBM model is units invariant, monotone, and translation invariant. With the translation invariance property, the IMSBM model can evaluate the efficiency of a particular DMU containing negative or zero value in the input-output data without any prior data transformation. is property ensures the effectiveness of the IMSBM model application in the existence of negative data. e IMSBM model puts aside the assumption of proportionate changes in inputs and outputs and deals with slacks directly. Although interval SBM models have the same ability, in the existing interval SBM models, translation invariant is not always consistent, and sometimes efficiency scores may be negative when negative inputs or outputs are employed in the evaluation process. However, efficiency measured by the IMSBM model always ranges from 0 to 1, even with the existence of negative data.

Classification and the Ranking of the DMUs
Since the efficiency score measured by the IMSBM model is calculated in an interval form, a simple and practical approach is needed for comparing and ranking the performance of the DMUs.
Firstly, the DMUs are classified into three subsets according to the interval efficiency (see [4,15,24]): (1) e strictly efficient subset is E ++ � DMU j , j � 1, 2, . . . , n | ρ j � 1, ρ k � 1 : both the lower and upper bounds of the interval efficiency score are equal to 1, indicating the observed DMU performs efficiently no matter in the most unfavourable or most favourable situation. (2) e weakly efficient subset is E + � DMU j , j � 1, 2, . . . , n | ρ j < 1, ρ k � 1 : the lower bound of the interval efficiency score is less than 1 and the upper bound of the interval efficiency is equal to 1, indicating the observed DMU performs efficiently only in the most favourable situation. (3) e inefficient subset is E − � DMU j , j � 1, 2, . . . , n | ρ j < 1, ρ k < 1 : both the lower and upper bounds of the interval efficiency score are less than 1, indicating the observed DMU performs inefficiently in the most unfavourable and most favourable situation.
Obviously, in complex systems, each subset contains more than one DMU. In addition to the classification, a ranking approach is needed in the last two subsets. Wang et al. [30] proposed the degree of preference approach to rank interval data by a matrix.
Suppose there are two interval efficiency denoted as , then the degree of preference of ρ k 1 over ρ k 2 (ρ k 1 > ρ k 2 ) can be defined as Symmetrically, the degree of preference of ρ k 2 over ρ k 1 (ρ k 2 > ρ k 1 ) can be defined as (25) It is easy to prove P(ρ k 1 > ρ k 2 ) + P(ρ k 2 > ρ k 1 ) � 1 and It can be verified if P(ρ k 2 > ρ k 1 ) ≥ 0.5 and P(ρ k 3 > ρ k 2 ) ≥ 0.5, then P(ρ k 3 > ρ k 1 ) ≥ 0.5, indicating the degree of preference satisfies transitivity. e ranking progress is outlined as follows: Step 1: calculate a n × n matrix of the degree of preference to reflect the interrelationship among DMUs: where Step 2: find out a row in which all of the elements except the diagonal one are not less than 0.5. e corresponding DMU k is regarded as the strongest performing one within the remaining DMUs.
Step 3: remove the k th row and k th column from the matrix.
Step 4: repeat step 2 and step 3 in the reduced matrix until only one DMU remains.

Property 1.
ere is a row in the matrix of the degree of preference in which all of the elements except the diagonal one are not less than 0.5.
If p 1n ≥ 0.5, then p 1j ≥ 0.5, j � 2, . . . , n. us, in the 1 st row of the n × n matrix, all of the elements except p 11 are not less than 0.5.
is proof is complete.

Numerical Illustration
To demonstrate the proposed IMSBM model, we use banking DMUs with positive and negative interval data. For performance evaluation, we used 20 commercial banks operating in the Gulf Cooperation Council (GCC) countries [24]. Table 2 illustrates three input ((1) total assets (ASST), (2) capital (EQTY), and (3) deposits (DEPO)) and two output ((1) loans (LOAN) and (2) profit (PROF)) data of 20 commercial banks. Table 2 shows the input-output data. According to the available data, some banks have negative profit at both lower and upper bounds (e.g., DMU 9 , DMU 11 , DMU 18 , DMU 19 , and DMU 20 ), some banks have negative profit at their lower bound but positive profit at upper bound (e.g., DMU 1 and DMU 12 ), and the rest have positive profit at both bounds. Now, the IMSBM model is applied to evaluate the interval efficiency scores of these banks. To simplify the problem, as it is presented in Table 3, the inputs and outputs are weighted equally, respectively. e interval efficiency scores and the classification of the 20 banks are shown in Table 4. As a comparison, the interval efficiency scores evaluated by the interval SORM model and the corresponding classification are shown in the last two columns. Table 4 shows the efficiency scores of all 20 DMUs evaluated by the IMSBM model. DMU 1 , DMU 3 , DMU 5 , DMU 7 , DMU 9 , and DMU 20 are strictly efficient, DMU 2 , DMU 11 , DMU 14 , DMU 15 , and DMU 19 are weakly efficient, and the rest of the DMUs are inefficient.
Comparing the efficiency scores calculated by the IMSBM model with the efficiency scores calculated by interval SORM model, it can be seen that strictly efficient DMUs in the IMSBM model are still strictly efficient in interval SORM model (e.g., DMU 1 , DMU 3 , DMU 5 , DMU 7 , DMU 9 , and DMU 20 ), but strictly efficient DMUs in interval SORM model are not always strictly efficient in IMSBM model (e.g., DMU 15 ). e reason behind these results is that the interval SORM model just focuses on radial efficiency while the nonradial inefficiency is ignored, which fails to reflect the inefficiency caused by nonradial slacks. However, the IMSBM model considers the inefficiency caused not only by radial slacks but also by nonradial slacks. erefore, the efficiency score evaluated by the IMSBM model cannot be greater than the interval SORM model.
In addition to the classification, the detail of the performance ranking is needed. e strictly efficient DMUs are ranked top position and the remaining DMUs are assigned the ranks according to the degree of preference. Table 5 shows the degree of preference among the weakly efficient and inefficient DMUs.
From the degree of preference matrix, the relationship among the weakly efficient and inefficient DMUs is established as DMU 14  DMUs in the top position and remaining in the second position, all the DMUs are ranked as shown in Table 6.
With the allowance to alter the input and output weights, we adjust them to illustrate the effect of weights on the efficiency scores. e unequal weights are shown in Table 7. e interval efficiency scores, classification, and the ranks of the 20 banks with unequal weights are shown in Table 8. e comparison with the interval SORM model is omitted just because it is not directly relevant at this stage.
Comparing Table 8 with Table 4, we find that adjusting the weights has no impact on the classifications of the

Conclusion
Most commonly used conventional DEA models assume that input-output data are precise and nonnegative, but in complex situations, it is not always possible that this assumption is satisfied. e literature suggests that several models are developed to handle the problem of imprecise and negative data. However, till yet, there are seldom models developed to handle imprecise data and negative data simultaneously. In this study, the IMSBM model is proposed to evaluate the relative efficiency of a set of DMUs with imprecise and negative data. e novelties of this model are that it could handle the data with these two mentioned characteristics simultaneously, and it puts aside the assumption of proportionate changes in inputs and outputs and deals with slacks directly, which ensures the efficiency obtained considering both radial and nonradial slacks. After restraining the limitation of conventional DEA models, the IMSBM model is more superior in practice.
is research proves that the IMSBM model is units invariant, monotone, and translation invariant. Moreover, the lower and upper bounds of the interval efficiency score are in the range of [0,1], even with the existence of negative data. A numerical example illustrates the application of the IMSBM model, and the efficiency scores obtained are compared with those evaluated by the interval SORM model.    Further classifying the DMUs into three subsets, the degree of preference approach is referenced as a simple and effective tool to rank the weakly efficient and inefficient DMUs. With the allowance to alter the input and output weights, we adjust them and find out that only the inefficient scores fluctuate with the weights. Further work based on this paper is combining the IMSBM model with other theoretical studies that possess the abilities to weight slacks.

Data Availability
All the data used to support the models' application were collected by Hatami-Marbini et al. from different sources, including BANKSCOPE database. e data are included within the article (see Table 2).


Implementation of evacuation measures during natural disasters under conditions of the novel coronavirus (COVID-19) pandemic based on a review of previous responses to complex disasters in Japan

We aimed to investigate how evacuation measures could be effectively implemented in the event of multiple disasters caused by natural hazards under conditions of the novel coronavirus infection (COVID-19) pandemic, which is rapidly spreading worldwide. We conducted a review of literature focusing on complex disasters, entailing natural disasters in combination of outbreaks or endemics of infectious diseases. Using the Google Scholar search engine, we identified and reviewed 24 papers sourced from academia, governments, and concerned organizations, and associated data on such disasters, commencing with the Great Hanshin-Awaji Earthquake, which occurred in 1995. In light of our review, we developed a summary of correspondences and problems linked to compound disasters involving conjunctions of outbreaks/endemics and natural disasters that could offer insights for developing measures to deal with natural disasters that occur in the context of the COVID-19 pandemic. We subsequently attempted to differentiate the characteristics of evacuation measures relating to COVID-19 from those relating to other infectious diseases using three sets of extracted keywords: (1) surveillance and information sharing, (2) evacuation center environment and stockpiled supplies, and (3) community disaster risk reduction and community leadership. We identified issues relating to evacuation measures that would need to be explored further to improve disaster management and preparedness in the future.

Background
Following the initial occurrence of COVID-19 in the city of Wuhan in Hubei Province, China in December 2019, this highly infectious disease rapidly spread throughout China and the world, prompting the World Health Organization (WHO) to declare a pandemic on March 12, 2020 [1]. As of May 31, 2020, there were 16,851 cases of CIVID-19 infections and 891 deaths in Japan [2]. COVID-19 has a post-infection incubation period of 1-14 days. The main symptoms reported by many infected people are cold-like symptoms, such as fever and dry cough, excessive fatigue, and dysgeusia. Approximately 80% of COVID-19 patients experience spontaneous remission, but 20% go on to develop pneumonia/pneumonitis. Of the latter, the high-risk group comprises not only older individuals and those with certain predisposing risk factors, such as hypertension, diabetes, and/or cardiac diseases but also some young adults, who develop severe illness.
Existing antivirals and related drugs have only provided partial, if any, beneficial outcomes. Moreover, there are fears that the severe disruptions of economies and daily life caused by the pandemic will be prolonged rather than transient phenomena. Therefore, there is an urgent need to develop and establish effective drugs and vaccines to suppress and overcome the pandemic.
At the time of writing, the rainy season is approaching in Japan, leading to growing concerns about the potential occurrence of natural disasters like flooding coinciding with the COVID-19 pandemic. The Cabinet Office of Japan has therefore issued multiple notifications providing evacuation guidelines, and various organizations have issued calls for preparations for complex disasters involving a conjunction of COVID-19 and natural disasters [3].
The main concerns at the time of occurrence of such complex disasters relate to evacuation procedures. The first volume of the Preliminary Report on the Spread of Novel Coronavirus Infection [4], published in 2020 by the Disaster Reduction and Human Renovation Institution and the Novel Coronavirus Evacuation Support Book [5] both describe concrete methods for operating evacuation centers and measures to be taken for each evacuee. The option of dispersal of evacuees, with suggested evacuation points, is Progress in Disaster Science 8 (2020) 100127 also included in the Recommendations Regarding Evacuation, issued by the Japan Society for [6].
The Great Hanshin-Awaji Earthquake, which occurred in January 1995, prompted an evaluation of countermeasures implemented during the simultaneous occurrence of large-scale disasters and infectious diseases. A group of researchers who implemented "A study on construction of health risk management system for dental health care in large-scale disaster," hereinafter referred to as the Study Group, reported that aspiration pneumonia was prevalent among evacuees, especially older evacuees, who were physically and mentally exhausted after this earthquake [7]. Subsequent natural disasters, notably the Great East Japan Earthquake (March 2011), the Kanto and Tohoku Heavy Rains (September 2015), and the Kumamoto Earthquake (April 2016) have all been associated with outbreaks of infectious diseases at evacuation centers [8]. Outside of Japan, there have been reports of acute gastroenteritis following Hurricane Katrina (August 2005) [9] and of cholera followed by the Haiti Earthquake (January 2010) [10].

Purpose of this study
Each of the above-mentioned studies focused either on the particular natural disaster examined or on the associated pandemic. In light of their finding that only a few studies have linked disaster risk reduction to biological hazards, such as COVID-19, Zhang and Shaw [11] have called for studies that incorporate various aspects of complex disasters (pandemic response, recovery, and long-term development). To date, there have been no attempts to compile and systematically organize information on past occurrences of complex disasters, entailing a combination of natural disasters and infectious diseases and to discuss evacuation measures that specifically relate to COVID-19, distinguished from other infectious diseases. While organizations have provided recommendations, and individual local governments have published evacuation manuals (e.g. [12]), a notable gap in the literature concerns measures relating to evacuation and the operation of evacuation centers in the case of a complex disaster in which COVID-19 and natural disasters occur simultaneously.
Therefore we aimed to conduct a systematic review of various available studies and reports on natural disasters and infectious disease epidemics. Accordingly, we compared evacuation procedures during natural disasters in Japan, which are frequent occurrences, in the context of common infectious diseases and subsequently extracted specific issues that would apply to evacuees during the COVID-19 pandemic.

Methodology
We conducted a search of the Google Scholar database using "disaster" and "infection" as keywords for identifying and extracting reports and papers focusing on disasters associated with infectious diseases in Japan, commencing with the Great Hanshin-Awaji Earthquake in 1995. Our search yielded a total of 24 academic and non-academic documents and papers on measures adopted to handle outbreaks of infectious diseases at evacuation centers and other places in the event of disasters. As of the end of May 2020, we have been unable to find any literature that focused on COVID-19 and evacuation during a natural disaster using the keywords "COVID-19" and "evacuation."

Infectious diseases and natural disasters
The WHO recommends the adoption of systematic measures relating to the following steps: (1) rapid assessment, (2) prevention of infections, (3) surveillance, (4) disease outbreak control, (5) disaster management, and (6) evaluation aimed at controlling the spread of infectious disease during disasters [13]. However, these measures are difficult to implement in a situation where damage is so extensive that medical institutions and administrative organizations are also at risk of being affected because the medical support staff at hospitals are themselves potential victims of the disaster. Surveillance was implemented 20 days to 1 month after the 2011 Great East Japan Earthquake and 5 days after the 2018 Kumamoto Earthquake [14]. Although systematic measures and mechanisms for enabling quick responses have greatly improved, in the event of a large-scale disaster, they may not function during the initial post-disaster stage. Surveillance entails various constraints, such as the preparation time required, disruption of reporting procedures, and an excessive burden placed on staff members at the evacuation centers. In particular, many small evacuation centers do not have permanently stationed medical professionals, and in most cases, the victims' situations are not monitored. In the event of a large-scale disaster, it is necessary to develop and strengthen human resources for implementing countermeasures to control infectious diseases because not only specialists, such as public health nurses, are required to deal with infectious diseases within evacuation centers but also other local government personnel have important roles to play [8]. Furthermore, a system should be established for disaster preparation that enables cooperation and information sharing with specialized organizations, such as local government departments, medical institutions, and universities during times of non-crisis.
There are three key factors that define the epidemiology and pathophysiology of infections: pathogens, hosts, and environments, of which environmental factors reportedly have the greatest influence on the risk of infectious disease outbreaks occurring after natural disasters [15]. The deterioration of hygiene conditions in disaster-affected areas and the forced confinement of many victims within small spaces in evacuation centers increase the risk of transmission of infectious diseases. Therefore, a countermeasure focusing on maintaining a sanitary environment within evacuation centers is critical.
Kamase and Tokita [16] have pointed out that there would be differences in the storage locations of stockpiled goods, the maintenance of records at evacuation centers, and the preparation of information for evacuees, depending on whether evacuees have previously experienced a disaster. Clearly, another countermeasure relates to appropriate response of administrators. However, in the event of a large-scale earthquake, it is likely that administrative agencies themselves will be damaged. In addition, not only the staff of the evacuation centers but also the evacuees must protect themselves against infectious diseases at small evacuation centers because of the lack of human resources. The evacuees are required to be self-reliant. Okada et al. [17] noted that community empowerment has greatly contributed to the maintenance of healthy environments at evacuation centers.
In light of the above considerations, we extracted three sets of keywords to explore the relationship between infectious diseases and natural disasters that may have been issues during previous disasters. These keywords were "surveillance and information sharing," "evacuation center environment and stockpiled supplies," and "community-based disaster risk reduction and community leadership." In the following sections, focusing on these three sets of keywords, we explore the differences between COVID-19 and other infectious diseases within responses to previous natural disasters and infectious diseases described in the reviewed literature.

Aspiration pneumonia during the great Hanshin-Awaji earthquake
The Great Hanshin-Awaji Earthquake that erupted in Japan's Hyogo Prefecture in 1995 caused significant damage in the cities of Kobe and Osaka and left 6434 people dead. Of these deaths, 5512 were directly attributable to the earthquake, caused by collapsed buildings that led to crushing and suffocation of victims. Of the remaining victims, 922 died of pneumonia, strokes, and myocardial infarctions induced by the disaster. Approximately 60-80% of pneumonia cases in older evacuees at the time of the earthquake were thought to be or diagnosed as aspiration pneumonia. Reports on responses to the Great Hanshin-Awaji Earthquake and on aspiration pneumonia were compiled by a team of researchers [7].
Most cases of aspiration pneumonia that occurred among older, immunocompromised individuals are believed to have been caused by the aspiration of saliva rich in oral bacteria because of reduced oral care during the extensive disaster. It has been reported that immediately after the Great Hanshin-Awaji Earthquake many older individuals were unable to maintain oral hygiene practices, such as gargling, because of an extreme shortage of drinking water or because of an increase in oral bacteria caused by poor cleaning of dentures. According to the findings of one study, oral care that is thoroughly performed, thus preventing an increase in oral bacteria while keeping the oral cavity and denture surfaces clean, can lead to a reduction in incidences of pneumonia among the elderly by 40% [18]. However, in the event of large-scale disasters, the failure of the water supply system results in difficulties in procuring water at evacuation centers. Therefore, there is a possibility that sanitation practices required for effective health management, such as hand washing, gargling, and brushing teeth, cannot be performed. As noted in the report, the issue of privacy relating to denture removal also arose at the evacuation centers. In the absence of water, chewing sugarless gum containing xylitol is considered an effective alternative oral hygiene practice. In addition, mouthwashes, especially "toothpaste sheets," are considered effective, and stockpiles of these items should be maintained at evacuation centers [18].

Influenza and infectious gastroenteritis after the great East Japan earthquake
The Great East Japan Earthquake, which occurred in March 2011, caused extensive damage over a wide area, compelling the evacuation of approximately 300,000 people. Influenza and infectious gastroenteritis spread in the disaster-affected area because the earthquake occurred during the cold weather season when there are frequent outbreaks of such infectious diseases, even in the absence of disaster-related events (e.g., [8]). As this was a large-scale earthquake, medical supplies and equipment fell short in the medical facilities as well as at the evacuation centers. Within the medical facilities, personal protective equipment, such as alcoholbased disinfectants, masks, and aprons were generally sufficient, but supplies of paper towels, liquid soap, containers for infectious medical waste, and catheters, which are used frequently on a daily basis, were inadequate. At the evacuation centers, there were concerns about the high risk of infectious disease transmission within deteriorating sanitary environments, given large numbers of people living in close proximity in spaces such as school gymnasiums and halls and the scarcity of water for washing hands, cleaning, and food sanitation caused by the suspension of water supplies., Alcohol-based disinfectants, masks, and Tamiflu stockpiled for influenza outbreaks were procured for the evacuation centers through the coordinated efforts of the prefectural government and medical institutions.
Surveillance is one of the measures applied for monitoring and controlling infectious diseases [19]. However, at the time of the Great East Japan Earthquake, information could not be transmitted because of the damage or destruction of medical institutions and power outages, making it difficult to conduct accurate assessments of trends of infectious disease occurrence. Under such circumstances, two types of surveillance were implemented for infectious diseases at evacuation centers in Miyagi Prefecture because the operation method was changed during the course of its implementation. According to reports obtained from 34 municipalities within the prefecture, the first type of surveillance was implemented from March 18 to May 13, 2011. The second type of surveillance was conducted from May 10 to November 6, 2011 within 256 shelters across 27 municipalities. The implementation of surveillance immediately after the disaster was particularly difficult because of gasoline shortages and traffic disruptions. One week after the disaster, only 4.4% of the evacuation centers were covered. Surveillance was limited for 2 weeks after the earthquake at a time when the number of occupied shelters and victims peaked [20].
In closed or semi-closed environments, such as evacuation centers, there is an increased risk of infections and their outbreaks. According to Endo et al. [21], it is important to implement basic measures, such as nonpharmacological interventions (NPIs) (e.g., hand hygiene, cough etiquette, ventilation, and isolation), early detection of symptomatic persons, rapid test performance, isolation of infected individuals, and monitoring of close contacts. Proper implementation of the NPI in the midst of infectious disease outbreaks, such as influenza and infectious gastroenteritis, in disaster-affected areas includes the conduct of appropriate and accurate educational activities, an example being the distribution of the "eight articles on infection prevention" educational posters. Posters of this type for enhancing NPI literacy are posted at evacuation centers.
According to [8], adequate communication of information was considered the most important issue when dealing with infectious diseases in the aftermath of the Great East Japan Earthquake. For several days after the disaster, all means of communication, including fixed phones, mobile phones, and the Internet, were unusable, including in the city of Sendai, which is the largest city in the Tohoku region. In rural coastal areas that were severely damaged by the accompanying tsunami, mobile phones were not usable for a month after the disaster. Under such circumstances, cooperation is necessary not only among hospitals capable of dealing with infectious diseases in large cities but also among rural communities and hospitals, social welfare facilities, and other relevant agencies. Moreover, evacuation centers and administrative organizations must respond in a unified manner. In particular, the construction of a system that enables the restoration of medical institutions and the transmission and sharing of information, right from the initial stage of recovery when information transmission is challenging, is essential [8].

Torrential rain in the Kanto and Tohoku regions
In September 2015, Typhoon No. 18 and other heavy rainfall events that occurred in the regions of northern Kanto and southern Tohoku caused levees to collapse and flooding to occur in several areas. A heavy rainfall emergency warning was issued throughout Ibaraki Prefecture, and a total of 229 evacuation centers were set up in 35 municipalities at the peak of the crisis. In Ibaraki Prefecture, in light of lessons learned from the Great East Japan Earthquake, the surveillance of evacuation centers was incorporated into the prefectural disaster prevention plan. Immediately after the occurrence of the flood disaster, the prefectural government's health prevention division applied its evacuation center surveillance system [22].
Information was collected and transmitted to the public health center by fax or to the Infectious Disease Information Center of the Prefectural Institute of Public Health by email. Even when there were no reports of disease, the Infectious Disease Information Center called the individuals in charge of the evacuation centers to check their status. Because the surveillance started on the day of the flooding disaster caused by torrential rain in the Kanto and Tohoku regions, information on the occurrence of infectious diseases in evacuation centers could be collected quickly and shared among the persons in charge in the municipalities and public health centers. Thus, the provision of health guidelines at an early stage contributed to effective interventions to contain outbreaks of infectious diseases. In addition to the prior incorporation of the surveillance of evacuation centers into the prefecture's regional disaster prevention plan and disaster response manual, other important pre-disaster measures are required. These measures include formulating specific guidelines for smoother implementation and conducting drills to familiarize the concerned parties with surveillance operations at the time of the establishment of evacuation centers.

Infectious gastroenteritis during the Kumamoto earthquake
In the case of the Kumamoto Earthquake, which occurred on April 16, 2016, evacuation centers were set up on the day of the main shock and medical care was initiated the same day. Localized torrential rainfall, measured at 105.5 mm, continued unabated for 9 h on April 21, resulting in the issuance of an evacuation advisory that led to increased numbers of occupants at the evacuation centers. At that time, there were reports of increased numbers of individuals suffering from diarrhea at the evacuation centers in north-eastern Kumamoto Prefecture; testing with a Norovirus rapid diagnosis kit confirmed a positive result for infectious gastroenteritis.
According to Goto and Okamoto [23], the sanitary environment of the evacuation center was inadequate, with no partitions in the living space provided by a school gymnasium. People wore their shoes, which were covered in sediment and excrement from the rain, to pass in and out of this space through a corridor. Because of the water shortage and the lack of disinfectants, lavatories could only be cleaned with water stored in buckets, and the wearing of gloves was the only protective measure taken to prevent infections. Thorough hand washing with water and soap was difficult to perform because of the water shortage, and some evacuees did not use soap and water at all to wash their hands.
On the same day that an evacuation order was announced, posters calling for hand washing with water and soap were displayed in the clinic. Further, the wearing of shoes was strictly prohibited throughout the gymnasium. Additional measures were implemented within 72 h of the increase of infected individuals, which included isolating patients with symptoms of acute gastroenteritis.
While many of the required environmental measures were initiated within 24 h of the disaster, surveillance could not be implemented because of the lack of staff at the medical institutions and the large numbers of evacuees. If the surveillance had been carried out, individuals with symptoms of acute gastroenteritis would have been identified from an early stage and the spread of the infection could have been prevented. Further, it would have been possible to work with administrative officials at evacuation centers from an early stage [23].
Most of the evacuation centers that the Kagoshima Prefecture Medical Association assisted were established within schools. Preparations for classes that began simultaneously made it difficult to use classrooms and health rooms because evacuees and patients were being attended to in these rooms. Thus, places where individuals with infectious diseases could be isolated were limited. In cases where it was difficult for such patients to return home, hospitalization was considered, and pre-emptive medication was administered to close contacts at the evacuation centers. If a gastroenteritis infection is suspected, regardless of whether the results of the norovirus rapid test are positive or negative, the patient is asked to return home if he or she is able to do so. While all of these measures were taken at designated evacuation centers, it cannot be confirmed from information available with the government whether sufficient measures were implemented at nondesignated evacuation centers and at shelters that did not receive relief supplies, including masks and hand disinfectants.
The performance of administrative functions mostly continued because of the efforts of the staff and the clear definitions of their roles established in the regional disaster prevention plan before the disaster struck. In addition, the medical association and the local government had built up a good relationship through pre-disaster collaborative activities, such as home medical care. Consequently, whereas activities relating to surveillance and infection control at the evacuation sites began 20 days to 1 month after the occurrence of the Great East Japan Earthquake, they began as early as 5 days after the occurrence of the disaster in Kumamoto. What was critically required at that time was not only information sharing among evacuation centers and medical rescue teams but also cooperation among these organizations. In the case of the Kumamoto Earthquake, the "Surveillance in Post Extreme Emergencies and Disasters, Japan version," known as "J-SPEED," was introduced on a trial basis for the first time. It is expected that in future, this tool will enable the number of patients to be visualized through the inputting of information on the victims treated by medical relief teams at the emergency headquarters.
One important characteristic of the Kumamoto Earthquake was that many evacuations occurred at night and many evacuees spent the nights in their cars. Determining the symptoms of the infectious disease among evacuees who stayed in their cars was especially difficult. To address such issues, evacuees should be alerted, their self-reporting should be facilitated, and the managers of evacuation centers should devise surveillance strategies for them. In addition, because the government was not aware of nondesignated evacuation centers, which were consequently omitted during the patrols, it is possible that information regarding the spread of infectious diseases would not have been reported to medical institutions [14].

Differences between COVID-19 and other infectious diseases during natural disasters
We applied the three previously mentioned keywords as an axis for considering evacuation issues in the context of the COVID-19 pandemic, focusing on differences between COVID-19 and other infectious diseases. Table 1 presents a comparison of evacuation status during previous complex disasters and pertinent issues under conditions of the COVID-19 pandemic.

Surveillance and information sharing
Whereas rapid diagnostic immunochromatographic kits are available for influenza and norovirus, they are only partially available for COVID-19. Evidently, rapid diagnosis of COVID-19 infected persons is essential, but the only method currently available for diagnosing COVID-19 is polymerase chain reaction (PCR) testing, which is difficult to carry out at evacuation centers at the time of a disaster. While the establishment of a surveillance system that includes the use of rapid and sensitive diagnosis kits should be a future priority, at present, this system is limited to isolating infected individuals, which is difficult to achieve given that many people are asymptomatic. In the case of infectious diseases, such as infectious gastroenteritis, contact transmission is dependent on evacuation centers' environments, whereas in the case of COVID-19, which is regarded as an infection transmitted through both contact and droplets, the disease may spread rapidly from the infected person. There were significant delays in carrying out post-disaster surveillance at evacuations centers in the case of events such as the Great East Japan Earthquake. However, in the context of COVID-19, because subjective symptoms may be difficult to identify, an individual may unknowingly transmitted the infection to others leading to its rapid spread. Therefore, it is critical that surveillance is conducted immediately after the occurrence of a disaster and that the stipulated sequence of measures is promptly initiated, such as immediate isolation in the case of a symptomatic individual. To prevent the spread of infection in the event that an individual is symptomatic, evacuees should implement health management on their own, using health check sheets and other relevant tools, and they should record the names of their contacts.
Initiating early surveillance is difficult in the event of a major disaster, as medical and administrative institutions may have been extensively damaged. Nevertheless, the establishment of a pre-disaster surveillance method in collaboration with the concerned individuals at evacuation centers is necessary to detect occurrences of infectious diseases at an early phase. In particular, a strategy of dispersed evacuation is recommended under conditions of the COVID-19 pandemic, while conducting continual surveillance, even when evacuation is dispersed. To ensure efficient information sharing, non-designated evacuation centers and evacuees should be listed simultaneously. A surveillance method based on self-reporting should be designed, and check sheets should be prepared in advance to facilitate responses to surveillance at a later date. In addition, surveillance of evacuees as well as external staff and visitors entering the centers should be considered.

Evacuation center environments and stockpiled supplies
Schools were designated as evacuation centers during previous disasters, and in some cases, it was not possible to secure spaces for isolating individuals with infectious diseases. In the case of the COVID-19 pandemic, the issue of securing space for isolation is critical for preventing the spread of the infection. In general, whereas the area to be occupied by evacuees is calculated using the standard prescription of 1.57-2.93 square meters per person in Japan [24], the international "Sphere criteria" standard, which provides several guidelines on sanitation and maintenance of the living environments of evacuation centers, stipulates a minimum area of 3.5 square meters per evacuee [25]. Combined with social distancing of 2 m, the total area required per person would be 6 square meters according to the international standard. Accordingly, the number of people who could be accommodated in shelters would be reduced from one-third to a quarter of normal occupation. Evidently, the designated evacuation centers would not be sufficient to accommodate all of the evacuees. Provided that dispersed evacuation is conducted along with surveillance and information sharing, as discussed above, it would be appropriate. Another potential issue concerns the difficulty of procuring and distributing stockpiled goods, such as masks, tents, and cardboard boxes for separating compartments allocated to each evacuee at evacuation centers in the event of a pandemic. Therefore, countermeasures such as private procurement of supplies should be considered.

Community disaster risk reduction and community leadership
According to Okada [17], there is an increased risk of outbreaks of infectious diseases at evacuation centers during disasters, and hand hygiene in excess of conventional practices is required as an infection control measure. However, judgments and responsibilities for maintaining hand hygiene lie with the evacuees, who should be self-reliant. Strong "leadership of the people" is reported to have contributed significantly to the maintenance of sanitary environments in evacuation centers in the past [17]. Therefore, raising awareness to prevent the spread of infection within communities and efforts to maintain sanitary environments are essential. The question of whether "leadership of the people" can be demonstrated in the case of dispersed evacuation remains a critical one.

Conclusion
In this paper, we have presented a comprehensive review of countermeasures taken during previous disasters and outbreaks of infectious diseases and have outlined issues relating to the formulation of evacuation measures required during complex disasters under conditions of the COVID-19 pandemic in preparation for complex disasters. For example, while the evacuation of residents living in high-risk areas is essential, the practice of keeping them concentrated within evacuation centers needs to be revised. Given the capacities of evacuation centers and the need to practice social distancing, a strategy of dispersed evacuation is necessary. In the case of dispersed evacuation under conditions of the COVID-19 pandemic, providing that disaster risks are not high, evacuees' homes and cars may provide alternative shelters to evacuation centers. However, the problems of information sharing, identification of evacuees, and surveillance need to be addressed. Evacuation methods may also differ depending on the duration of the evacuation (shortterm or long-term), so more specific and appropriate evacuation methods need to be developed.
In addition, asymptomatic or mildly ill patients may be treated at home or at accommodation facilities. More specific options for evacuating such individuals need to be considered. To reduce the numbers of evacuees, it is essential to develop systematic approaches and measures for evacuees that are differentiated according to the targeted hazards.
Future studies should focus on examining more concrete evacuation measures. One study could focus on the responses of India and Bangladesh concerning evacuations that were compelled by a cyclone in the Indian Ocean at the end of May 2020. Comparative studies of Japanese and foreign case studies relating to evacuation associated with natural disasters under conditions of COVID-19, ways of running evacuation centers, and various available options could yield useful insights. In addition, guidelines on evacuation methods and shelter management methods specific to COVID-19, which contribute to a reduction of the complex disaster risk, should be prepared on an urgent basis and disseminated to governments at home and abroad, local governments, and other administrative organizations.  In the case of COVID-19, which is regarded as an infection that is spread through contact or droplets, there is a risk of rapid spread from infected persons. 20 days to 1 month after the Great East Japan Earthquake Therefore, a system is required that enables post-disaster surveillance to be carried out simultaneously with the establishment of evacuation centers.

Disclosure of funding
5 days after the earthquake in the case of the Kumamoto Earthquake

Method of implementing surveillance
Continuous implementation of measures without omissions, even for small-scale evacuation centers and evacuees who are dispersed, is essential.
Surveillance was conducted by public health nurses and evacuation center staff using surveillance systems.

Method of sharing information
A system for ensuring that information reaches evacuees, including those who are dispersed or in small-scale evacuation centers, is necessary.
Sharing information with small-scale evacuation centers was challenging.
Evacuation center environment and stockpiled supplies (public assistance) Evacuation space 6 m 2 per person is required for securing 2 m of social distance. Typically, 1.57-2.93 m 2 of space per person was maintained at evacuation centers. The number of individuals who can be accepted at evacuation centers will be about one-third of the number usually accepted, making it more difficult to secure evacuation space.

Spaces for isolation
Because droplets are the infectious agent, securing space for isolation is the most critical issue.
In some evacuation centers established at schools designated for this purpose, it was impossible to secure spaces for isolation. Stockpiled supplies During pandemics, masks and alcohol disinfectants are in short supply.
Xylitol gum and mouthwash are effective for oral care when the water supply is cut off. Therefore, evacuees need to bring these items with them.
Supplies of masks and alcohol-based disinfectants could be maintained through stockpiling. Supplies could be provided to meet the shortage. Community disaster risk reduction and community leadership (self-help and mutual assistance)

Sanitary environment
Hand hygiene that extends beyond conventional practices is necessary and is performed according to individual evacuees' judgments and sense of responsibility.
Knowledge dissemination through visiting doctors and education of public health nurses at evacuation centers Autonomous activity Self-governance entailing residents' leadership is challenging to implement in the case of dispersed evacuees.
A hygienic environment can be maintained at environmental centers through forms of leadership existing among residents, such as residents' associations.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.


Sustainable development management: analysis of interaction of social institutions (on the example of the Republic of Tatarstan)

This work focuses on the changes that occur in the geopolitical and economic systems and directly affect the functioning of the institution of social protection of the population. The purpose of this article is to analyze the impact of state management processes on the institution of social protection of the population in terms of statistics. With the help of a secondary analysis of sociological research, federal and regional regulatory framework, statistical indicators of the 2012-2018 period, the author considers social phenomena that cause the transition to sustainable development. Researchers study the assessment of the impact of social institutions in detail, among them: economics, politics, international activities, health care, religion, education for the society in the context of modern trends and prospects for sustainable economic development. The article examines the economic and geopolitical crises and their impact on the sphere of social protection of the population. The analysis made it possible to conclude that the political institution determines the vector of development of social protection of the country as a whole, and the institution of religion locally provides assistance to certain segments of the population. The close relationship of the field of health and education with each other is shown, as well as the relationship with other social spheres, in order to ensure sustainable development of the territories.

Introduction
The solution of socially significant issues lying in the field of intersection of different spheres of life requires close cooperation with the specialists from a wide range of scientific knowledge in the field of health care, religious studies and others. Below we will consider the interaction of the institution of social protection of the population with other institutions in more detail. The main task of social protection of the population is the implementation and improvement of state policy and public administration in the field of improving the level and quality of life, well-being of the population. Various factors influence the institution of social protection of the population and the social policy of the country as a whole. Quantitatively and qualitatively, these factors are extremely numerous, diverse and multidirectional. Their combinations are even more varied, which determines the greater complexity of their classification. Factors such as the state of the economy, the political situation, scientific and technological progress, sociocultural and international events have an indirect impact, that is, they have a certain potential for impact, without exerting it directly and immediately. In this article, the authors, using the secondary analysis method, reveal the interaction and influence of state processes on the functioning of the institution of social protection of the population.

Materials and methods
The article presents the results of a secondary analysis of the following studies: "Economic crisis and consumption" (2014-2015, Levada Center) and "Indices of social well-being"

Results and Discussion
The state, as a political institution, is responsible for the safety of a society. The state performs various internal functions, such as regulating the economy, maintaining the stability of the society, ensuring the social harmony, ensuring the protection of the population, and many others. Let us consider in more detail how the state influences the functioning of the institution of social protection of the population. The institution of politics is determined by various trends, including the sociocultural ones.
Interest groups and public, volunteer, charitable organizations are also an element of the political institution. It is these social agents that can influence the political sphere in which social service issues are raised. For example, in the subject of Russia -the Republic of Tatarstan (hereinafter -RT), the problem of disabled people attracted the attention of such a social agent as the All-Russian Society of Disabled People, contributed to the adoption of various kinds of legislative acts: 1) long-term target program of the Republic of Tatarstan "Accessible Environment Globalization, development of the scientific field and the emergence of new technologies have led to the information revolution. There is an opportunity to exchange information between the regions, countries and international organizations, the leaders of the states. This, in turn, determines the emergence of not only the norms of international law themselves, but also the emergence of an international institution. The institution of social protection of the population also does not stand aside, and actively interacts with international organizations and institutions, which in turn leads to improvement, changes in the institution of social protection and its parts. For example, consider how international relations affect the institution of social protection of the population. First of all, we will describe sports events such as 2013 Universiade, 2015 World Aquatics Championships and 2018 FIFA World Cup, the 45th World Skills World Championship of 2019. First of all, these events have a huge legacy. This includes, for example, the construction of Kazan-Arena sports facilities, a water sports palace and other facilities that meet international standards and requirements, including the requirement to provide a barrier-free environment, thanks to which the sports infrastructure is gradually becoming accessible to people with disabilities. So, from 2010 to 2013, an increase in the number of equipped sports facilities can be observed, which was previously not at all a priority in sports policy, and today many sports facilities are adapted for sports for people with disabilities [1,47]. If in 2011 the share of disabled people involved in sports was 4.25%, then by 2013 their share had grown to 6.9%, and by 2018 -already up to 18.3% [2]. Thus, after the international events, the quality of life of people with disabilities has reached a new level.
The well-being of the country's population is primarily based on a balanced sustainable economy. Thanks to the social protection of the population, it becomes possible to smooth out a social injustice. The interrelation of economic and social protection institutions is especially noticeable during the economic crises. For example, the economic crisis leads to the introduction of additional measures to support the population on the part of the state. In this regard, we will analyze the main indicators of the socio-economic development of the Republic of Tatarstan and study their impact on the organization of social protection of the population during the economic crisis in 2015 [3, p.18] .
One of the main negative events in 2015 was the decline in real incomes of the population (-4.0%), the beginning of which, due to the growth of inflation, can be observed already in 2014 (-0.7%) [3, p. 17]. The average salary in the Russian Federation in 2014 amounted to 33,925 rubles, in the Republic of Tatarstan -29,337.6 rubles. By 2015, the average wage in the republic decreased by 6.3% compared to the previous year, and in the country -by 9.5%, while the real disposable income of the population decreased by 4.8% and 4% respectively.
The decline in wages of the population affected all sectors of the economy and also affected other components of disposable income as a result of the excess of the inflation rate, which overlapped their indexing. By the end of the year, the real amount of assigned pensions decreased by 4.8%, which has not happened since 2009. The situation is charged due to the growth of the consumer price index in 2014-2015.
The In February 2015, the experts of the Levada Center company assessed the opinion of the population and revealed the deterioration of the country's economic situation in the views of the absolute majority of Russians (70%). For example, a quarter of respondents (24%) reported about the dismissal of their relatives. At the same time, the majority (68%) of Russians did not have any cases of losing their jobs among their friends and relatives. Exactly half (50%) of respondents believe that the layoff will not occur, but expect it (regarding their work or in relation to their relatives) with some degree of probability 38% of Russians (including 7% are convinced of this or observe similar circumstances) [5].
A decrease in the real income of the population, an increase in the number of poor citizens, an increase in the number of unemployed have had a tremendous impact on the organization of social protection of the population. Firstly, there is a sharp need for additional measures to support the population, and secondly, the number of citizens who have the right to already existing social support measures has increased. The current situation led to an increase in the number of applications from the consumers of the social services to the organization of social protection, which by that time were not ready to receive a large number of citizens. The lack of the experts led to long queues and a corresponding increase in the level of dissatisfaction of the population with social protection organizations.
The analysis shows that the economic institution has a direct impact on the activities of social protection organizations. The regions, adapting to the conditions of the economic crisis, began to gradually reduce the social obligations to the population. The main action strategies include: suspension of indexation of payments, introduction of targeting mechanisms, reduction of social support, cancellation of some support measures, expansion or adoption of new support measures for certain categories of citizens.
Another important institution that influences the social support of the population is the institution of religion. For a long time, religion has performed the functions of protecting the weak, the disadvantaged and the sick ones, it lays the principles of love, beauty and mercy in people. Over time, social protection took over these functions. However, even today, religion interacts with state and municipal bodies, public organizations and individuals on issues of social protection of the population [6, p. 105].
At present, a synodal department is functioning at the Russian Orthodox Church (hereinafter -the ROC). This department is responsible for the charitable work of the church, as well as for the work of social service. It should be noted that a great responsibility and hope are laid on the church, because there are 2-5 charitable canteens for needy citizens in each diocese. Churches and chapels function in medical institutions, sisterhoods and various Orthodox medical societies have been created. Church ministers also work with drug addicts and alcoholics, work in orphanages and correctional camps. For example, all correctional camps and pre-trial detention centers, prisons have church premises, and in most of them (75%) there are church communities [7. p. 87].
With the development of healthcare, there are more chances to prevent the onset and exacerbation of socially significant diseases, which reduces the level of disability and the subsequent burden on social protection organizations [8]. And vice versa, it is in the organization of social protection that citizens apply after getting the diagnoses and having obtained the "disabled" category . As part of this approach to maintaining health, the role of social work in the health care system is significantly increasing. Institutes of health care and social protection interact in solving common problems of citizens and improve the quality of life of the population. Thus, medical and social work is the achievement of the highest possible level of health, functioning and adaptation of persons with physical and mental pathologies, as well as with social troubles [9. p. 33].
There are several areas where the institutions of health care and social protection interact: the fields of psychiatry, narcology, oncology, family planning. Social work in the provision of palliative care is of particular importance, since this area has just begun to develop in Russia. D. M. da Silva, C. V. Dendask and E. de Oliveira conducted a bibliographic study of the experience of interaction of social work experts with cancer patients in 2010-2015 and came to the conclusion that the inclusion of social work in the overall process of patient care allows improve the quality of life of cancer patients [10]. Changes in the behavior of the patient and his relatives, in addition to the disease itself, causes the patient's attitude towards him, which in most cases requires correction and intervention from the outside. By engaging in the process of providing care, social protection organizations make a fundamental contribution to cooperation to improve the patient's life.
The institute of education also turns out to be closely related to social protection of the population. One of the topical areas of interaction between the educational institutions and social protection of the population is inclusive education of children with the disabilities. For the full inclusion of children with disabilities in the learning process at any stage (preschool, secondary, higher education), joint colossal efforts of these two institutions are required. So, for example, O.S. Stepanova and A.A. Nikolaeva analyzed the current problems of inclusive education in Russia [11]. According to the results of a sociological survey conducted by the researchers, more than thirty similar problems have been identified. The most acute of them: the problem of relations between ordinary students and children with disabilities; the problem of the financial capabilities of schools to create an accessible environment in order to form inclusive education, etc.

Conclusion
So, we can say that the influence of various institutions on the organization of social protection of the population manifests itself in different ways. Nevertheless, the general mechanism of influence is obvious: social agents draw attention to socially significant problems of the population, which leads to increased activity on the part of the state in solving these problems.
Foreign policy contributes not only to the exchange of experience between the countries, but also leaves its own legacy. For example, thanks to the holding of international sports competitions, the population, including people with disabilities, have the opportunity to go in for sports.
The unstable economic situation of the country has a negative impact on the activities of the institution of social protection, therefore, in case of economic crises, it is important to promptly take measures to improve the work of social protection institutions. As the analysis has shown, the economic crisis has led to an increase in the flow of consumers of social services due to a decrease in the population's income and an increase in the number of citizens who find themselves below the poverty line.
Religious organizations have a positive impact on social protection organizations, really helping the socially vulnerable groups of the population to cope with difficult life situations.
Institutions such as health and education ones work closely with social protection organizations and with each other to achieve the common goals.