1 Introduction

According to the National Infrastructure Protection Plan established by the United States Homeland Security, resilience is defined as the ability to adapt to changing conditions and withstand and rapidly recover from disruption due to emergencies. Cimellaro et al. (2010) define resilience as the capacity of engineering and socioeconomic systems to recoil after a severe disaster. McAllister (2016) defines resilience as “the concept that addresses the way that communities prepare for and recover from disruptive events.” Baho et al. (2017) express resilience as the period required for an ecosystem to reassemble to pre-disturbance conditions. Cere et al. (2017) describe community resilience through the material property application of elasticity. “Elastic” resilience signifies the idea of returning to the preexisting equilibrium. This is referred as the static concept of resilience. Consequently, “ductile” resilience is seen as a progression of continuous self-alteration and modification that can be interpreted as bouncing forward. This is referred to as the dynamic concept of resilience. Many times, the definitions of sustainability and resilience become merged into one. A sustainable community can only be sustainable if it holds some degree of resilience, but for a community to be resilient, sustainability is not necessarily required. Instead, resilience heightens the prospect of sustainable development in the future. Risk management is within resilience and resilience is within sustainability (Saunders and Becker 2015). During the 2010–11 Canterbury earthquakes in New Zealand, the reoccurring catastrophic events urged the country to seek out sustainability and resilience measures (Saunders and Becker 2015). The New Zealand Treasury had stated that resilience should be concentrated more on short- and long-term compliance, while sustainability would take a slower term for the future.

This paper presents a state-of-the-art review on community resilience computational models in three sections, as shown in  Fig.  1. Section 2 shows the search methodology implemented in this review. Section 3 addresses critical terminology, community interdependencies, and current resilience guides within community resilience comprehension. Section 4 reviews static and dynamic computational models used, modeling in uncertain environments, rating models for community resilience assessment, optimization-based modeling for resilient community design, game theory, agent-based, and probabilistic dynamical modeling. Section 3 provides a summary of challenges and promising opportunities for future research directions.

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Descriptive diagram of the structure of the review paper

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2 Methodology

2.1 Search strategy

Scopus and American Society of Civil Engineering (ASCE) electronic databases were searched from January 1, 2011, to September 6, 2021. Selected articles outside this date range were selected based on high citations. The databases were selected based on their likelihood of including both community resilience modeling approaches and physical infrastructure data. Two main subject categories were included in our searches: static and dynamic modeling. Static modeling search terms were selected using the community resilience terms, including analysis, assessments, and frameworks that considered physical infrastructure, and hazard management. Dynamic modeling search terms related to agent-based modeling or game theory modeling were combined with “or” statements. These terms were used in combination with hazard search terms related to man-made hazards, natural hazards, and natural disasters were combined with “and” statements.

2.2 Selection process

Articles were included if (a) computational modeling was an outcome variable of interest, (b) infrastructure data were collected for resilience analysis, and (c) results involved associations or differences in either natural or man-made hazards. The searches were restricted to articles that (a) were written in English and (b) examined hazards only. The articles identified in the Scopus database were selected by: (a) Impact Factor, (b) Most Cited, and (c) Date (Newest). Appendix A shows the list of Keywords used for the search process. The review protocol was not preregistered at the University of Kentucky libraries. The first author reviewed the titles and abstracts independently in a blinded manner using the eligibility criteria stated above. The first author exported each article found in Scopus database searches and uploaded these articles into Microsoft OneDrive web application. OneDrive is a web application that is used to facilitate screening of titles and abstracts for reviews. The first author accessed assigned articles via the OneDrive web interface, reviewed titles and abstracts, and recorded decisions to include or exclude each article.

Community resilience has been a subject of interest in industry and government agencies; Fig. 2 shows the distribution of resources that were studied in this review and summarizes the breadth and extension of the search conducted in this review to include government publications, reports, academic centers, and authoritative publications. Figure 3 summarizes the number of documents investigated per year of publication. Note that the papers that had higher citation record and selected foundational papers in this area were selected to provide insight on the community resilience pioneering work; hence, few papers outside the last 5-year period are included in this review. Von Neuman (1928) paper is excluded from this list to aid in the visualization of the figure. Figure 4 summarizes study selection of the peer-reviewed journal articles that were examined in this review paper along with their respective impact factor.

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Distribution of selected document types reviewed in this paper

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Fig. 3
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Distribution of selected articles reviewed per year of publication

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Fig. 4
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Distribution of selected peer-reviewed journal articles reviewed in this paper

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3 Community resilience comprehension

The engagement of the community members (government, private organizations, academy, and industry) plays a fundamental role in order to successfully approach an integrated examination of direct and indirect consequences from multi-hazard events on infrastructure and devise adequate provisions for community resilience during and after their occurrence. As well-compelled community resilience guides are developed, the decision-making for community recovery increasingly considers more alternative factors and methodologies.

3.1 Critical terminology

Community resilience is characterized by the following terms: preparedness, mitigation, response, and recovery. Preparedness and mitigation are two different concepts related to community resilience that are important to distinguish. Preparedness is the action taken to improve emergency response for the aftermath, while mitigation is an action taken to reduce or eliminate long-term risk to hazards (Baxter 2013). Response is defined as the activities immediately conducted after the disruptive event in order to reduce the damage caused. Finally, Recovery is related to assist the affected community to bounce back to its normal conditions (Seaberg et al. 2017). Another secondary concept is Functionality; it is a factor that measures a structure’s recovery status and its capability to remain serviceable (Baxter 2013). Examples being hospitals delivering health care in a timely manner, and water distribution systems delivering potable water to a community (McAllister 2016).

The resilience of a community or a system within the community is most often compared to its performance. The manner at which the system absorbs the damage of the impact and then recovers describes the performance, i.e., resilience (Ayyub 2014), displayed in Fig. 5, shows how a system’s performance is measured before, at, and after an impact. The system’s performance is measured on the y-axis while the time is on the x-axis. The time at which the incident occurs is denoted as \({t}_{i}\), the time at which the failure occurs is \({t}_{f}\), and the time at which the system commences its recovery is labeled as \({t}_{r}\). \(\Delta {T}_{d}\), \(\Delta {T}_{f}\), and \(\Delta {T}_{r}\) are the time durations of the disruption, failure, and recovery, respectively. Three failure events are portrayed in the graph labeled as \({f}_{graceful}\), \({f}_{ductile}\), and \({f}_{brittle}\), meaning a graceful failure, a ductile failure, and a brittle failure. Six different recovery patterns are shown: \({r}_{1}\), \({r}_{2}\), \({r}_{3}\), \({r}_{4}\), \({r}_{5}\), and \({r}_{6}\), signifying a better than new recovery, a good as new recovery, a better than old recovery, a good as old recovery, a good as old recovery (linear), and a worse than old recovery, respectively. These different failure types and recovery patterns give perspective into how differently and unique a community can react after the impact of an incident. The initial and residual capacity and strength after the disturbance describe its degree of robustness. Ramirez-Marquez et al. (2018) stated a performance-based approach formulated from three dimensions to quantify resilience in systems: reliability, vulnerability, and recoverability. These dimensions are also shown in Fig. 5. The reliability dimension aims to investigate the steady-state performance of the system during an initial time interval before the disruptive event. In the vulnerability dimension, the disruptive event reduces the system's performance to a failure condition, and the comparison of the system's prevailing behavior to its initial state becomes a necessary subject to analyze. Finally, the recoverability dimension examines the needed provisions to restore the system's performance to an expected level, even though it is similar, better, or worse than the original performance. Multiple hazards can affect a community. Prevalent and more perilous flooding is anticipated because of extreme climate change and sea level rise. Also, as the temperature rise of oceans continue to occur, intense storm activity is predicted (English et al. 2017), which puts communities in severe risk. In order to mitigate against flood damage, the National Flood Insurance Program suggests elevating the house, but this action makes the house more vulnerable to larger wind exposure. It is difficult to reduce vulnerability from wind and flood damage concurrently because mitigating solutions may contradict each other. One alternative solution can be amphibious construction in coastal regions to help mitigate hurricane damage from flood and wind damage (English et al. 2017). An amphibious structure relies on buoyancy to offer momentary flotation (i.e., floating docks) and vertical guidance to prevent lateral movement. Present design codes and standards emphasize the building’s life cycle, and current regulations address the dependability on the utilities’ functionality; however, these documents generally do not direct attention to the resilience or interdependency issues (McAllister 2016). It can be observed through the efforts of enhancing the seismic resilience of communities (Bruneau et al. 2003) and the research performed on community-driven disaster planning for long-term mitigation recovery plans (Chacko et al. 2016) that a solution comprehending and satisfying the community interdependencies is still not well understood.

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Resilience of a community subjected to a natural disaster

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3.2 Community interdependencies

A reliable and quantitative methodology for economic risk analysis modeling that accounts community interdependencies is needed to properly predict direct and indirect costs of destruction to properly prepare for a hazard event. The interdependencies such as social, human health, safety and general welfare, physical infrastructure systems, security, protection, emergency response, business continuity, and buildings are critical in the search of solutions to achieve community resilience, and this has yet to be properly instituted in pre-decision modeling strategies (Cimellaro and Piqué 2016; Dennis et al. 2021).

One approach to investigating community interdependencies to achieve resilience in a civilian community is examining resilience from the ecology perspective. Baho et al. (2017) approached the intent for resilience from an ecological standpoint. The environment in which organisms live in is not only affected by natural disasters, but also by agriculture, land use and climate change, species invasions, and infectious diseases. The authors’ approach to ecological resilience is broken down into four parts: (1) scale, (2) adaptive capacity, (3) thresholds, and (4) alternative regimes. The scale part considers the amount of species having the same functional traits, the impact of disturbance dispersed upon the ecosystem in study, and range of responses to disturbance, in order to grasp the overall physical and psychological impact. The adaptive capacity part considers the ecosystem’s response to environmental disturbance or changes. It takes into consideration how differently rare species react to environmental change. The thresholds part considers reorganization of an ecological community after a disturbance, and the alternative regimes part covers the idea of an ecosystem adapting new roles in the surviving community. These four attributes are used together to measure resistance, persistence, variability, and recovery. By evaluating and calculating the numerous characteristics of resilience, the general resilience assessment will move one step forward toward understanding the general resilience of ecosystems and other complex systems.

The cost estimation of infrastructure recovery methodologies associated with interdependencies facilitates the study of infrastructure performance and resilience (Zimmerman et al. 2017). Cimellaro et al. (2014) proposed a resilience index to evaluate the resilience of a region affected by a disaster considering infrastructure interdependency using the 2011 Tohoku Earthquake in Japan as a case study. First, a resilience index was given to every infrastructure in the region combined with others by weighted factors. Then, the regional resilience index is calculated based on the weighted factors of each infrastructure. Cimellaro and Piqué (2016)  analyzed the role of interdependencies by investigating the resiliency of a hospital. The authors developed a discrete event simulation model imitating the dynamic operation of complex systems used to analyze the resilience of a hospital subjected to earthquake loading. A hospital is defined as a departmental unit where an internal interdependent organization along with the physical dimension at different levels is what drives a successful operation on a day-to-day basis. The authors used the following interdependent attributive parameters: the number of beds, the number of doctors, and the operation efficiency. The predetermination of the resilience of a hospital during a natural disaster can be vital in decision-making for future events and directly correlate into the resilience assessment of a community.

Koliou et al. (2017) investigated the resilience of natural gas systems considering the interconnectivities between pipelines, port facilities, fuel delivery, and airport and train operations. The individual risk analysis is deficient in responding to emergency events of critical infrastructure systems. Hence, adequate hazard event management connects risk analysis and community resilience (Park et al. 2013). Some alternative frameworks to evaluate the resilience of communities have considered provisions from existing regulatory risk assessments. Linkov et al. (2018) proposed a resilience assessment tiered approach intended to provide decision support tools (e.g., screening-level assessments, performance–time graphs, scorecards, etc.) that explain the performance and interdependencies of critical systems and concurrently improve risk mitigation strategies.

3.3 Current resilience guides

The public’s understanding and perception of community resilience is critical (Amaya et al. 2021); thus, providing adequate resources are needed to improve resiliency. There is an extensive array of community resilience guides and a few of those are summarized below. The seven guides are: (1.) the National Institute of Standards and Technology (NIST) Community Resilience Planning Code, (2.) the San Francisco Bay Area Planning and Urban Research (SPUR) Association Framework, (3.) Baseline Resilience Indicators for Communities (BRIC), (4.) the Community and Regional Resilience Institute's (CARRI) Community Resilience System, (5.) the Oregon Resilience Plan, (6.) the National Oceanic and Atmospheric Administration (NOAA) Coastal Resilience Index, and (7.) the Communities Advancing Resilience Toolkit (CART). These resilience guides are summarized in Table 1 and compared based on four parameters: (1.) the definition of resilience stated in the respective guide, (2.) type of guide, (3.) the degree of community interaction, and (4.) community interdependencies addressed for within the guide for successful community functionality. Although all seven are considered US resilience guides, most of the material and messages are not stakeholder-friendly, thus claiming as unsuitable for accessible public adoption. The Oregon Resilience Plan is a document addressed to the public officials within Oregon, not the stakeholders who reside in the community (OSSPAC 2013). The guide was made to influence policy makers. The Community and Regional Resilience Institute's Community Resilience System Report, however, addresses the leadership team within a community and then implements interactive workshops with the civilians. Within the community resilience system report, all key community interdependencies fell into similar categories of transportation, medical facilities, emergency management services, water, and telecommunication services, except for in CART. This was the only guide to address faith-based organizations (Pfefferbaum 2011). The Federal Emergency Management Agency (FEMA) provides two guides for community resilience: Are you Ready? An In-depth Guide to Citizen Preparedness (FEMA 2004) and Mitigation Ideas: A Resource for Reducing Risk to Natural Hazards (Baxter 2013) provide step-by-step procedures for community members. The following guides are not included in Table 1 because of their tended audience being local rather than on a national scale. FEMA’s Mitigation Ideas: A Resource for Reducing Risk to Natural Hazards is an informative document made to help communities identify natural disasters/hazards and know the proper mitigation steps to take after. The guide addresses: drought, earthquake, extreme temperatures, flood, tornado, tsunami, wildfire, and multiple hazards. For each disaster, recommended mitigation actions are summarized for the purposes of local planning and regulations, structure and infrastructure projects, natural systems protection, and education and awareness programs (Baxter 2013). The Are you Ready? An In-depth Guide to Citizen Preparedness brochure is intended to aid citizens in learning the proper protection measures needed against all categories of hazards. The in-depth guide teaches you to improve, train for, and have emergency plans that should be done before, during, and after a disaster to protect people, property, and the community in totality (FEMA 2004).

Table 1 US community resilience guides for natural disaster and hazards
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4 Computational models

The need to model community resilience triggered the development of static and dynamic computational models. Static models include curve analysis and probabilistic approaches while dynamic models consist of game theory modeling and agent-based modeling.

4.1 Static models

Modeling community resilience by static models has attracted research in recent years. Kammouh et al. (2018a) proposed a framework using distribution/density, composition, and socioeconomic indicators as input leading to an output of a resilience function showing the serviceability of the community for a given period following the disaster.

4.1.1 Probabilistic modeling in uncertain environments

Advancements in risk analysis assessments provide decision-making capabilities for implementing disaster risk reduction plans in the presence of highly uncertain environments.

A probabilistic risk assessment is a systematic and comprehensive methodology used to evaluate risks associated with a complex engineered technological entity or the effects of stressors on the environment (Salgado et al. 2016). Risk in this type of analysis measures the severity of the consequences and the likelihood of occurrence. The total risk is calculated through the sum of the products of consequences multiplied by the probability of the negative activities’ likelihoods of occurring. Salgado et al. (2016) developed CAPRA, a comprehensive approach to probabilistic risk assessment, to obtain physical risk indicators through damage and loss events. This probabilistic risk assessment platform was used to perform a risk assessment for the city of Medellin, Colombia, using seismic hazard, exposure, and socioeconomic descriptors as predictive event data indicators. Bozza et al. (2017) modeled the city of Sarno, Italy, as a hybrid social–physical network and evaluated resilience using synthetic and time-independent resilience measures during a seismic and landslide scenario.

Fragility curves are useful in quantifying the structural damage attained after an event (Kammouh et al. 2018b). Alternatively, the restoration phase has also actively been modeled for purposes of better understanding the structural performance. Kammouh et al. (2018b) used the data from 32 earthquakes to plot restoration curves for four lifelines: power, water, gas, and telecommunication. These results calculated the downtime for each lifeline and showed how the power system was always the first to recover with the telecommunications systems recovering second. Power systems were brought up quicker and with shorter downtime since the other critical lifelines were dependent on power to operate.

Rather than evaluating the community as a whole, other frameworks assess the buildings’ resilience and the individual infrastructure assets that make up the community. Dunn et al. (2018) proposed an empirical modeling approach, as of a database collected from the National Fault and Interruption Scheme of the UK electrical operators, to generate fragility curves for overhead electrical lines of an electrical distribution network subjected to windstorm scenario. The methodology exhibited could be considered for alternative infrastructure systems threatened by this hazard event. Burton et al. (2015) proposed a framework for computing each building’s damage measures that inform, repair, and replace activities through hazard, damage, and structural analyses. From there, a new decision variable is derived from the limit states describing the recovery of functionality at the building level. Originally developed by the Pacific Earthquake Engineering Research Center, Burton et al. (2015) applied the performance-based earthquake engineering framework to model the post-earthquake recovery of a community of residential houses. The collective occupancy loss over of the recovery period can be obtained from the recovery curve. This provides insight into the long-term economic impact on the community. HAZUS and OpenQuake were used to simulate scenario earthquakes. HAZUS is a standardized methodology that estimates physical, economic, and social impacts of disasters using GIS technology, and OpenQuake is a web-based platform used for the integrated assessment of earthquake risk. The hazard analysis in the framework was based on the ground motion intensities in the study region location for multiple scenario earthquakes. The structural analysis was measured by story drift, residual story drift, and floor acceleration. The damage analysis was measured based on the deficiencies for structural analysis components. The building damage was then categorized into one of four: (1.) safe and operational, (2.) safe and usable during repair, (3.) safe but not repairable, or (4.) unsafe. Individual house fragility curves were generated to enable the creation of a global community fragility curve. Nazari et al. (2013) introduced a procedure in computing the probability of the collapse of a two-story wood frame townhouse due to the aftershock of an earthquake. Using incremental dynamic analysis, fragility curves were created for the building under four different intensity scenarios: main shock-only, maximum considered earthquake-level main shock-aftershock, design earthquake-level main shock-aftershock, and a 0.8 g level main shock-aftershock. The results showed that the probability of structural failure has no significant relation to the aftershock therefore deeming it as unnecessary to implement aftershock design in performance based seismic design.

Guidotti et al. (2016) used the implementation of a six-step probabilistic method for a critical infrastructure assessment on the virtual community of Centerville after the impact of a 6.5 magnitude earthquake. The six steps are: (1.) generate a network model for the system, (2.) generate the hazard for the network area, (3.) assess direct physical damage to network components through fragility curves, (4.) define the network damage state weighed through network dependencies, (5.) assess functionality loss (e.g., ability to provide essential goods and services), and (6.) predict recovery time for network functionality. The potable water distribution network system was evaluated separately and then once again based on the cascading effects due to its dependency on the electric power network. The probabilistic procedure includes models of damage, functionality, and recovery. The results showed a higher standard deviation for the coupled water distribution network and electric power network system than the water distribution network system alone, reflecting a higher level of uncertainty. The recovery time also increased through coupled networks. Salman and Li (2018) proposed a framework that integrates a probabilistically weighted deterministic hazard analysis model, the system performance level, a network component measure, and a life cycle analysis using power networks located in Charleston, SC, and New York, NY.

De Iuliis (2019a, b) proposed a methodology based on fuzzy logic to determine the downtime of a building. Using this logic, downtime is estimated as the compound action of three elements that involve the actual damage, irrational delays, and utilities disruption. De Iuliis (2021) proposed a probabilistic framework based on Bayesian networks to estimate the downtime of power and telecommunication systems following an earthquake. The results showed an improved performance of the probabilistic model in highly uncertain scenarios.

4.1.2 Rating models for community resilience assessment

Recent studies have proposed different metrics and rating systems to quantify resilience of communities at the city and country level. Ouyang and Dueñas-Osorio (2012) studied a time-dependent assessment using a power transmission grid in Harris County, Texas, with output given as post-blackout improvement factors and different resilience strategies. The results showed that when the post-blackout improvement factors were small, the resilience curves were decreasing functions, and vice versa for large improvement factors.

Francis and Bekera (2014) developed a resilience assessment framework consisting of five components: (1.) system identification, (2.) vulnerability analysis, (3.) resilience objective setting, (4.) stakeholder engagement, and (5.) resilience capacities. A case study was performed on the fictional city of Micropolis evaluating the electric power infrastructure resilience in Category 3 and Category 5 hurricane storm surge zones. The underground electric power infrastructure east of the railroad, the infrastructure east of the railroad in the commercial area only, and the infrastructure as is in totality were assessed through three different scenarios. The results indicated that undergrounding electric power infrastructure east of the transmission line attained higher resilience and entropy resilience scores.

Panteli et al. (2017) introduced what they called the resilience trapezoid to quantify the operational and infrastructure resilience of a power system in the presence of extreme events. For example, Kammouh et al. (2017) and Kammouh et al. (2018c) presented a method that quantifies risk at the country level based on resilience, hazard, and exposure as an indicator for resilience assessment. Liu et al. (2020) evaluated a static importance-based strategy of water distribution networks during the post-earthquake recovery interval by a seismic resilience index. This seismic resilience index evaluated the performance level and recovery trajectory of the pipe damaged. The work by Zona et al. (2020) studied the availability of resources, known as resourcefulness, as an important criterion to evaluate community resilience at the country level. The authors show that more resourceful countries are more resilient during catastrophic events as they have mechanisms to provide solutions that minimize the impact of such events.

4.1.3 Optimization-based modeling for resilient community design

Modeling approaches seeking to optimize the resilience community design process and decision-making have gained interest in recent years. Flint et al. (2016) approached a resolution toward community resilience during multi-hazard disasters by optimizing building’s subsystems (i.e., soil, foundation, structure, and envelope) while still in the early design stage. This holistic approach was focused on the effects on mid-rise commercial buildings exposed to hurricane, earthquake, and tsunami hazards. The framework consists of three modules. Module 1 identifies soil, foundation, structure, and envelope (SFSE) systems that have the potential for optimal performance at a given site. Module 2 assesses multi-hazard exposure, SFSE system performance before and after hazard events, and life cycle metrics associated with construction, operation, repair, and recovery. Finally, Module 3 uses a multi-objective decision-making algorithm to simultaneously optimize several conflicting objectives. Disregarding envelope systems, the authors found 92 potentially viable SFSE systems compared to the 132 total systems. Nateghi (2018) proposed a resilience framework using data from the impact of Hurricane Katrina on an electric power distribution system located in the Central Gulf Coast Region. Resilience was modeled by hazard characteristics, system topology and the area’s climate and topography using a multivariate tree boosting algorithm. The results from the model predicted the number of outages, the number of customers without power, and the total cumulative outage durations.

4.2 Dynamic models

Dynamic models see the elements of the community interdependencies as the (changing over time) variables of a dynamic system where community resilience is a state of certain variables. An example being the COPEWELL, composite of post-event well-being model (Schoch-Spana et al. 2019). This model was funded by the CDC, US Centers for Disease Control and Prevention, whose focus was to establish a model that could predict the well-being of communities after the event of a natural or man-made hazard (Links et al. 2018). A multi-disciplinary group of experts identified interconnectivities within a community and assigned measurements focused on the community’s functioning, the community’s capability of providing critical services to its inhabitants (Links et al. 2018), producing a rubric assessment for the area under study. This model translates a conceptual approach into a systems dynamics computational model using a standard stock-and-flow model. The input is the magnitude and time duration of the disaster event, and the output is a summary of the single-county results displayed through curves/plots and the entire country displayed in color-coded maps. Murray-Tuite (2006) applied a man-made hazard event in the Washington DC area of Reston, Virginia, during a late evening and examined the transportation systems for resilience with ten parameters: redundancy, diversity, efficiency, autonomous components, strength, collaboration, adaptability, mobility, safety, and the ability to recover quickly. A traffic assignment-simulation methodology was applied to the event and was examined through different degrees of vulnerability based on government support, public attention, and capacities such as adapting and coping.

4.2.1 Game theory modeling

The synergy of cyber technology and physical infrastructure has allowed advancement in the various fields of political science, economics, management science, and engineering. The concept of game theory is modeled through agent-based models studying real-world interactions between players (e.g., intelligent individuals) and systems (e.g., community). Game theory, first developed by John Von Neumann and Oskar Morgenstern (1928), is a mathematical approach in studying strategic and economic interactions in rational decision makers. It is a discipline in mathematics that aims at modeling situations in which decision makers must choose specific actions that have mutual, and possibly conflicting, consequences (Sun et al. 2017). The “use of game theory enables the modeling and analysis of multiple players/decision makers. Each is involved in his own optimization problem but with interactions with other decision makers through objective functions and constraints. This allows the modeler/analyst to capture the complexity and scale of humanitarian post-disaster operations in a more accurate and astute manner” (Nagurney et al. 2019).

Game theory has also been used to model poverty. Factors such as: income, education, health, inequality, social exclusion, and security can explain the poverty paradigm (Passino 2016). The application of poverty models rationalizes the social interdependency of a community. A poverty model, shown in Fig. 6, is an influence diagram with quantitative measures assigned by importance where wealth, health, and knowledge are the basis of what dictates the degree of poverty for an individual or community. Wealth gives you the ability to adopt better health habits. Without good health, your ability to go to school and gain more knowledge is difficult. Income positively dictates your wealth, but expenses affect it negatively: the environment a person lives in and the health care a person has affects their health, and the school and experience an individual has impacts their degree of knowledge. By using this elaborate definition of poverty, a solution for the greater good of a community when faced under a natural disaster can be found. Recently, Hobbs et al. (2018) have studied the effects of the introduction of waste-to-energy systems in rural communities considering the following factors: economics, energy, environment, community acceptance, and community engagement. Another potential research direction is modeling of decision-making in rural communities in terms of the adoption of technology considering the exogenous and endogenous factors (Nejat and Damnjanovic 2012).

Fig. 6
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Poverty model

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In 2005, the destruction impacted by Hurricane Katrina in the USA was estimated from $100 billion to $125 billion (Nagurney 2017). Disaster management is comprised of decision makers’ tactics and direction from the government, private entities, and non-profit establishments, singling out game theory as an applicable practice to emphasize (Seaberg et al. 2017). Game theory can reveal new knowledge in optimizing decision-making schemes for the players (e.g., buildings, community, government officials, and emergency management team) involved. Chakravarty (2011) used game theory to address resource allocation between the government and multiple private and public companies when faced with a hazard. Zhuang et al. (2012) applied game theory in preparedness management in natural hazards. Vahidnia et al. (2015) implemented a geographic agent-based model to simulate agent interaction finding the best forms of evacuation and relief when in the wake of a hazard. Chan (2015) simulated a game theory inspired network for predicting mitigation strategies per hazard or attack. The players in this scenario are federal, local, and foreign governments, private citizens, and adaptive adversaries. Their goal is to seek protection for their lives, property, and critical infrastructure against man-made and natural hazards.

Game theory can be of two types: cooperative or non-cooperative. The cooperative game theory calculates the gain of each player in a supportive-everyone wins methodology while non-cooperative game theory focuses on the specific moves' players should rationally make to win individually. Every game is comprised of three elements which are players, player actions, and payoff functions (Muhuri et al. 2017). Rubas et al. (2008) studied a non-cooperative 3 player (USA, Canada, and Australia) game to evaluate the economic linkage between a country using climate forecasts or not. Vasquez et al. (2013) modeled a non-cooperative game for the usage of project scheduling when prioritizing which actions should be taken first after a disaster such as the 2011 Fukushima, Japan, nuclear accident. Chen et al. (2016) investigate the evolution of cooperation between individuals on a public goods game model that considers a person's reputation as well as behavior diversity. Muhuri et al. (2017) proposed a cooperative game theory-based methodology for road traffic management in a disaster situation. The vehicles acted as players in the game and each vehicle’s goal was to reach its destination by choosing the shortest travel time path without disrupting the other vehicles’ paths. The payoff was calculated considering its arrival time, priority, and velocity. 200 random vehicles were evaluated as players in a disaster area consisting of six road blockages. Alvarez et al. (2019) used a cooperative game to model land-use management for flood retention as a useful tool for flood risk management. The game is situated around the accordance of possible agreements among landowners and the establishment of cost/benefit criteria through land development agreements. When in a state of disaster recovery, Peng et al. (2014) revealed the practicality of concentrated rural settlement through the usage of game theory. Bouzat and Kuperman (2014) demonstrated the usage of game theory and Evolutionary Prisoner’s Dilemma for optimizing the best pedestrian room evacuation routes. Lai et al. (2015) applied game theory for computing the combination weight of flood risk. When deciding the best evacuation plan after a natural hazard, the first step is understanding the pedestrians’ movement. The 2-by-2 symmetric games were used where the players, the pedestrians, have access to the same set of strategies and payoffs. Eid et al. (2015) thrive to find an optimum balance between post-disaster insurance plans bought by resident families, retailed by insurance companies, and post-disaster relief executed by a government agency. The resident families acted as the main controller of the game’s environment, and the insurance companies and the government operated as supportive players for analysis.

Attacker-defender games are games with several defenders defending a resource or territory and a number of attackers attempting to destroy or capture that defended resource or territory (Sims 2016). Many times, these games are represented through payoff matrices or decision trees. Zhuang and Bier (2007) investigated resource allocation stabilization for the protection of natural hazards. The attacker-defender game model used was both consecutive and instantaneous with the attacker having an incessant degree of effort. Hausken et al. (2009) introduced a two-player, attacker-defender game to study the trade-offs among financing in protection from natural disasters or man-made attacks. In this circumstance, the defender is finding a solution on how to properly allocate investments based on different defense mechanisms. The defender could invest either in defense against a natural disaster, defense against terrorism, or defense for all-hazards protection. Hamilton and McCain (2009) used an attacker-defender game for the development of defense strategies when a community is being threatened with a smallpox attack. Ferdowsi (2017) implemented a zero-sum non-cooperative game consisting of an attacker who seeks to alter the conditions of the gas-power-water critical infrastructure to upsurge the power generation fee and a defender who distributes communication resources to local areas to oversee the infrastructure. Although Ferdowsi (2017) used this application for the case of a man-made disaster, it can also be directly correlated to the community’s lifeline dependencies during a natural disaster.

Haphuriwat and Bier (2011) used an attacker-defender game theory model to embody the resource distribution problem during natural disasters for emergency response management. Horiuchi (2012) presented a modified hawk-dove game (Maynard-Smith 1982) for showing the situation during and after a disaster where people assemble groups to support each other through the recovery stage of disaster management. In a hawk-dove game, when speaking in terms of resources, the best payoff results from two doves sharing the resources equally, but in this scenario a dove-hawk-bourgeois game is being played, where the doves are in competition for the resources. Ergun et al. (2014) used a cooperative game of telecommunications optimization for maximizing supply chain effectiveness when in response to a disaster. Nagurney et al. (2019) introduced an integrated financial and logistical game theory model for humanitarian organizations or non-governmental organizations. In the occurrence of a natural hazard, an influx of resources is sent to the affected area. More than half of the items that arrive at a disaster site are non-priority items. Victims are then suffering more because they do not receive the critical needed supplies in a timely manner due to the disorganization of dealing with the non-priority supplies. Non-cooperative games were played with the relief item movements and the utilities of the non-governmental organizations and then applied to the situation through game theoretic algorithms. Smyrnakis and Leslie (2010) use a stochastic fictitious play model to determine the proper steps to take in the response phase of disaster management. Coles and Zhuang (2011) introduced a method to provide and aid decision makers in emergency surroundings on how to choose and sustain relationships to advance resource utilization in a disaster. Mulyono (2015) used game theory to model a community’s effectiveness in establishing resilient energy production, distribution, and consumption when impacted by a disaster. For more global issues, namely global climate change, Vasconcelos et al. (2015) modeled the effectiveness of a multicentered architecture of several minor-scale agreements through the application of the evolutionary game theory of polycentric governance.

Table 2 displays the comparative summary of the literature review on selected research papers that studied game theory during a natural or man-made hazards.

Table 2 Game theory studies in natural and man-made hazards
Full size table

4.2.2 Agent-based modeling

Efforts to model resilience through game theory applications are still relatively new. On the other hand, agent-based modeling has been used in an extensive array of applications such as hazard mitigation (Gutierrez Soto and Adeli 2017; Florez et al. 2021), software engineering (Kir and Erdogan 2020; Railsback et al. 2006), geo-simulation (Macatulab and Blanco 2019; Zia et al. 2013), economics (Zambrano et al. 2021; Arthur 2006), sociology (Squazzoni 2012), ecology (Gimblett 2002; Zhang 2012), and architecture design (Chen 2012). Agent-based modeling simulates the dynamics of an environment in which multiple agents act according to a set of basic rules. The goal of this type of modeling is to evaluate the emergent behavior of the system as a unique entity that results from the interaction between the agents. Agent-based modeling extends a promising option to evaluate and test resilience-related measures (Brudermann et al. 2016). An agent-based framework was used to quantify the seismic resilience of an electric power supply system using two agents, the electric power supply system operator, and the community administrator (Sun et al. 2019). Eid and El-adaway (2018) used an agent-based model for post-disaster recovery simulations to address how the primary fixation in achieving sustainable disaster recovery lies in two ideas: (1.) integration of stakeholders into the recovery decision-making processes and (2.) impact of redevelopment, economically, environmentally, and socially speaking, on the host communities’ vulnerabilities to hazard events. The five-step research methodology implemented social, economic, and environmental vulnerability assessments, and used residents, the economic sector, insurance companies, and government agencies as the four interacting agents in the agent-based model. The holistic approach was applied to three Mississippi coastal counties during the aftermath of Hurricane Katrina. The results categorized the regions by vulnerability with each region of the three counties being measured from least vulnerable to above average vulnerability for the environmental vulnerability assessment enabling an overall sustainability plan to be put into place for each county. Agent-based modeling has also been used to evaluate people's behaviors before the hazard event. Gao and Wang (2021) use agent-based modeling to evaluate the impact of the hurricane warning messages on residents' decision evacuate. The results of the case study for Hurricane Dorian (Kijewski-Correa et al. 2019) suggest the need to use a finer spatial scale for geo-targeted warnings.

In an attempt to model community resilience, four different forms are commonly known among researchers: technical (i.e., capability to function and perform), organization (i.e., organization’s aptitude to manage the system), social (i.e., society’s effort in dealing with the services’ deficiencies), and economical (i.e., the competence to decrease both indirect and direct economic costs) (Cimellaro et al. 2016). Bruneau et al. (2003) describe four resilience attributes: robustness, redundancy, resourcefulness, and rapidity. The PEOPLES (Cimellaro et al. 2016; Kammouh et al. 2018d) framework is an example of a framework that incorporates all four types of resilience and the four attributes integrating a hybrid model of a network system and agent-based modeling. PEOPLES is beneficial to influence decision makers under emergency situations due to its ability to identify different resilience aspects of a community split into seven dimensions (each dimension corresponds to a letter of the acronym). The dimensions are: (1.) population and demographics, (2.) environmental and ecosystem, (3.) organized governmental services, (4.) physical infrastructure, (5.) lifestyle and community competence, (6.) economic development, and (7.) social-cultural capital. Within each dimension lies several indicators with quantitative indices available for the user’s input. At last, the performance functions of each dimension are aggregated into a single serviceability function that embodies the performance of the community after natural disasters. The framework can be studied as a simulation-based approach or an indicator-based approach (Cimellaro et al. 2016). Each approach applies an extreme event scenario to the community and performs a fragility analysis. The performance metrics of losses, restoration time, performance index, and resilience index are compared among the other layers. This framework was applied to the city of San Francisco after the 1989 Loma Prieta Earthquake (Kammouh et al. 2019). The physical infrastructure dimension was the only dimension of the resilience framework evaluated in this scenario. The results showed a need for better resilience in facilities compared to lifelines. Recently, the PEOPLES framework has been used to quantify the resilience of a rural Appalachian region, Harland county, Kentucky, after a severe flooding event (Melendez and Gutierrez Soto, TBP).

Integrating agent-based modeling in the sociotechnical networks and studying the impact on community resilience is an interesting perspective in dynamic models. Zoumpoulaki et al. (2010) used the BDI, beliefs-desires-intentions, agent-based model of the first responders of a natural disaster. Cimellaro et al. (2016) integrated the BDI agent model in the seventh dimension of the PEOPLES framework. Schut and Wooldridge (2000) and Zhang and Hill (2000) have previously implemented BDI intelligent agents into their work, but this specific BDI design incorporates the Five Factor Model (Costa and McCrae 1992), OCEAN, which includes five personality traits, Openness, Conscientiousness, Extraversion, Agreeableness, and Neuroticism. The BDI architecture is very similar to a simple reflex agent, but the BDI perception relies heavily on the agent’s emotional and personality states. The perception phase is first and begins with the agent obtaining new information based on its surroundings through sensors. As the perception is informed, the agent’s previously stated beliefs are updated then are run through an appraisal process. The emotional state gets updated based on its new beliefs, and then, a desire is generated based on its weighted personality and emotion vectors. The appropriate OCEAN personality traits are then assigned to each agent, and then, all actions are formed to replicate human actions during an emergency situation. Another attempt at devising a meticulous and comprehensive approach for modeling agent-based complex systems was through pattern-oriented modeling (Grimm et al. 2005). This strategy at evaluating a pattern was used to optimize model structure, test and contrast theories for agent behavior, and reduce parameter vulnerability. Future agent-based modeling implementations using a goal-based, utility-based, or learning agent instead of the BDI agent could be applied to the community resilience frameworks. The work in Marasco et al. (2021) proposed a computational platform that integrated data analysis and real-time simulation to provide an assessment of the seismic resilience of a community in large-scale urban areas. This platform unifies different sources of information that come from data and agent-based simulations to model the interdependency between buildings and road and water, power, and transportation networks.

4.2.3 Probabilistic dynamical modeling

Several models have been proposed to model systems that change over time in uncertain environments. These models typically characterize the relationship between different variables of the system and how they evolve over time. For example, Tabandeh et al. (2019) and Kammouh et al. (2020) proposed dynamical Bayesian networks to predict the impact of negative events on engineering systems and evaluate their resilience and recovery times. The work in Zhao et al. (2017) used hidden Markov models to quantify resilience in infrastructure systems considering adaptive, absorptive, and recovery capacity when the system in under disruptive scenarios. Dhulipala and Flint (2020) and Thekdi and Chatterjee (2019) considers inter-event dependencies during the system recovery process to model infrastructure resilience using hidden Markov models.

5 Conclusions and future research directions

The public’s understanding of community resilience is critical; and thus, providing adequate resources is important for improving resiliency. Modeling community resilience through static and dynamic computation models has also attracted research effort in recent years. Risk analysis simulations to advance the execution and efficiency decision-making before and after disastrous events (Salgado et al. 2016), fragility curves in quantifying structural damage after a natural disaster (Kammouh et al. 2018a), and the implementation of performance-based earthquake engineering frameworks to model the post-earthquake recovery of a community of residential houses (Burton et al. 2015) have all contributed into finding a solution for bettering our communities' resilience. Nejat et al. (2019) used a spatial regression model to predict households’ recovery decisions from data available of the aftermath of Hurricane Sandy.

Along with different dynamic computational models, game theory allows autonomous systems’ modeling. Planned collaborations among multiple decision makers, diverse ranks of government, private entities, and non-profit establishments are needed for disaster management therefore making game theory appropriate to study (Seaberg et al. 2017). It has been used in the application of natural disasters through many strategies. When determining the proper steps to take in the response phase of disaster management, methods such as the stochastic fictitious play model Smyrnakis and Leslie (2010) proposed can make a difference. Coles and Zhuang (2011) introduced a method to provide and aid decision makers in emergency surroundings on how to choose and sustain relationships to advance resource utilization in a disaster, and Nagurney et al. (2019) introduced an integrated financial and logistical game theory model for humanitarian organizations or non-governmental organizations. Waddell (2002) introduced UrbanSim, a GIS overlay modeling software that develops models to support land use, transportation planning, and growth management. This simulation platform is currently used by urban planners to address the housing crises faced in San Francisco, California. This type of 3D visualization simulation platform combined with community resilience models provides a potential transformative strategy for decision-making capabilities to evaluate different disaster risk reduction plans.

Concepts of game theory have been applied to modeling agents. The PEOPLES resilience framework applies a hierarchical methodology addressing interdependency between communal attributes (Cimellaro et al. 2016). Community resilience is still under investigation in finding the best solution for a community to achieve it. The authors suggest the application of a different concept of game theory to be applied to the simulation-based approach of the PEOPLES framework. BDI is used to model emergency response team, but further research can be done with different agent models as well as adopting other game theories concepts. The advancement and multi-deployment of machine learning and data-driven techniques also have influenced the perspective of community resilience. The concept of resilience analytics arose as the implementation of big data analytics based on statistical and mathematical models to examine, understand, and evaluate interdependent critical infrastructure systems in order to strengthen community resilience, even for unforeseen disruptive events named as fundamental surprises (Eisenberg et al. 2019).

This paper suggests the following future directions:

  • The study of community resilience frameworks in other environments such as rural communities and evaluating the effects of multiple hazards (concurrent vs. sequential).

  • Study simulation-based computation methods based on game theory concepts integrated to community resilience frameworks.

  • The study of poverty models for dictating the degree of resiliency within a community to assign discrete measures appropriately to the community under evaluation.

  • Investigating robustness of advanced mitigation strategies into community resilience frameworks (Javadinasab Hormozabad and Gutierrez Soto 2021; Palacio-Betancur and Gutierrez Soto 2019).

  • Incorporating endogenous or direct attributes to an agent in agent-based models (i.e., age, health and socioeconomic status).

  • Incorporating exogenous or indirect attributes to an agent in agent-based models (i.e., signals from policy makers for community commitment, or climate change).

  • Machine learning such as reinforcement learning and artificial intelligence were recently used to train game-winning agents (e.g., chess or strategy games) to evolve a community that wins battles and has an adequate use of resources (Tan and Guo 2020). In reinforcement learning, software agents interact with an environment where they learn the best set of policies that maximize a reward. In relation, the policies can be instituted to learn and maximize metrics of community resilience.

As a result, the resilience framework could enable faster disaster planning for communities after a natural disaster making multi-agent systems transform the understanding on individual and systems’ decisions affecting community resilience subjected to multiple hazard events.

Another potential future research direction is incorporating the field reconnaissance data obtained by the structural extreme event reconnaissance network on different hazard events, for example, the Nashville Tornadoes (Wood et al. 2020), the Hurricanes Michael (Alipour et al. 2018) and Dorian (Kijewski-Correa et al. 2019) and the Palu Earthquake and Tsunami (Robertson and Kijewski-Correa 2020).