Mathematical and computational approaches to epidemic modeling: a comprehensive review

Assessment Model for Rapid Suppression of SARS-CoV-2 Transmission under Government Control

The rapid suppression of SARS-CoV-2 transmission remains a priority for maintaining public health security throughout the world, and the agile adjustment of government prevention and control strategies according to the spread of the epidemic is crucial for controlling the spread of the epidemic. Thus, in this study, a multi-agent modeling approach was developed for constructing an assessment model for the rapid suppression of SARS-CoV-2 transmission under government control. Different from previous mathematical models, this model combines computer technology and geographic information system to abstract human beings in different states into micro-agents with self-control and independent decision-making ability; defines the rules of agent behavior and interaction; and describes the mobility, heterogeneity, contact behavior patterns, and dynamic interactive feedback mechanism of space environment. The real geospatial and social environment in Taiyuan was considered as a case study. In the implemented model, the government agent could adjust the response level and prevention and control policies for major public health emergencies in real time according to the development of the epidemic, and different intervention strategies were provided to improve disease control methods in the simulation experiment. The simulation results demonstrate that the proposed model is widely applicable, and it can not only judge the effectiveness of intervention measures in time but also analyze the virus transmission status in complex urban systems and its change trend under different intervention measures, thereby providing scientific guidance to support urban public health safety.

The CP-ABM approach for modelling COVID-19 infection dynamics and quantifying the effects of non-pharmaceutical interventions

The motivation for this research is to develop an approach that reliably captures the disease dynamics of COVID-19 for an entire population in order to identify the key events driving change in the epidemic through accurate estimation of daily COVID-19 cases. This has been achieved through the new CP-ABM approach which uniquely incorporates Change Point detection into an Agent Based Model taking advantage of genetic algorithms for calibration and an efficient infection centric procedure for computational efficiency. The CP-ABM is applied to the Northern Ireland population where it successfully captures patterns in COVID-19 infection dynamics over both waves of the pandemic and quantifies the significant effects of non-pharmaceutical interventions (NPI) on a national level for lockdowns and mask wearing. To our knowledge, there is no other approach to date that has captured NPI effectiveness and infection spreading dynamics for both waves of the COVID-19 pandemic for an entire country population.

Validating and Testing an Agent-Based Model for the Spread of COVID-19 in Ireland

Agent-based models can be used to better understand the impacts of lifting restrictions or implementing interventions during a pandemic. However, agent-based models are computationally expensive, and running a model of a large population can result in a simulation taking too long to run for the model to be a useful analysis tool during a public health crisis. To reduce computing time and power while running a detailed agent-based model for the spread of COVID-19 in the Republic of Ireland, we introduce a scaling factor that equates 1 agent to 100 people in the population. We present the results from model validation and show that the scaling factor increases the variability in the model output, but the average model results are similar in scaled and un-scaled models of the same population, and the scaled model is able to accurately simulate the number of cases per day in Ireland during the autumn of 2020. We then test the usability of the model by using the model to explore the likely impacts of increasing community mixing when schools reopen after summer holidays.

Moderating Effect of a Cross-Level Social Distancing Policy on the Disparity of COVID-19 Transmission in the United States

Currently, coronavirus disease 2019 (COVID-19) remains a global pandemic, but the prevention and control of the disease in various countries have also entered the normalization stage. To achieve economic recovery and avoid a waste of resources, different regions have developed prevention and control strategies according to their social, economic, and medical conditions and culture. COVID-19 disparities under the interaction of various factors, including interventions, need to be analyzed in advance for effective and precise prevention and control. Considering the United States as the study case, we investigated statistical and spatial disparities based on the impact of the county-level social vulnerability index (SVI) on the COVID-19 infection rate. The county-level COVID-19 infection rate showed very significant heterogeneity between states, where 67% of county-level disparities in COVID-19 infection rates come from differences between states. A hierarchical linear model (HLM) was adopted to examine the moderating effects of state-level social distancing policies on the influence of the county-level SVI on COVID-19 infection rates, considering the variation in data at a unified level and the interaction of various data at different levels. Although previous studies have shown that various social distancing policies inhibit COVID-19 transmission to varying degrees, this study explored the reasons for the disparities in COVID-19 transmission under various policies. For example, we revealed that the state-level restrictions on the internal movement policy significantly attenuate the positive effect of county-level economic vulnerability indicators on COVID-19 infection rates, indirectly inhibiting COVID-19 transmission. We also found that not all regions are suitable for the strictest social distancing policies. We considered the moderating effect of multilevel covariates on the results, allowing us to identify the causes of significant group differences across regions and to tailor measures of varying intensity more easily. This study is also necessary to accomplish targeted preventative measures and to allocate resources.

Modeling the Spatial and Temporal Spread of COVID-19 in Poland Based on a Spatial Interaction Model

This article describes an original methodology for integrating global SIR-like epidemic models with spatial interaction models, which enables the forecasting of COVID-19 dynamics in Poland through time and space. Mobility level, estimated by the regional population density and distances among inhabitants, was the determining variable in the spatial interaction model. The spatiotemporal diffusion model, which allows the temporal prediction of case counts and the possibility of determining their spatial distribution, made it possible to forecast the dynamics of the COVID-19 pandemic at a regional level in Poland. This model was used to predict incidence in 380 counties in Poland, which represents a much more detailed modeling than NUTS 3 according to the widely used geocoding standard Nomenclature of Territorial Units for Statistics. The research covered the entire territory of Poland in seven weeks of early 2021, just before the start of vaccination in Poland. The results were verified using official epidemiological data collected by sanitary and epidemiological stations. As the conducted analyses show, the application of the approach proposed in the article, integrating epidemiological models with spatial interaction models, especially unconstrained gravity models and destination (attraction) constrained models, leads to obtaining almost 90% of the coefficient of determination, which reflects the quality of the model’s fit with the spatiotemporal distribution of the validation data.

An integrated simulation framework for the prevention and mitigation of pandemics caused by airborne pathogens

In this work, we developed an integrated simulation framework for pandemic prevention and mitigation of pandemics caused by airborne pathogens, incorporating three sub-models, namely the spatial model, the mobility model, and the propagation model, to create a realistic simulation environment for the evaluation of the effectiveness of different countermeasures on the epidemic dynamics. The spatial model converts images of real cities obtained from Google Maps into undirected weighted graphs that capture the spatial arrangement of the streets utilized next for the mobility of individuals. The mobility model implements a stochastic agent-based approach, developed to assign specific routes to individuals moving in the city, through the use of stochastic processes, utilizing the weights of the underlying graph to deploy shortest path algorithms. The propagation model implements both the epidemiological model and the physical substance of the transmission of an airborne pathogen (in our approach, we investigate the transmission parameters of SARS-CoV-2). The deployment of a set of countermeasures was investigated in reducing the spread of the pathogen, where, through a series of repetitive simulation experiments, we evaluated the effectiveness of each countermeasure in pandemic prevention.

Epidemic modeling as a means to reimagine health education and policy post-COVID

Purpose

As illustrated by coronavirus disease 2019 (COVID-19), epidemic models are powerful health policy tools critical for disease prevention and control, i.e. if they are fit for purpose. How do people ensure this is the case and where does health education fit in?

Design/methodology/approach

This research takes a multidisciplinary approach combining qualitative secondary and primary data from a literature review, interviews and surveys. The former spans academic literature, grey literature and course curriculum, while the latter two involve discussions with various modeling stakeholders (educators, academics, students, modeling experts and policymakers) both within and outside the field of epidemiology.

Findings

More established approaches (compartmental models) appear to be favored over emerging techniques, like agent-based models. This study delves into how formal and informal education opportunities may be driving this preference. Drawing from other fields, the authors consider how this can be addressed.

Practical implications

This study offers concrete recommendations (course design routed in active learning pedagogies) as to how health education and, by extension, policy can be reimagined post-COVID to make better use of the full range of epidemic modeling methods available.

Originality/value

There is a lack of research exploring how these methods are taught and how this instruction influences which methods are employed. To fill this gap, this research uniquely engages with modeling stakeholders and bridges disciplinary silos to build complimentary knowledge.

Matrix-Based Formulation of Heterogeneous Individual-Based Models of Infectious Diseases: Using SARS Epidemic as a Case Study

Heterogeneities of individual attributes and behaviors play an important role in the complex process of epidemic spreading. Compared to differential equation-based system dynamical models of infectious disease transmission, individual-based epidemic models exhibit the advantage of providing a more detailed description of realities to capture heterogeneities across a population. However, the higher granularity and resolution of individual-based epidemic models comes with the cost of increased computational complexities, which result in difficulty in formulating individual-based epidemic models with mathematics. Furthermore, it requires great effort to understand and reproduce existing individual-based epidemic models presented by previous researchers. We proposed a mathematical formulation of heterogeneous individual-based epidemic models using matrices. Matrices and vectors were applied to represent individual attributes and behaviors. We derived analytical results from the matrix-based formulations of individual epidemic models, and then designed algorithms to force the computation of matrix-based individual epidemic models. Finally, we used a SARS epidemic control as a case study to verify the matrix-based formulation of heterogeneous individual-based epidemic models.

Reinforcement learning-based decision support system for COVID-19

Globally, informed decision on the most effective set of restrictions for the containment of COVID-19 has been the subject of intense debates. There is a significant need for a structured dynamic framework to model and evaluate different intervention scenarios and how they perform under different national characteristics and constraints. This work proposes a novel optimal decision support framework capable of incorporating different interventions to minimize the impact of widely spread respiratory infectious pandemics, including the recent COVID-19, by taking into account the pandemic's characteristics, the healthcare system parameters, and the socio-economic aspects of the community. The theoretical framework underpinning this work involves the use of a reinforcement learning-based agent to derive constrained optimal policies for tuning a closed-loop control model of the disease transmission dynamics.

Modeling epidemic spread in transportation networks: A review

The emergence of novel infectious diseases has become a serious global problem. Convenient transportation networks lead to rapid mobilization in the context of globalization, which is an important factor underlying the rapid spread of infectious diseases. Transportation systems can cause the transmission of viruses during the epidemic period, but they also support the reopening of economies after the epidemic. Understanding the mechanism of the impact of mobility on the spread of infectious diseases is thus important, as is establishing the risk model of the spread of infectious diseases in transportation networks. In this study, the basic structure and application of various epidemic spread models are reviewed, including mathematical models, statistical models, network-based models, and simulation models. The advantages and limitations of model applications within transportation systems are analyzed, including dynamic characteristics of epidemic transmission and decision supports for management and control. Lastly, research trends and prospects are discussed. It is suggested that there is a need for more in-depth research to examine the mutual feedback mechanism of epidemics and individual behavior, as well as the proposal and evaluation of intervention measures. The findings in this study can help evaluate disease intervention strategies, provide decision supports for transport policy during the epidemic period, and ameliorate the deficiencies of the existing system.

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Reviewed epidemic spread models and their applications in transportation networks.

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Analyzed the advantages and limitations of epidemic spread model applications in transportation systems.

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Summarized the emerging modeling requirements brought by the COVID-19 pandemic.

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Proposed research trends and prospects for epidemic spread modeling in transportation networks.

Predictive modeling of disease propagation in a mobile, connected community using cellular automata

We present numerical results obtained from the modeling of a stochastic, highly connected, and mobile community. The spread of attributes like health and disease among the community members is simulated using cellular automata on a planar two-dimensional surface. With remarkably few assumptions, we are able to predict the future course of propagation of such a disease as a function of time and the fine-tuning of parameters related to interactions among the automata.

Localized spatial distributions of disease phases yield long-term persistence of infection

We explore the emergence of persistent infection in two patches where the phases of disease progression of the individuals is given by the well known SIRS cycle modelling non-fatal communicable diseases. We find that a population structured into two patches with significantly different initial states, yields persistent infection, though interestingly, the infection does not persist in a homogeneous population having the same average initial composition as the average of the initial states of the two patches. This holds true for inter-patch links ranging from a single connection to connections across the entire inter-patch boundary. So a population with spatially uniform distribution of disease phases leads to disease extinction, while a population spatially separated into distinct patches aids the long-term persistence of disease. After transience, even very dissimilar patches settle down to the same average infected sub-population size. However the patterns of disease spreading in the patches remain discernibly dissimilar, with the evolution of the total number of infecteds in the two patches displaying distinct periodic wave forms, having markedly different amplitudes, though identical frequencies. We quantify the persistent infection through the size of the asymptotic infected set. We find that the number of inter-patch links does not affect the persistence in any significant manner. The most important feature determining persistence of infection is the disparity in the initial states of the patches, and it is clearly evident that persistence increases with increasing difference in the constitution of the patches. So we conclude that populations with very non-uniform distributions, where the individuals in different phases of disease are strongly compartmentalized spatially, lead to sustained persistence of disease in the entire population.

The Dynamics of Avian Influenza: Individual-Based Model with Intervention Strategies in Traditional Trade Networks in Phitsanulok Province, Thailand

Avian influenza virus subtype H5N1 is endemic to Southeast Asia. In Thailand, avian influenza viruses continue to cause large poultry stock losses. The spread of the disease has a serious impact on poultry production especially among rural households with backyard chickens. The movements and activities of chicken traders result in the spread of the disease through traditional trade networks. In this study, we investigate the dynamics of avian influenza in the traditional trade network in Phitsanulok Province, Thailand. We also propose an individual-based model with intervention strategies to control the spread of the disease. We found that the dynamics of the disease mainly depend on the transmission probability and the virus inactivation period. This study also illustrates the appropriate virus disinfection period and the target for intervention strategies on traditional trade network. The results suggest that good hygiene and cleanliness among household traders and trader of trader areas and ensuring that any equipment used is clean can lead to a decrease in transmission and final epidemic size. These results may be useful to epidemiologists, researchers, and relevant authorities in understanding the spread of avian influenza through traditional trade networks.