Mathematical and computational approaches are important tools for understanding epidemic spread patterns and evaluating policies of disease control. In recent years, epidemiology has become increasingly integrated with mathematics, sociology, management science, complexity science, and computer science. The cross of multiple disciplines has caused rapid development of mathematical and computational approaches to epidemic modeling. In this article, we carry out a comprehensive review of epidemic models to provide an insight into the literature of epidemic modeling and simulation.We introduce major epidemic models in three directions, including mathematical models, complex network models, and agent-based models. We discuss the principles, applications, advantages, and limitations of these models. Meanwhile, we also propose some future research directions in epidemic modeling. Table 1 Classification of epidemic models Types Names Methods Mathematical models Compartmental models, Reed-Frost models Differential equations, stochastic process, Monte Carlo, Markov chains Complex network models System dynamics models in complex networks, numerical simulations of epidemics in complex networks, metapopulation models, weighted networks, adaptive networks Differential equations, stochastic processes Agent-based models

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Existing studies on the propagation of infectious diseases have not sufficiently considered the uncertainties that are related to individual behavior and its influence on individual decision making to prevent infections, even though it is well known that changes in behavior can lead to variations in the macrodynamics of the spread of infectious diseases. These influencing factors can be categorized into emotion-related and cognition-related components. We present a fuzzy cognitive map (FCM) denotative model to describe how the factors of individual emotions and cognition influence each other. We adjust the weight matrix of causal relationships between these factors by using a so-called nonlinear Hebbian learning method. Based on this FCM model, we can implement individual decision rules against possible infections for disease propagation studies. We take the simulation of influenza A [H1N1] spreading on a campus as an example. We find that individual decision making against infections (frequent washing, respirator usage, and crowd contact avoidance) can significantly decrease the at-peak number of infected patients, even when common policies, such as isolation and vaccination, are not deployed.

In order to tackle the infeasibility of building mathematical models and conducting physical experiments for public health emergencies in the real world, we apply the Artificial societies, Computational experiments, and Parallel execution (ACP) approach to public health emergency management. We use the largest collective outbreak of H1N1 influenza at a Chinese university in 2009 as a case study. We build an artificial society to simulate the outbreak at the university. In computational experiments, aiming to obtain comparable results with the real data, we apply the same intervention strategy as that was used during the real outbreak. Then, we compare experiment results with real data to verify our models, including spatial models, population distribution, weighted social networks, contact patterns, students' behaviors, and models of H1N1 influenza disease, in the artificial society. In the phase of parallel execution, alternative intervention strategies are proposed to control the outbreak of H1N1 influenza more effectively. Our models and their application to intervention strategy improvement show that the ACP approach is useful for public health emergency management.Index Terms-Agent-based simulation, artificial societies, computational experiments, emergency management, parallel execution (ACP), public health.