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Mathematical and computational approaches to epidemic modeling: a comprehensive review

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Abstract

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.

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Authors and Affiliations

  1. Center of Computational Experiments and Parallel Systems Technology, College of Information Systems and Management, National University of Defense Technology, Changsha, 410073, China

    Wei Duan, Zongchen Fan, Peng Zhang, Gang Guo & Xiaogang Qiu

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  1. Wei Duan
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  2. Zongchen Fan
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  3. Peng Zhang
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  4. Gang Guo
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  5. Xiaogang Qiu
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Correspondence to Wei Duan.

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Wei Duan received PhD degree in 2014 in control science and engineering from the National University of Defense Technology, China. His research interests include complex networks, epidemic modeling, information diffusion, agent-based simulation, and social computing.

Zongchen Fan is a PhD candidate in the College of Information Systems and Management, National University of Defense Technology, China. His research interests include agent-based modeling and simulation, opinion dynamics, and parallel emergency management.

Peng Zhang received his BS degree in 2009 and his MS degree in 2011 in control science and engineering from the National University of Defense Technology, China, where he is currently a PhD candidate. His research interests include artificial societies, domain specific modeling and knowledge engineering.

Gang Guo received his BS degree in 1999 and his PhD degree in 2004 in control science and engineering from the National University of Defense Technology, China. His research interests include environment modeling and simulation, and simulation software and platforms.

Xiaogang Qiu received his PhD degree in system simulation from the National University of Defense Technology, China. He is a professor in the College of Information Systems and Management, National University of Defense Technology, China. His research interests include simulation, multi-agent systems, knowledge management, and parallel control.

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Duan, W., Fan, Z., Zhang, P. et al. Mathematical and computational approaches to epidemic modeling: a comprehensive review. Front. Comput. Sci. 9, 806–826 (2015). https://doi.org/10.1007/s11704-014-3369-2

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