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Impact of heterogeneity on the dynamics of an SEIR epidemic model

1. Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., V8W 3R4

## Abstract    Related pages

An SEIR epidemic model with an arbitrarily distributed exposed stage is revisited to study the impact of heterogeneity on the spread of infectious diseases. The heterogeneity may come from age or behavior and disease stages, resulting in multi-group and multi-stage models, respectively. For each model, Lyapunov functionals are used to show that the basic reproduction number $\mathcal{R}_0$ gives a sharp threshold. If $\mathcal{R}_0\leq 1$, then the disease-free equilibrium is globally asymptotically stable and the disease dies out from all groups or stages. If $\mathcal{R}_0>1$, then the disease persists in all groups or stages, and the endemic equilibrium is globally asymptotically stable.
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Citation: Zhisheng Shuai, P. van den Driessche. Impact of heterogeneity on the dynamics of an SEIR epidemic model. Mathematical Biosciences and Engineering, 2012, 9(2): 393-411. doi: 10.3934/mbe.2012.9.393

• 1. Ling Zhang, Jingmei Pang, Jinliang Wang, Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates, Abstract and Applied Analysis, 2013, 2013, 1, 10.1155/2013/354287
• 2. Lianwen Wang, Zhijun Liu, Xingan Zhang, Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence, Applied Mathematics and Computation, 2016, 284, 47, 10.1016/j.amc.2016.02.058
• 3. Wei Duan, Zhichao Song, Xiaogang Qiu, Heterogeneous edge weights promote epidemic diffusion in weighted evolving networks, Modern Physics Letters B, 2016, 30, 21, 1650300, 10.1142/S0217984916503000
• 4. F. Capone, V. De Cataldis, R. De Luca, On the Stability of a SEIR Reaction Diffusion Model for Infections Under Neumann Boundary Conditions, Acta Applicandae Mathematicae, 2014, 132, 1, 165, 10.1007/s10440-014-9899-7
• 5. Aberrahman Iggidr, Gauthier Sallet, Max O. Souza, On the dynamics of a class of multi-group models for vector-borne diseases, Journal of Mathematical Analysis and Applications, 2016, 441, 2, 723, 10.1016/j.jmaa.2016.04.003
• 6. Lin Zhao, Zhi-Cheng Wang, Shigui Ruan, Traveling wave solutions in a two-group SIR epidemic model with constant recruitment, Journal of Mathematical Biology, 2018, 10.1007/s00285-018-1227-9
• 7. Florinda Capone, Valentina De Cataldis, Roberta De Luca, Influence of diffusion on the stability of equilibria in a reaction–diffusion system modeling cholera dynamic, Journal of Mathematical Biology, 2015, 71, 5, 1107, 10.1007/s00285-014-0849-9
• 8. Haitao Song, Weihua Jiang, Shengqiang Liu, Global dynamics of two heterogeneous SIR models with nonlinear incidence and delays, International Journal of Biomathematics, 2016, 09, 03, 1650046, 10.1142/S1793524516500467
• 9. F. Capone, V. De Cataldis, R. De Luca, On the nonlinear stability of an epidemic SEIR reaction-diffusion model, Ricerche di Matematica, 2013, 62, 1, 161, 10.1007/s11587-013-0151-y
• 10. Xiaomei Feng, Zhidong Teng, Fengqin Zhang, Global dynamics of a general class of multi-group epidemic models with latency and relapse, Mathematical Biosciences and Engineering, 2014, 12, 1, 99, 10.3934/mbe.2015.12.99
• 11. Jinliang Wang, Xianning Liu, Modeling diseases with latency and nonlinear incidence rates: global dynamics of a multi-group model, Mathematical Methods in the Applied Sciences, 2016, 39, 8, 1964, 10.1002/mma.3613
• 12. Jinhu Xu, Yicang Zhou, Global stability of a multi-group model with vaccination age, distributed delay and random perturbation, Mathematical Biosciences and Engineering, 2015, 12, 5, 1083, 10.3934/mbe.2015.12.1083
• 13. R. N. Mohapatra, Donald Porchia, Zhisheng Shuai, , Mathematical Analysis and its Applications, 2015, Chapter 51, 619, 10.1007/978-81-322-2485-3_51
• 14. Matthias Ehrhardt, Jáan Gasper, Sona Kilianováa, SIR-based Mathematical Modeling of Infectious Diseases with Vaccination and Waning Immunity, Journal of Computational Science, 2019, 10.1016/j.jocs.2019.101027