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Modeling and Analysis of Epidemic Diffusion with Population Migration

Author

Listed:
  • Ming Liu
  • Yihong Xiao

Abstract

An improved Susceptible‐Infected‐Susceptible (SIS) epidemic diffusion model with population migration between two cities is modeled. Global stability conditions for both the disease‐free equilibrium and the endemic equilibrium are analyzed and proved. The main contribution of this paper is reflected in epidemic modeling and analysis which considers unequal migration rates, and only susceptible individuals can migrate between the two cities. Numerical simulation shows when the epidemic diffusion system is stable, number of infected individuals in one city can reach zero, while the number of infected individuals in the other city is still positive. On the other hand, decreasing population migration in only one city seems not as effective as improving the recovery rate for controlling the epidemic diffusion.

Suggested Citation

  • Ming Liu & Yihong Xiao, 2013. "Modeling and Analysis of Epidemic Diffusion with Population Migration," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:583648
    DOI: 10.1155/2013/583648
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    References listed on IDEAS

    as
    1. Ming Liu & Yihong Xiao, 2012. "Modeling and Analysis of Epidemic Diffusion within Small-World Network," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, June.
    2. Zhiwei Gao & Dexing Kong & Chuanhou Gao, 2012. "Modeling and Control of Complex Dynamic Systems: Applied Mathematical Aspects," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Peilin Shi & Lingzhen Dong, 2012. "Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Peilin Shi & Lingzhen Dong, 2012. "Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-20, January.
    5. Ming Liu & Yihong Xiao, 2012. "Modeling and Analysis of Epidemic Diffusion within Small‐World Network," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Zhiwei Gao & Dexing Kong & Chuanhou Gao, 2012. "Modeling and Control of Complex Dynamic Systems: Applied Mathematical Aspects," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-5, December.
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    Cited by:

    1. Alicia Barriga & Richard A. Dunn, 2025. "The effect of mass migration on disease transmission: Evidence from the Venezuelan refugee crisis," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 44(2), pages 428-455, March.

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