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Multigroup SIR epidemic model with stochastic perturbation

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  • Ji, Chunyan
  • Jiang, Daqing
  • Shi, Ningzhong

Abstract

In this paper, we discuss a multigroup SIR model with stochastic perturbation. We deduce the globally asymptotic stability of the disease-free equilibrium when R0≤1, which means the disease will die out. On the other hand, when R0>1, we derive the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. Furthermore, we prove the system is persistent in the mean which also reflects the disease will prevail. The key to our analysis is choosing appropriate Lyapunov functions. Finally, we illustrate the dynamic behavior of the model with n=2 and their approximations via a range of numerical experiments.

Suggested Citation

  • Ji, Chunyan & Jiang, Daqing & Shi, Ningzhong, 2011. "Multigroup SIR epidemic model with stochastic perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1747-1762.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:10:p:1747-1762
    DOI: 10.1016/j.physa.2010.12.042
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    1. Carletti, M. & Burrage, K. & Burrage, P.M., 2004. "Numerical simulation of stochastic ordinary differential equations in biomathematical modelling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 271-277.
    2. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
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    15. Pan, Tao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Extinction and periodic solutions for an impulsive SIR model with incidence rate stochastically perturbed," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 385-397.
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