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Dynamics Analysis of a Stochastic SIR Epidemic Model

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  • Feng Rao

Abstract

We investigate an SIR epidemic model with stochastic perturbations. We assume that stochastic perturbations are of a white noise type which is directly proportional to the distances of three variables from the steady-state values, respectively. By constructing suitable Lyapunov functions and applying Itô’s formula, some qualitative properties are obtained, such as the existence of global positive solutions, stochastic boundedness, and permanence. A series of numerical simulations to illustrate these mathematical findings are presented.

Suggested Citation

  • Feng Rao, 2014. "Dynamics Analysis of a Stochastic SIR Epidemic Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, March.
    • Handle: RePEc:hin:jnlaaa:356013
    DOI: 10.1155/2014/356013
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    Cited by:

    1. Debasis Mukherjee, 2022. "Stochastic Analysis of an Eco-Epidemic Model with Biological Control," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2539-2555, December.
    2. Benito Chen-Charpentier, 2021. "Stochastic Modeling of Plant Virus Propagation with Biological Control," Mathematics, MDPI, vol. 9(5), pages 1-16, February.
    3. Rathinasamy, A. & Chinnadurai, M. & Athithan, S., 2021. "Analysis of exact solution of stochastic sex-structured HIV/AIDS epidemic model with effect of screening of infectives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 213-237.

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