Asymptotic behavior of stochastic multi-group epidemic models with distributed delays

Qun Liu, Daqing Jiang, Ningzhong Shi, Tasawar Hayat and Ahmed Alsaedi

Physica A: Statistical Mechanics and its Applications, 2017, vol. 467, issue C, 527-541

Abstract: In this paper, we introduce stochasticity into multi-group epidemic models with distributed delays and general kernel functions. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by using the method of stochastic Lyapunov functions, we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number R0. If R0≤1, the solution of the stochastic system oscillates around the disease-free equilibrium E0, while if R0>1, the solution of the stochastic model fluctuates around the endemic equilibrium E∗. Moreover, we also establish sufficient conditions of these results.

Keywords: Stochastic multi-group epidemic model; Distributed delay; Disease-free equilibrium; Endemic equilibrium; Lyapunov functional (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:467:y:2017:i:c:p:527-541

DOI: 10.1016/j.physa.2016.10.034

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