Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

Qun Liu, Daqing Jiang, Tasawar Hayat and Bashir Ahmad

Physica A: Statistical Mechanics and its Applications, 2017, vol. 482, issue C, 209-217

Abstract: In this paper, we investigate two stochastic SIR epidemic models with higher order perturbation. For the nonautonomous periodic case of the model, by using Has’minskii’s theory of periodic solution, we show that the system has at least one nontrivial positive T-periodic solution. For the system disturbed by both the white noise and telephone noise, we establish sufficient conditions for positive recurrence and the existence of ergodic stationary distribution of the positive solution.

Keywords: Stochastic SIR epidemic model; Periodic solution; Stationary distribution and ergodicity; Higher order perturbation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:482:y:2017:i:c:p:209-217

DOI: 10.1016/j.physa.2017.04.056

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