Stochastic analysis of a novel nonautonomous periodic SIRI epidemic system with random disturbances

Weiwei Zhang and Xinzhu Meng

Physica A: Statistical Mechanics and its Applications, 2018, vol. 492, issue C, 1290-1301

Abstract: In this paper, a new stochastic nonautonomous SIRI epidemic model is formulated. Given that the incidence rates of diseases may change with the environment, we propose a novel type of transmission function. The main aim of this paper is to obtain the thresholds of the stochastic SIRI epidemic model. To this end, we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable Lyapunov functions and using stochastic analysis technique. Furthermore, we show that the stochastic system has at least one nontrivial positive periodic solution. Finally, numerical simulations are introduced to illustrate our results.

Keywords: Stochastic SIRI epidemic model; Lyapunov function; Extinction and persistence in mean; Periodic solution (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:492:y:2018:i:c:p:1290-1301

DOI: 10.1016/j.physa.2017.11.057

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