Extinction and periodic solutions for an impulsive SIR model with incidence rate stochastically perturbed

Tao Pan, Daqing Jiang, Tasawar Hayat and Ahmed Alsaedi

Physica A: Statistical Mechanics and its Applications, 2018, vol. 505, issue C, 385-397

Abstract: In this paper, we consider an impulsive SIR model with incidence rate stochastically perturbed. First, we prove the existence and uniqueness of the global positive solution by constructing the equivalent system without impulse. Second, we obtain a sufficient condition which determines epidemic to extinct. Then we demonstrate the existence and global attraction of the boundary periodic solution under the certain condition. Finally, we present a sufficient condition which allows the existence of a positive periodic solution.

Keywords: SIR epidemic model; Stochastic perturbation; Impulsive effect; Periodic solution; Global attraction (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:505:y:2018:i:c:p:385-397

DOI: 10.1016/j.physa.2018.03.012

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