A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps

Kuangang Fan, Yan Zhang, Shujing Gao and Shihua Chen

Physica A: Statistical Mechanics and its Applications, 2020, vol. 544, issue C

Abstract: A stochastic susceptible–infectious–recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity, vaccination, and Le.́vy jumps on the transmission of diseases. We first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system. Sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable Lyapunov functions. Based on the analysis, we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system.

Keywords: Extinction; Lévy jumps; Nonlinear incidence rate; Stochastic delayed epidemic model; Vaccination (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:544:y:2020:i:c:s0378437119318898

DOI: 10.1016/j.physa.2019.123379

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