Abstract
A stochastic susceptible–infectious–recovered epidemic model with temporary immunity and media coverage is proposed. The effects of Lévy jumps on the dynamics of the model are considered. A unique global positive solution for the epidemic model is obtained. Sufficient conditions are derived to guarantee that the epidemic disease is extinct and persistent in the mean. The threshold behavior is discussed. Numerical simulations are given to verify our theoretical results.
Highlights
1 Introduction Epidemics have a huge impact on human life, and controlling and eradicating infectious diseases have been a vital problem that needs to be urgently solved in eco-epidemiology research
Temporary immunity is another important phenomenon in the transmission of epidemic diseases, such as influenza, Chlamydia trachomatis, and Salmonella infection [12]
Considering the effects of temporary immunity and media coverage on a stochastic susceptible–infectious–recovered (SIR) epidemic model driven by Lévy noise:
Summary
Epidemics have a huge impact on human life, and controlling and eradicating infectious diseases have been a vital problem that needs to be urgently solved in eco-epidemiology research. Considering the effects of temporary immunity and media coverage on a stochastic susceptible–infectious–recovered (SIR) epidemic model driven by Lévy noise: By virtue of the condition (2) and (2.12), we obtain lim sup ln I(t) ≤ (μ + γ ) t→∞ t
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