The long time behavior of DI SIR epidemic model with stochastic perturbation. (English) Zbl 1194.92053

Summary: We present a differential infectivity (DI) SIR epidemic model with two categories of stochastic perturbations. The long time behavior of the two stochastic systems is studied. Mainly, we show how the solution goes around the infection-free equilibrium and the endemic equilibrium of the deterministic system under different conditions.


92C60 Medical epidemiology
34F05 Ordinary differential equations and systems with randomness
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
92D30 Epidemiology
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