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Analysis of an improved epidemic model with stochastic disease transmission. (English) Zbl 1245.35136

Summary: This paper proposes an improved logistic epidemic model and carries out the complete parameters analysis of asymptotic behavior of infectious diseases. Some interesting details such as the threshold value of outbreak of epidemics and critical states of disease spread are derived. The mean and variance of proportion of infected population are given explicitly. The results show that our model is more reasonable and applicable to describe the real situation. Especially, \(P\frac12\) might be considered as the alarm for relate institutions to make effective policies to prevent and control some epidemics.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D30 Epidemiology
35Q84 Fokker-Planck equations
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