Abstract
In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.
Highlights
We propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients
By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function
SIR models are the foundation for a large number of compartmental models in mathematical epidemiology which classify the population into three classes: Susceptible, Infected and Removed
Summary
SIR models are the foundation for a large number of compartmental models in mathematical epidemiology which classify the population into three classes: Susceptible, Infected and Removed (see [1]-[19]) These models admit two types of equilibrium: disease free and endemic equilibrium. In [16], Tornatore proved the stability of disease-free equilibrium under some restricted conditions They didn’t consider the dynamics of the endemic equilibrium. We investigate the stochastic asymptotic stability of disease free equilibria and the dynamics of endemic equilibria which has not been discussed in [16].
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