On a stochastic SIR model

A Space-Heterogeneous Stochastic SIR Model

Exact solution of a stochastic SIR model

Abstract The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible S can become infectious with an infection rate β by an infectious Itype provided that both are in contact. The Itype may recover with a rate γ and from then on stay immune. Due to the coupling between the differ...

Stability of Stochastic Delayed Sir Model

A stochastic version of the SIR model is investigated in this paper. The stability in probability of the steady state of the system is proved under suitable conditions on the white noise perturbations. Linearizations of the systems both with and without delay are given and their exponentially mean square stabilities are studied.

Stochastic Model of SIR Epidemic Modelling

Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with demography. The behaviour of the model approached by deteministic and stochastic models will be introduced, mainly using simulations. Furthermore, we will also in...

A Fractional Order Recovery SIR Model from a Stochastic Process.

Over the past several decades, there has been a proliferation of epidemiological models with ordinary derivatives replaced by fractional derivatives in an ad hoc manner. These models may be mathematically interesting, but their relevance is uncertain. Here we develop an SIR model for an epidemic, including vital dynamics, from an underlying stochastic process. We show how fractional differentia...