Abstract
This article represents Legendre spectral collocation method based on Legendre polynomials to solve a stochastic Susceptible, infected, Recovered (SIR) model. The Legendre polynomials on stochastic SIR model that convert it to a system of equations has been applied and then solved by the Legendre spectral method, which leads to excellent accuracy and convergence by implementing Legendre–Gauss–Lobatto collocation points permitting to generate coarser meshes. The numerical results for both the deterministic and stochastic models are presented. In case of probably small noise, the verge dynamics is analyzed. The large noise will show eradication of disease, which controls disease spreading. Various graphical results demonstrate the effectiveness of the proposed method to SIR model.
Highlights
There are many classical epidemic models which have been intentional and recommended for modeling of spread process of the infectious diseases, like Susceptible, infected, Recovered (SIR), Susceptible infected, Recovered, Susceptible (SIRS), and Susceptible, Exposed, infected Recovered models
A mathematical model was proposed by RA Ross[12] in 1911 to study the dynamics of malaria
The aim of this study is to implement present method for numerical solution of stochastic SIR model given in equation (2)
Summary
There are many classical epidemic models which have been intentional and recommended for modeling of spread process of the infectious diseases, like Susceptible, infected, Recovered (SIR), Susceptible infected, Recovered, Susceptible (SIRS), and Susceptible, Exposed, infected Recovered models. These models have been proposed by many researchers to study the dynamics of disease spread and controls.[1,2,3,4,5,6,7,8,9]. A mathematical model was proposed by RA Ross[12] in 1911 to study the dynamics of malaria. The first classical SIR model was proposed by WO Kermack and AG McKendrick,[17] where the population is considered in three compartments, that is susceptible, infected, and recovered
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