A reliable numerical analysis for stochastic dengue epidemic model with incubation period of virus

Advances in Difference Equations

Ali Raza¹  Muhammad Shoaib Arif¹  Muhammad Rafiq² 

[1] Department of Mathematics, Air University;Faculty of Engineering, University of Central Punjab;

关键词: Dengue virus;    Stochastic differential equations;    Euler–Maruyama method;    Stochastic Euler method;    Stochastic Runge–Kutta method;    Stochastic NSFD method;   

DOI  :  10.1186/s13662-019-1958-y

来源: DOAJ

【 摘 要 】

Abstract This article represents a numerical analysis for a stochastic dengue epidemic model with incubation period of virus. We discuss the comparison of solutions between the stochastic dengue model and a deterministic dengue model. In this paper, we have shown that the stochastic dengue epidemic model is more realistic as compared to the deterministic dengue epidemic model. The effect of threshold number R1 $R_{1}$ holds in the stochastic dengue epidemic model. If R1<1 $R_{1} <1$, then situation helps us to control the disease while R1>1 $R_{1} >1$ shows the persistence of disease in population. Unfortunately, the numerical methods like Euler–Maruyama, stochastic Euler, and stochastic Runge–Kutta do not work for large time step sizes. The proposed framework of stochastic nonstandard finite difference scheme (SNSFD) is independent of step size and preserves all the dynamical properties like positivity, boundedness, and dynamical consistency.

【 授权许可】

Unknown