Stochastic modeling of a mosquito-borne disease

Advances in Difference Equations

article

Witbooi, Peter J.¹  Abiodun, Gbenga J.¹  van Schalkwyk, Garth J.¹  Ahmed, Ibrahim H. I.² 

[1] Department of Mathematics and Applied Mathematics, University of the Western Cape;SA MRC Bioinformatics Unit, South African National Bioinformatics Institute, University of the Western Cape

关键词: SDE model;    Basic reproduction number;    Exponential stability;    Malaria;    Extinction;   

DOI  :  10.1186/s13662-020-02803-w

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We present and analyze a stochastic differential equation (SDE) model for the population dynamics of a mosquito-borne infectious disease. We prove the solutions to be almost surely positive and global. We introduce a numerical invariant${\mathcal{R}}$ of the model with${\mathcal{R}}<1$ being a condition guaranteeing the almost sure stability of the disease-free equilibrium. We show that stochastic perturbations enhance the stability of the disease-free equilibrium of the underlying deterministic model. We illustrate the main stability theorem through simulations and show how to obtain interval estimates when making forward projections. We consulted a wide range of literature to find relevant numerical parameter values.

【 授权许可】

CC BY