Advances in Difference Equations | |
Stochastic modeling of a mosquito-borne disease | |
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
【 预 览 】
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