Stochastic modeling of a mosquito-borne disease

• Main Authors: Peter J. Witbooi, Gbenga J. Abiodun, Garth J. van Schalkwyk, Ibrahim H. I. Ahmed
• Format: Article
• Language: English
• Published: SpringerOpen 2020-07-01
• Series: Advances in Difference Equations
• Subjects: SDE model; Basic reproduction number; Exponential stability; Malaria; Extinction
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02803-w

Abstract 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 R ${\mathcal{R}}$ of the model with R < 1 ${\mathcal{R}}<1$ 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.