Stochastic modeling of a mosquito-borne disease

Abstract

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.

Keywords

• SDE model
• Basic reproduction number
• Exponential stability
• Malaria
• Extinction