Advances in Difference Equations (Jul 2020)

Stochastic modeling of a mosquito-borne disease

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

DOI
https://doi.org/10.1186/s13662-020-02803-w
Journal volume & issue
Vol. 2020, no. 1
pp. 1 – 15

Abstract

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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