Related Experiment Video
Updated: Dec 9, 2025

Vector Competence Analyses on Aedes aegypti Mosquitoes using Zika Virus
Published on: May 31, 2020
Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds
1Mathematical Sciences Department, University of Malawi, Chancellor College, P. O. Box 280, Zomba, Malawi. mmaliyoni@cc.ac.mw.
Abstract:
Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov chain, for the transmission dynamics of West Nile virus in birds is developed based on the assumptions of its analogous deterministic model. The branching process is applied to derive the extinction threshold for the stochastic model and conditions for disease extinction or persistence. The probability of disease extinction computed from the branching process is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of both models are compared to ascertain the effect of demographic stochasticity on West Nile virus dynamics. Analytical and numerical results show differences in model predictions and asymptotic dynamics between stochastic and deterministic models that are crucial for the prevention of disease outbreaks. It is found that there is a high probability of disease extinction if the disease emerges from exposed mosquitoes unlike if it emerges from infectious mosquitoes and birds. Finite-time to disease extinction is estimated using sample paths and it is shown that the epidemic duration is shortest if the disease is introduced by exposed mosquitoes.
Related Concept Videos
Causality in Epidemiology
Viral Mutations
Viral Recombination
Mutation, Gene Flow, and Genetic Drift
Steps in Outbreak Investigation
Conservation of Declining Populations

