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Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds

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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.

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Acknowledgements

I am grateful to the University of Malawi, Chancellor College for sponsoring my doctoral studies at the University of KwaZulu-Natal (UKZN) in South Africa. I extend my heartfelt gratitude to Dr. Faraimunashe Chirove (University of Johannesburg, South Africa) Professor Keshlan S. Govinder (UKZN), and Professor Holly D. Gaff (Old Dominion University, USA) for mentoring me and introducing me to stochastic epidemic modelling when I was their PhD student from November 2015 to November 2018.

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  1. Mathematical Sciences Department, University of Malawi, Chancellor College, P. O. Box 280, Zomba, Malawi

    Milliward Maliyoni

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Maliyoni, M. Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds. Acta Biotheor 69, 91–116 (2021). https://doi.org/10.1007/s10441-020-09391-y

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