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A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence

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Abstract

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton–Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.

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Acknowledgements

MM thanks the University of Malawi (Chancellor College) for financial support. KSG thanks the National Research Foundation of South Africa and the University of KwaZulu-Natal for ongoing support. The authors are grateful to two anonymous reviewers for their valuable suggestions which improved the paper.

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, 3201, South Africa

    Milliward Maliyoni, Faraimunashe Chirove, Holly D. Gaff & Keshlan S. Govinder

  2. Department of Biological Sciences, Old Dominion University, Norfolk, VA, 23529, USA

    Holly D. Gaff

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  1. Milliward Maliyoni
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  2. Faraimunashe Chirove
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  3. Holly D. Gaff
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  4. Keshlan S. Govinder
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Correspondence to Milliward Maliyoni.

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Maliyoni, M., Chirove, F., Gaff, H.D. et al. A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence. Bull Math Biol 79, 1999–2021 (2017). https://doi.org/10.1007/s11538-017-0317-y

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  • DOI: https://doi.org/10.1007/s11538-017-0317-y

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