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A stochastic epidemic model for the dynamics of two pathogens in a single tick population

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

Abstract

Understanding tick-transmitted pathogens in tick infested areas is crucial for the development of preventive and control measures in response to the increasing cases of tick-borne diseases. A stochastic model for the dynamics of two pathogens, Rickettsia parkeri and Rickettsia amblyommii, in a single tick, Amblyomma americanum, is developed and analysed. The model, a continuous-time Markov chain, is based on a deterministic tick-borne disease model. The extinction threshold for the stochastic model is computed using the multitype branching process and conditions for pathogen extinction or persistence are presented. The probability of pathogen extinction is computed using numerical simulations and is shown to be a good estimate of the probability of extinction calculated from the branching process. A sensitivity analysis is undertaken to illustrate the relationship between co-feeding and transovarial transmission rates and the probability of pathogen extinction. Expected epidemic duration is estimated using sample paths and we show that R. amblyommii is likely to persist slightly longer than R. parkeri. Further, we estimate the duration of possible coexistence of the two pathogens.

Suggested Citation

  • Maliyoni, Milliward & Chirove, Faraimunashe & Gaff, Holly D. & Govinder, Keshlan S., 2019. "A stochastic epidemic model for the dynamics of two pathogens in a single tick population," Theoretical Population Biology, Elsevier, vol. 127(C), pages 75-90.
    • Handle: RePEc:eee:thpobi:v:127:y:2019:i:c:p:75-90
    DOI: 10.1016/j.tpb.2019.04.004
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    2. Neil M. Ferguson & Alison P. Galvani & Robin M. Bush, 2003. "Ecological and immunological determinants of influenza evolution," Nature, Nature, vol. 422(6930), pages 428-433, March.
    3. Luca Ferreri & Mario Giacobini & Paolo Bajardi & Luigi Bertolotti & Luca Bolzoni & Valentina Tagliapietra & Annapaola Rizzoli & Roberto Rosà, 2014. "Pattern of Tick Aggregation on Mice: Larger Than Expected Distribution Tail Enhances the Spread of Tick-Borne Pathogens," PLOS Computational Biology, Public Library of Science, vol. 10(11), pages 1-12, November.
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    Cited by:

    1. Shanshan Chen & Yijun Ran & Hebo Huang & Zhenzhen Wang & Ke-ke Shang, 2022. "Epidemic Dynamics of Two-Pathogen Spreading for Pairwise Models," Mathematics, MDPI, vol. 10(11), pages 1-18, June.

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