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

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

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1999-2021
Number of pages23
JournalBulletin of Mathematical Biology
Issue number9
Publication statusPublished - 1 Sept 2017
Externally publishedYes


  • Ehrlichiosis
  • Multitype branching process
  • Stochastic model
  • Tick-borne disease

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry,Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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