Document Type


Publication Date




Publication Title

Frontiers in Applied Mathematics and Statistics




1122410 (1-13)


Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the largest patch reproduction number and for connected patches it lies between the minimum and maximum of the patch reproduction numbers. Numerical simulations for a two-patch deterministic and stochastic differential equation models are performed to illustrate the dynamics of the disease for varying migration rates. Our results show that the probability of eliminating or minimizing the disease in both patches is high when there is no migration unlike when it is present. The results imply that the probability of disease extinction can be increased if deer and tick movement are controlled or even prohibited especially when there is an outbreak in one or both patches since movement can introduce a disease in an area that was initially disease-free. Thus, screening of infectives in protected areas such as deer farms, private game parks or reserves, etc. before they migrate to other areas can be one of the intervention strategies for controlling and preventing disease spread.


© 2023 Maliyoni, Gaff, Govinder and Chirove.

This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0). The use, distribution or reproduction in other forums is permitted, provided the original authors and the copyright owners are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Data Availability

Article states: "The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author."

"The Supplementary Material for this article can be found online at:"

Corresponding author: Milliward Maliyoni

Original Publication Citation

Maliyoni, M., Chirove, F., Gaff, H. D., & Govinder, K. S. (2023). Multipatch stochastic epidemic model for the dynamics of a tick-borne disease. Frontiers in Applied Mathematics and Statistics, 9, 1-13, Article 1122410.