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| Modeling of Lone Star Ticks with Deer Migration to Canada |
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| KeyWord:Lone star tick deer migration disease modeling asymptotic stability sensitivity analysis |
| Author Name | Affiliation | | Jemisa Sadiku | Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada | | Zilong Song | Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada | | Jianhong Wu | Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada |
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| Abstract: |
| Due to climate change and an increase of favourable habitat, ticks and tick-borne diseases are reported to expand to northern areas in north America. One main factor for lone star ticks to be established in Canada is due to the migration of white-tailed deers from US. In this work, we formulate a compartmental model to study the dynamics of lone star ticks and white-tailed deers, with a focus on migration effect of white-tailed deers. The tickhost interaction and the effect of deer migration are explored analytically and numerically. The positivity of the populations in the model is proved, and the unique positive equilibrium is proved to be asymptotically stable. We conduct sensitivity analysis on a set of parameters, revealing the correlation between the parameters and equilibrium populations. Numerical results show that migration rate of white-tailed deer is one crucial parameter that increases the populations of (infected) ticks and (infected) hosts. |
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