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A mathematical model of Lyme disease is formulated to incorporate a spatially heterogenous structure. The basic reproduction number R₀ of the disease and its computational formulae are established. It is shown that R₀ serves as a threshold value between extinction and persistence in the evolution of Lyme disease. Numerical simulations indicate that spatial heterogeneity of the disease transmission coefficient increases the basic reproduction number, but spatial heterogeneity of the carrying capacity of mice alleviates the value of R₀. Moreover, the influence of host population in size, destruction of tick habitats, and deployment of vaccinations is studied to give insights into optimal control of the disease.
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Wang et al. (2015) studied this question.
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