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Ticks and tick-borne diseases present a well known threat to the health ofpeople in many parts of the globe. The scientific literature devoted both tofield observations and to modeling the propagation of ticks continues to grow.So far the majority of the mathematical studies were devoted to models based onordinary differential equations, where spatial variability was taken intoaccount by a discrete parameter. Only few papers use spatially nontrivialdiffusion models, and they are devoted mostly to spatially homogeneousequilibria. Here we develop diffusion models for the propagation of ticksstressing spatial heterogeneity. This allows us to assess the sizes of controlzones that can be created (using various available techniques) to produce apatchy territory, on which ticks will be eventually eradicated. Using averagedparameters taken from various field observations we apply our theoreticalresults to the concrete cases of the lone star ticks of North America and ofthe taiga ticks of Russia.

On the control over the distribution of ticks based on the extensions of the KISS model