ИСТИНА

We develop diffusion models for the propagation of ticks stressing spatial heterogeneity. This allows us to assess the sizes of control zones that can be created (using various available techniques) to produce a patchy territory, on which ticks will be eventually eradicated. Using averaged parameters taken from various field observations we apply our theoretical results to the concrete cases of the lone star ticks of North America and of the taiga ticks of Russia. From the mathematical point of view, what we are doing is getting criteria for negativity of a class of diffusion operators with piecewise continuous symbols. The negativity of the diffusion operators that govern the propagation of ticks ensures that the population will eventually die out (in the region considered).