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

TL;DR

This paper develops spatially heterogeneous diffusion models for tick propagation, enabling assessment of control zones to eradicate ticks, with applications to North American and Russian tick species.

Contribution

It introduces novel diffusion models emphasizing spatial heterogeneity for tick spread, extending beyond previous homogeneous models.

Findings

Control zones can effectively reduce tick populations.

Models applied to North American and Russian tick species.

Spatial heterogeneity is crucial for accurate tick spread prediction.

Abstract

Ticks and tick-borne diseases present a well known threat to the health of people in many parts of the globe. The scientific literature devoted both to field observations and to modeling the propagation of ticks continues to grow. So far the majority of the mathematical studies were devoted to models based on ordinary differential equations, where spatial variability was taken into account by a discrete parameter. Only few papers use spatially nontrivial diffusion models, and they are devoted mostly to spatially homogeneous equilibria. Here 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.