Blocking of bistable front propagation: Application to Wolbachia population replacement

Saoussen Latrach; Nicolas Vauchelet; Hatem Zaag

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arXiv · 2610.13497

Blocking of bistable front propagation: Application to Wolbachia population replacement

Saoussen Latrach·Nicolas Vauchelet·Hatem Zaag

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Abstract

In order to control epidemics of mosquito-borne diseases such as dengue, for which there is still no vaccine available, several strategies aim to directly target the mosquito population. One technique involves introducing a symbiotic bacterium called Wolbachia into the population, which blocks the transmission of pathogens. A mathematical model of the introduction of this bacterium and the replacement of the mosquito population with a population carrying this bacterium has been developed, proving that in a homogeneous environment, there is spatial propagation of the replacement. The objective of this paper is to study the blocking of this propagation in cases where the environment is not homogeneous. In particular, we are considering scenarios where the environmental carrying capacity varies significantly across different regions of the spatial domain. To achieve this objective, we first reduce the original 2x2 reaction-diffusion system to a single closed equation, providing a simplified framework for studying the dynamics of Wolbachia propagation. We then investigate the blocking of the propagation in the population replacement process, focusing on the effects of spatial variations in the environmental carrying capacity. Numerical simulations have been performed to validate the theoretical results.

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Saoussen Latrach, Nicolas Vauchelet, Hatem Zaag. 2026-10-09. Blocking of bistable front propagation: Application to Wolbachia population replacement. https://arxiv.org/abs/2610.13497

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