Résumé
Despite the fact that it is well known that vectors do not visit hosts randomly, many epidemiological models of vector-borne diseases do not take into account this biological fact. Indeed, vectors may be differentially attracted toward infected and uninfected hosts depending on whether they carry the pathogen or not. We would like to know what would be the implication for the long-term dynamics of our system. This talk is based on publication [1].We consider a system of partial differential equations with vector diffusion. For the non-spatial model, we show that conditional vector preferences may induce bistability between the disease-free equilibrium and an endemic equilibrium. Backward bifurcation may also occur. For the model with diffusion, we show that bistable travelling waves may exists with positive or negative spreading speeds such that the disease either invades or retreats into space. When a monostable travelling wave occurs, we show that the disease spreading speed depends on conditional vectorial preferences. We illustrate the theoretical results with several simulations. We also discuss the implication of our findings in terms of control strategies.Reference:[1] Frédéric M. Hamelin, Frank M. Hilker, Yves Dumont. Spatial spread of infectious diseases with conditional vector preferences. Journal of Mathematical Biology, 2023, 87 (2), pp.38.