A Reaction-Advection-Diffusion Model for Quasi-neutral Dynamics of Coinfected Strains

Thi Minh Thao Le (1) , Sten Madec (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

This paper studies dynamical system of coinfected strains with spatial diffusion, under a quasi similarity assumption. Such coinfection systems have been studied in several articles without spatial structure. In the present study, we add a spatial structure to comprehend the impact of spatial heterogeneity on the interaction between similar strains. The SIS model is then a reaction-diffusion system in which the coefficients are spatially heterogeneous. Two limiting cases are considered: the case of an asymptotically slow diffusion coefficient and the case of an asymptotically fast diffusion coefficient. In the case of small diffusion rates, we show that the slow system is a semilinear system of type "replicator equations," describing the spatiotemporal evolution of the strains' frequencies. This system is of the reaction-advection-diffusion type, in which the additional advection term explicitly involves the heterogeneity of the associated neutral system. In the case of fast diffusion, classical methods of aggregation of variables are used to reduce the spatialized SIS problem to a homogenized SIS system on which we can directly apply the results of the non-spatial model.

Mots clés: spatial quasi-Neutral dynamics; spatial SIS multi-strain dynamics; slow-fast dynamics; Tikhonov's Theorem; Central Manifold Theorem; co-infection system with diffusion

Domaines: Systèmes dynamiques [math.DS]

Thi Minh Thao Le, Sten Madec. A Reaction-Advection-Diffusion Model for Quasi-neutral Dynamics of Coinfected Strains. 2021. ⟨hal-03467201⟩