Pulsating fronts for Fisher–KPP systems with mutations as models in evolutionary epidemiology. (August 2018)

• Record Type: Journal Article
• Authors: Alfaro, Matthieu; Griette, Quentin
• Is Part Of: Nonlinear analysis. Volume 42(2018)
• Page Start: 255
• Page End: 289
• Publication Date: 2018-08
• Subjects: Reaction diffusion systems -- Pulsating fronts -- Evolutionary epidemiology -- Bifurcation technics -- Bernstein gradient estimate -- Harnack inequality; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.01.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a periodic reaction diffusion system which, because of competition between u and v, does not enjoy the comparison principle. It also takes into account mutations, allowing u to switch to v and vice versa. Such a system serves as a model in evolutionary epidemiology where two types of pathogens compete in a heterogeneous environment while mutations can occur, thus allowing coexistence. We first discuss the existence of nontrivial positive steady states, using some bifurcation technics. Then, to sustain the possibility of invasion when nontrivial steady states exist, we construct pulsating fronts. As far as we know, this is the first such construction in a KPP situation where comparison arguments are not available.