Existence and qualitative properties of travelling waves for an epidemiological model with mutations

@article{Griette2014ExistenceAQ,
  title={Existence and qualitative properties of travelling waves for an epidemiological model with mutations},
  author={Q. Griette and G. Raoul},
  journal={arXiv: Analysis of PDEs},
  year={2014}
}
  • Q. Griette, G. Raoul
  • Published 2014
  • Mathematics
  • arXiv: Analysis of PDEs
  • In this article, we are interested in a non-monotone system of logistic reaction-diffusion equations. This system of equations models an epidemics where two types of pathogens are competing, and a mutation can change one type into the other with a certain rate. We show the existence of minimal speed travelling waves, that are usually non monotonic. We then provide a description of the shape of those constructed travelling waves, and relate them to some Fisher-KPP fronts with non-minimal speed. 

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 48 REFERENCES
    Travelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic Trait
    • 45
    • Highly Influential
    • Open Access
    Propagating fronts for competing species equations with diffusion
    • 125
    • Open Access
    Shock Waves and Reaction-Diffusion Equations
    • 3,632
    Invasion fronts with variable motility: Phenotype selection, spatial sorting and wave acceleration
    • 83
    • Open Access