Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2009 · 125 citations · 16 references
Natural SciencesInfectious DiseasesMathematicsDifferential EquationsDynamical SystemsStochastic ProcessesDiffusion ProcessesDisease SpreadInfectious Disease DynamicsPartial Differential EquationsPopulation Dynamics ModelingReaction-diffusion SystemsAge-structured Transmission ModelsDiffusion EquationEpidemic ModelsEpidemic Spreading ModelsFunctional EquationsModeling Of Outbreak SpreadReaction-diffusion EquationsTraveling Wave Solutions
In this article, we study the existence of travelling waves for a class of epidemic models structured in space and with respect to the age of infection. We obtain a necessary and sufficient condition for the existence of travelling waves for such a class of problems. As a consequence of our main result, we also derive the existence of travelling waves of a class of functional partial derivative equations.
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