Traveling waves of diffusive predator-prey systems: Disease outbreak propagation
Top Cited Papers
- 1 January 2012
- journal article
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete & Continuous Dynamical Systems
- Vol. 32 (9) , 3303-3324
- https://doi.org/10.3934/dcds.2012.32.3303
Abstract
We study the traveling waves of reaction-diffusion equations for a diffusive SIR model.The existence of traveling waves is determined by the basic reproduction number of the corresponding ordinary differential equations and the minimal wave speed.Our proof is based on Schauder fixed point theorem and Laplace transform.Keywords
This publication has 63 references indexed in Scilit:
- Travelling waves for a reaction–diffusion system in population dynamics and epidemiologyProceedings of the Royal Society of Edinburgh: Section A Mathematics, 2005
- Traveling Waves of Infection in the Hantavirus EpidemicsBulletin of Mathematical Biology, 2003
- Stage‐Structured Infection Transmission and a Spatial Epidemic: A Model for Lyme DiseaseThe American Naturalist, 2002
- Spatiotemporal patterns in the Hantavirus infectionPhysical Review E, 2002
- Mathematical Models in Population Biology and EpidemiologyPublished by Springer Nature ,2001
- Vaccination in a model of an epidemicInternational Journal of Mathematics and Mathematical Sciences, 2000
- The velocity of spatial population expansionJournal of Mathematical Biology, 1990
- Deterministic epidemic waves of critical velocityMathematical Proceedings of the Cambridge Philosophical Society, 1977
- Deterministic epidemic wavesMathematical Proceedings of the Cambridge Philosophical Society, 1976
- Measles Periodicity and Community SizeJournal of the Royal Statistical Society. Series A (General), 1957