Spreading fronts in a partially degenerate integro-differential reaction–diffusion system

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Abstract

This paper is concerned with the spreading and vanishing of an epidemic disease, which is described by a partially degenerate reaction–diffusion system with the nonlocal term and double free boundaries. We first consider the sign of the corresponding principal eigenvalue, which is determined by some given conditions. Then, we get the sufficient conditions that ensure the disease spreading or vanishing. At last, when spreading occurs, some rough estimates of the asymptotic spreading speed are given under some conditions.

Keywords

Epidemic model Partially degenerate Nonlocal Free boundary Spreading and vanishing 

Mathematics Subject Classification

35K57 35R35 92D30 35B40 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China
  2. 2.Department of Applied MathematicsLanzhou University of TechnologyLanzhouPeople’s Republic of China

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