### Abstract

A mathematical model is formulated for the fox rabies epidemic that swept through large areas of Europe during parts of the last century. Differently from other models, both territorial and diffusing rabid foxes are included, which leads to a system of partial differential, functional differential and differential-integral equations. The system is reduced to a scalar Volterra-Hammerstein integral equation to which the theory of spreading speeds pioneered by Aronson and Weinberger is applied. The spreading speed is given by an implicit formula which involves the space-time Laplace transform of the integral kernel. This formula can be exploited to find the dependence of the spreading speed on the model ingredients, in particular on those describing the interplay between diffusing and territorial rabid foxes and on the distribution of the latent period.

Original language | English (US) |
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Pages (from-to) | 2143-2183 |

Number of pages | 41 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 25 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1 2020 |

### Keywords

- Basic reproduction number
- Cumulative infectious force
- Home-range size
- Latent period of arbitrarily distributed length
- Proportion of diffusing rabid foxes

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics