# A Vector-Host Epidemic Model with Spatial Structure and Age of Infection

## TL;DR

This paper develops a reaction-diffusion epidemic model incorporating spatial structure and infection age, analyzing disease transmission dynamics between vectors and hosts with incubation periods.

## Contribution

It introduces a novel age-structured reaction-diffusion model for vector-host epidemics and studies its solution existence and long-term behavior.

## Key findings

- Existence of solutions established using operator semigroup methods.
- Asymptotic behavior of the epidemic model analyzed.
- Model captures complex transmission dynamics with incubation periods.

## Abstract

In this paper we study a diffusive age structured epidemic model with disease transmission between vector and host populations. The dynamics of the populations are described by reaction-diffusion equations, with infection age structure of the host population incorporated to account for incubation periods. The disease is transmitted between vector and host populations in crisscross fashion. The existence of solutions of the model is studied by operator semigroup methods, and the asymptotic behavior of the solution is investigated.