Analytic semigroup generated by the dispersal process of a sylvatic transmission model of Chagas disease

TL;DR

This paper develops a novel mathematical model for Chagas disease transmission involving reaction-diffusion equations and operator theory, demonstrating that the dispersal process generates an analytic semigroup.

Contribution

It introduces a new biological transmission model with skew Brownian motion at habitat interfaces and proves the main operator generates an analytic semigroup.

Findings

The model captures sylvatic transmission dynamics.

The main operator generates an analytic semigroup.

The model uses reaction-diffusion equations with interface conditions.

Abstract

In this work, we develop a new biological transmission model for Chagas disease. This model, set in two juxtaposed habitats with skew Brownian motion conditions at the interface, is composed of two reaction--diffusion equations and takes into account the sylvatic transmission. We write it as an abstract perturbed Cauchy problem using operator theory. Then, we show that the main operator, which models the dispersal process, generates an analytic semigroup in an adequate Banach space.