Abstract
An autonomous semi-linear hyperbolic pde system for the proliferation of bacteria within a heterogeneous population of animals is presented and analysed. It is assumed that bacteria grow inside the intestines and that they can be either attached to the epithelial wall or as free particles in the lumen. A condition involving ecological parameters is given, which can be used to decide the existence of endemic equilibria as well as local stability properties of the non-endemic one. Some implications on phage therapy are addressed.
Highlights
Most enteropathogenic microorganisms such as Salmonella, enterotoxigenic Escherichia, Yersinia or protozoans within the Giarda genus have the potential to infect a broad spectrum of animals, including humans and livestock
Reinfection phenomena of enteropathogens may have a critical role in epidemic outbreaks
In the present paper we have followed the ideas in [3] to show how the structure of the host population determines the proliferation of bacteria within the ecosystem
Summary
Most enteropathogenic microorganisms such as Salmonella, enterotoxigenic Escherichia, Yersinia or protozoans within the Giarda genus have the potential to infect a broad spectrum of animals, including humans and livestock. The aim of applying rigorously mathematical tools such as the linear stability principle lead us to make use of the so-called sun-dual formulation developed in [8] and [9] (see [11] for an application of the theory to population dynamics and [16] where it is used to treat a non-linear hyperbolic system similar to ours) Another important difference with respect to Boldin paper is that our framework makes possible to consider the spread of bacteria trough an heterogeneous group of hosts, while the model in [3] assumes an isolated animal.
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