An immuno-eco-epidemiological model of competition.

Souvik Bhattacharya, Maia Martcheva
Author Information
  1. Souvik Bhattacharya: a Center for Pharmacometrics and Systems Pharmacology, Department of Pharmaceutics, College of Pharmacy , University of Florida , Orlando , FL , USA.
  2. Maia Martcheva: b Department of Mathematics , University of Florida , Gainesville , FL , USA.

Abstract

This paper introduces a novel immuno-eco-epidemiological model of competition in which one of the species is affected by a pathogen. The infected individuals from species one are structured by time-since-infection and the within-host dynamics of the pathogen and the immune response is also modelled. A novel feature of the model is the impact of the species two numbers on the ability of species one to mount an immune response. The within-host model has three equilibria: an extinction equilibrium, pathogen-only equilibrium and pathogen and immune response equilibrium which exists if the immune response reproduction number R0 > 1. The extinction equilibrium is always unstable, the pathogen-only equilibrium is stable if R0 < 1, and the coexistence equilibrium is stable whenever it exists. The between-host competition model has six equilibria: an extinction equilibrium, three disease-free equilibria: species one-only equilibrium, species two-only equilibrium and a disease-free species coexistence equilibrium. There are also two disease-present equilibria: species one-only disease equilibrium and disease coexistence equilibrium. The existence and stability of these equilibria are governed by six reproduction numbers. Results show that for a non-fatal disease, the disease coexistence equilibrium is stable whenever it exists.

Keywords

MeSH Term

Ecology
Epidemics
Humans
Immune System
Models, Biological

Word Cloud

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