A Minimal Model Coupling Communicable and Non-Communicable Diseases

¹ Universidad de Alcalá, Departamento de Física y Matemáticas. Member of the research group Nonlinear Dynamics and Complex Systems. Alcalá de Henares 28807, Spain
² Dipartimento di Matematica “Giuseppe Peano”. Member of the INdAM research group GNCS. Univertitá di Torino, Torino, Italy

^* Corresponding author: marcos.marva@uah.es

Received: 28 June 2022
Accepted: 27 July 2023

Abstract

This work presents a model combining the simplest communicable and non-communicable disease models. The latter is, by far, the leading cause of sickness and death in the World, and introduces basal heterogeneity in populations where communicable diseases evolve. The model can be interpreted as a risk-structured model, another way of accounting for population heterogeneity. Our results show that considering the non-communicable disease (in the end, a dynamic heterogeneous population) allows the communicable disease to become endemic even if the basic reproduction number is less than 1. This feature is known as subcritical bifurcation. Furthermore, ignoring the non-communicable disease dynamics results in overestimating the basic reproduction number and, thus, giving wrong information about the actual number of infected individuals. We calculate sensitivity indices and derive interesting epidemic-control information.