"A Two-Patch Epidemic Model with Nonlinear Relapse"

Another of my papers came out in final form today. Here are some details.

Title: A Two-Patch Epidemic Model with Nonlinear Relapse

Authors: Juan G. Calvo, Alberto Hernández, Mason A. Porter, and Fabio Sanchez

Abstract (English version): The propagation of infectious diseases and its impact on individuals play a major role in disease dynamics, and it is important to incorporate population heterogeneity into efforts to study diseases. As a simplistic but illustrative example, we examine interactions between urban and rural populations on the dynamics of disease spreading. Using a compartmental framework of susceptible–infected–susceptible (SIŜ) dynamics with some level of immunity, we formulate a model that allows nonlinear reinfection. We investigate the effects of population movement in a simple scenario: a case with two patches, which allows us to model population movement between urban and rural areas. To study the dynamics of the system, we compute a basic reproduction number for each population (urban and rural). We also compute steady states, determine the local stability of the disease-free steady state, and identify conditions for the existence of endemic steady states. From our analysis and computational experiments, we illustrate that population movement plays an important role in disease dynamics. In some cases, it can be rather beneficial, as it can enlarge the region of stability of a disease-free steady state.

Note: The published paper also has a Spanish version of the abstract.