Invasion reproductive numbers for discrete-time models

Abstract

Although invasion reproductive numbers (IRNs) are utilized frequently in continuous-time models with multiple interacting pathogens, they are yet to be explored in discrete-time systems. Here, we extend the concept of IRNs to discrete-time models by showing how to calculate them for a set of two-pathogen SIS models with coinfection. In our exploration, we address how sequencing events impacts the basic reproductive number (BRN) and IRN. As an illustrative example, our models are applied to rhinovirus and respiratory syncytial virus co-circulation. Results show that while the BRN is unaffected by variations in the order of events, the IRN differs. Furthermore, our models predict copersistence of multiple pathogen strains under cross-immunity, which is atypical of analogous continuous-time models. This investigation shows that sequencing events has important consequences for the IRN and can drastically alter competition dynamics.

Decoding the double trouble: A mathematical modelling of co-infection dynamics of SARS-CoV-2 and influenza-like illness

“…Many diseases are endemic to certain regions around the globe and henceforth, giving rise to the cases of co-infection in the communities. Therefore, it becomes necessary to study invasion reproductive numbers (IRNs) ( Olawoyin and Kribs, 2019 , Nuño et al, 2007 , Britnee Crawford, 2009 ). It is defined as the number of secondary infections produced by an infected individual in a population where one or more other pathogens are endemic.…”