Reproduction numbers for infections with free-living pathogens growing in the environment

TLDR

The next generation matrix (NGM) method for computing the basic reproduction number ℛ0 can yield different expressions depending on how disease compartment interactions are interpreted. The study uses a susceptible–infectious–recovered–susceptible model with a free‑living pathogen to show that although different environmental roles produce distinct ℛ0 expressions, a unique type reproduction number exists under host‑population control strategies, thereby illustrating the strengths and limits of ℛ0 for quantifying control effects. While all ℛ0 expressions share the threshold value of one and similar magnitude, empirical estimates for salmonellosis and cholera differ markedly, underscoring the variability of ℛ0 across contexts.

Abstract

The basic reproduction number ℛ0 for a compartmental disease model is often calculated by the next generation matrix (NGM) approach. When the interactions within and between disease compartments are interpreted differently, the NGM approach may lead to different ℛ0 expressions. This is demonstrated by considering a susceptible–infectious–recovered–susceptible model with free-living pathogen (FLP) growing in the environment. Although the environment could play different roles in the disease transmission process, leading to different ℛ0 expressions, there is a unique type reproduction number when control strategies are applied to the host population. All ℛ0 expressions agree on the threshold value 1 and preserve their order of magnitude. However, using data for salmonellosis and cholera, it is shown that the estimated ℛ0 values are substantially different. This study highlights the utility and limitations of reproduction numbers to accurately quantify the effects of control strategies for infections with FLPs growing in the environment.