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

The basic reproduction number ℛ(0) 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 ℛ(0) 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 ℛ(0) expressions, there is a unique type reproduction number when control strategies are applied to the host population. All ℛ(0) 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 ℛ(0) 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.