Between-group pathogen transmission: From processes to modeling

Pathogen transmission is a key process in epidemiology and its mathematical form plays a pivotal role when modeling pathogen spread. Much work has been devoted to the transmission function applied to a homogeneous population structure. However, between-group transmission functions, required when different groups are identified to account for a distinct epidemiological risk, are much less documented. The aim of this study is to detail the mathematical form of five between-group transmission functions and to assess its influence on predictions in epidemiological modeling. Simulations with a two-group model were carried out so as to generate prediction differences among between-group transmission functions for a large range of situations, defined by the within-group transmission pattern, the basic reproduction number, the proportion of the whole transmission due to between-group transmission and the ratio of population sizes. Pathogen spread simulations highlighted differences in prevalence among four transmission functions (frequency-dependent, density-dependent and functions representing either a temporary mixing or a proportion of visitors exposed to infectious individuals). The differences could be seen either in long-term or in transient simulated dynamics. The fifth one, representing limited interactions at a gate, was shown to be equivalent to the density-dependent function in our parametrization when keeping constant group sizes. When considering population dynamics, particularly with increasing group sizes, this function and the density-dependent one were shown to behave opposite from each other and to differ from the other functions. This work highlights the need to carefully define the between-group transmission function when modeling pathogen spread in a heterogeneous structure. Our work brings insight into the biological grounds that could guide the choice of such a function.