Influence of the transmission function on a simulated pathogen spread within a population.

The mathematical function for the horizontal transmission of a pathogen is a driving force of epidemiological models. This paper aims at studying the influence of different transmission functions on a simulated pathogen spread. These functions were chosen in the literature and their biological relevance is discussed. A theoretical SIR (Susceptible-Infectious-Recovered) model was used to study the effect of the function used on simulated results. With a constant total population size, different equilibrium values for the number of infectious (NI) were reached, depending on the transmission function used. With an increasing population size, the transmission functions could be assimilated to either density-dependent (DD), where an equilibrium was obtained, or frequency-dependent (FD), with an exponential increase in NI. An analytical study corroborated the simulated results. As a conclusion, the choice between the different transmission functions, particularly between DD and FD, must be carefully considered for a varying population size.