Illustration of some limits of the Markov assumption for transition between groups in models of spread of an infectious pathogen in a structured herd

In epidemic models concerning a structured population, sojourn times in a group are usually described by an exponential distribution. For livestock populations, realistic distributions may be preferred for group changes (e.g. depending on sojourn time). We illustrated the effect on pathogen spread of the use of an exponential distribution, instead of the true distribution of the transition time, between groups for a population separated into two groups (youngstock, adults) when this true distribution is a triangular one. Concerning the epidemic process, two assumptions were defined: one type of excreting animal (SIR model), and two types of excreting animals (transiently or persistently infected animals). The study was conducted with two indirect-transmission levels between groups. Among the adults, the epidemic size and the last infection time were significantly different. For persistence, epidemic sizes (in the entire population and in youngstock) and first infection time, results varied according to models (excretion assumption, indirect-transmission level).