Stochastic dynamics of an epidemics with recurrent spillovers from an endemic reservoir

Marina Voinson; Alexandra Alvergne; Sylvain Billiard; Charline Smadi

To analyse the dynamics in the incidental host, three statistics will be studied The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/213579 doi: bioRxiv preprint Approximation by a branching process. The epidemiological model with recurrent introduction of the infection into an incidental host by a reservoir can be 135 approximated by a branching process with immigration from the reservoir to the incidental host at the beginning of the infectious process (thus assuming that individual "birth and death rates of infected individuals" are constant during the starting phase of an outbreak). The individual birth and death rates are respectively βS, the transmission rate and γ, the recovery rate and the 140 immigration rate corresponds to the spillover rate τ N at the beginning of the infection. In other words we assume that the number of susceptibles is N to study the beginning of the infection, which is a good approximation as long as few individuals have been infected. We distinguish between two regimes in the incidental host, the subcritical regime when R 0 < 1 and the supercritical regime 145 when R 0 > 1. We suppose that at time t = 0 a single individual is infected by the spillover transmission.