D. G. Kendall, On the generalised birth-and-death process, Ann. Math. Statist, vol.19, pp.1-15, 1948.

N. Bacaër, Approximation of the basic reproduction number R 0 for vectorborne diseases with a periodic vector population, Bull. Math. Biol, vol.69, pp.1067-1091, 2007.

N. Bacaër and E. H. Dads, On the probability of extinction in a periodic environment, J. Math. Biol, vol.68, pp.533-548, 2014.

. Ph and . Carmona, Pathogen emergence in seasonal environments, Montpellier, 2019.

F. W. Olver, Asymptotics and Special Functions, 1974.