title: A two-type population epidemic problem.
abstract: We consider a two-type population such that the birth rate of the second type depends on the size of the population of the first type. This problem was formulated by Kendall (1949) and Goodman (1953), then solved for constant parameters by Tapaswi & Roychoudhury (1984) and Gani & Tin (1984) (where the first type was female, and the second type, male). We generalize the known results to cases where the parameters are time dependent. Analytic expressions for the first two moments are found. For constant parameters, we derive the asymptotic law for the process.
authors.affiliation: Laboratoire de statistique medicale, Université de Paris V, France.
authors.forename: R
authors.initials: R
authors.lastname: Lounes
mesh_terms: D004813:Epidemiology; D006801:Humans; D015233:Models, Statistical; D011156:Population Density; D011336:Probability