Biological consistency of an epidemic model with both vertical and horizontal transmissions

A system of nonlinear integro-differential equations is investigated. The model describes an age structured S.I.S system of a disease with horizontal and vertical transmission. Global well-posedness is proved in L1L1space. The method is based on the contraction fixed point theorem. We exhibit a closed subset of a Banach space, on which a certain mapping is a strict contraction.