Abstract
A model is considered for a spatially distributed population of male and female individuals that mate and reproduce only once in their life during a very short reproductive season. Between birth and mating, females and males move by diffusion on a bounded domain \(\Omega \) under Dirichlet boundary conditions. Mating and reproduction are described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number \({\mathcal {R}}_0\) that acts as a threshold between extinction and persistence. If \({\mathcal {R}}_0 1\). \({\mathcal {R}}_0\) is the cone spectral radius of a bounded homogeneous map.
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