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Under natural assumptions a Feller type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, pos...
Abstract: We investigate the inhomogeneous Galton--Watson processes with immigration, where $\rho_n$ the offspring means in the $n^\textrm{th}$ generation tends to 1. We show that if the second deriva...
Guided by the relationship between the breadth- rst walk of a rooted tree and its sequence of generation sizes, we extend the Lamperti representation of continuous-state branching processes to allow i...
We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth inde...
Epidemics that are either introduced into a population or fuelled by immigrating infective individuals are subject to dynamics that must include infectiveness external to the population itself. Immig...
The immigration dynamics of infectives is sometimes an imprescindable modelling feature to fully understand and explain the diffusion of important infections. The inclusion of the dynamics of individu...

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