  In the stochastic network model of Britton and Lindholm [Dynamic random
networks in dynamic populations. Journal of Statistical Physics, 2010], the
number of individuals evolves according to a supercritical linear birth and
death process, and a random social index is assigned to each individual at
birth, which controls the rate at which connections to other individuals are
created. We derive a rate for the convergence of the degree distribution in
this model towards the mixed Poisson distribution determined by Britton and
Lindholm based on heuristic arguments. In order to do so, we deduce the degree
distribution at finite time and derive an approximation result for mixed
Poisson distributions to compute an upper bound for the total variation
distance to the asymptotic degree distribution.
