Extinction in host-vector infection models and the role of heterogeneity

For infections that become endemic in a population, the process may appear stable over a long time scale, but stochastic fluctuations can lead to eventual disease extinction. We consider the effects of model parameters and of population heterogeneities upon the expected time to extinction for host–vector disease systems. We find that non-homogeneous host selection by vectors increases persistence times relative to the homogeneous case, and that the effect becomes even more marked when there are strong associations between particular groups of vectors and hosts. Heterogeneity in vector lifespans, in contrast, is found to decrease persistence times relative to the homogeneous case. Neither the basic reproduction number R0, nor the endemic prevalence level in the corresponding deterministic model, is found to be sufficient to predict (for a given population size) time to extinction. The endemic level, in particular, proves a very unreliable guide to the duration of long-term persistence.