Stochasticity and heterogeneity in host-vector models

Demographic stochasticity and heterogeneity in transmission of infection can affect the dynamics of host-vector disease systems in important ways. We discuss the use of analytic techniques to assess the impact of demographic stochasticity in both well-mixed and heterogeneous settings. Disease invasion probabilities can be calculated using branching process methodology. We review the use of this theory for host-vector infections and examine its use in the face of heterogeneous transmission. Situations in which there is a marked asymmetry in transmission between host and vector are seen to be of particular interest. For endemic infections, stochasticity leads to variation in prevalence about the endemic level. If these fluctuations are large enough, disease extinction can occur via endemic fade-out. We develop moment equations that quantify the impact of stochasticity, providing insight into the likelihood of stochastic extinction. We frame our discussion in terms of the simple Ross malaria model, but discuss extensions to more realistic host-vector models.