The spatial spread and final size of models for the deterministic host-vector epidemic

A disease is considered which is transferred between two populations, termed hosts and vectors. The disease is transmitted solely from infected vector to uninfected host and from infected host to uninfected vector. Two models are formulated in which infectious individuals are introduced at time t = 0 into the populations of susceptibles, thus triggering an epidemic through those populations. Conditions are established for a major epidemic to occur, and the final size of the epidemic is obtained for these models when no spatial aspect is considered. When a spatial aspect is included in the models, again the condition for a major epidemic is obtained. The pandemic theorem is proved rigorously, giving a lower bound for the proportion of each population, at each point, who eventually suffer the epidemic. The behavior a long way from the initial focus of infection is also rigorously obtained.