AbstractDisease transmission in animal populations can be affected by density or by frequency of contacts between individuals, although many models assume linear density-dependent transmission. We used rabies and free-roaming dogs (Canis familiaris) in two Nepalese cities as a model system to explore the impact of linear and non-linear density-dependent disease transmission on disease elimination achieved through rabies vaccination or vaccination and sterilisation. Strongly non-linear transmission approximated realistic frequency dependent transmission. Free roaming dogs, abundant in many parts of the developing world, are responsible for most cases of rabies transmission to humans. Most models of rabies transmission assume that the disease transmission rate is linearly density-dependent, although a recent empirical study did not find evidence to support this assumption. Rabies vaccination, culling and dog sterilisation are employed to eliminate rabies or to reduce the numbers of human cases. We created a continuous-time deterministic compartmental model to describe rabies epidemiology within a dog population and to analyse the two modes of transmission. Under each transmission mode, we investigated the efficacy of dog vaccination and fertility control to eliminate rabies. To investigate the effect of dog density on disease control efforts, models were run for cities with high and low dog population densities using data from the Nepalese cities. The results showed that, at low population density, the amount of control effort required for disease elimination did not differ substantially between different transmission modes. At high population density, the effort required to achieve disease elimination was only higher for linear density-dependent than for non-linear transmission due to the exact value of the transmission rate, beta. The model suggests that although disease transmission mode may alter the impact of control on rabies elimination, this impact is relatively small and probably not relevant to disease management.
Recovering the non-linear density field from the galaxy distribution with a Poisson-lognormal filter
