Host-parasite population dynamics under combined frequency- and density-dependent transmission

Many host-parasite models assume that transmission increases linearly with host population density ('density-dependent transmission'), but various alternative transmission functions have been proposed in an effort to capture the complexity of real biological systems. The most common alternative (usually applied to sexually transmitted parasites) assumes instead that the rate at which hosts contact one another is independent of population density, leading to 'frequency-dependent' transmission. This straight-forward distinction generates fundamentally different dynamics (e.g. deterministic, parasite-driven extinction with frequency- but not density-dependence). Here, we consider the situation where transmission occurs through two different types of contact, one of which is density-dependent (e.g. social contacts), the other density-independent (e.g. sexual contacts). Drawing on a range of biological examples, we propose that this type of contact structure may be widespread in natural populations. When our model is characterized mainly by density-dependent transmission, we find that allowing even small amounts of transmission to occur through density-independent contacts leads to the possibility of deterministic, parasite-driven extinction (and lowers the threshold for parasite persistence). Contrastingly, allowing some density-dependent transmission to occur in a model characterized mainly by density-independent contacts (i.e. by frequency-dependent transmission) does not affect the extinction threshold, but does increase the likelihood of parasite persistence. The idea that directly transmitted parasites exploit different types of host contact is not new, but here we show that the impact on dynamics can be fundamental even in the simplest cases. For example, in systems where density-dependent transmission is normally assumed de facto, we show that parasite-driven extinction can occur if a small amount of transmission occurs through density-independent contacts. Many empirical studies are still guided by the traditional density/frequency dichotomy, but our combined transmission function may provide a better model for systems in which both types of transmission occur.