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

Abstract

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.

Costs and benefits of group living with disease: a case study of pneumonia in bighorn lambs ( Ovis canadensis )

“…Seasonally variable host aggregation and disease incidence patterns are consistent with a shift between frequency-and density-dependent transmission of chronic wasting disease incidence in white tailed deer [44]. However, despite the growing empirical support for scale-dependent approaches to transmission function, transmission in a system is still usually assumed to follow the same process: it is either frequency-or density-dependent, regardless of the scale of observation (but see [45]). This assumption may hinder model development and disease management, especially for systems transitioning from spillover to endemic, or with long-lived infectious stages [46].…”

Ranavirus Ecology and Evolution: From Epidemiology to Extinction

“…One common example of density-independent transmission is sexually transmitted infections, but any form of aggregation (e.g., localized feeding or breeding sites) can maintain high rates of transmission, regardless of host density. Even brief periods of density-independent transmission (e.g., during breeding) can lead to pathogen-driven extinction (Ryder et al 2007 ). Third, pathogens that have biotic (other species) or abiotic (environmental) reservoirs will also continue to infect hosts irrespective of host densities, and so have the potential to cause host extinction.…”

Maternal effects in disease resistance: poor maternal environment increases offspring resistance to an insect virus

“…Given that immune defence is costly [41,42], we would expect natural selection to favour individuals that invest more when there is the greatest threat of disease. If transmission is positively density-dependent [43][44][45], the risk of infection may increase at high density, leading to the idea that it may be optimal to invest more in defence in crowded conditions [31,46,47]. There is experimental evidence of this 'density-dependent prophylaxis' (DDP) within a generation in a number of systems and further evidence from comparative studies of social and solitary species [31,[46][47][48][49][50].…”