This article overviews the dynamics of disease transmission in one-host–one-parasite systems. Transmission is the result of interacting host and pathogen processes, encapsulated with the environment in a ‘transmission triangle’. Multiple transmission modes and their epidemiological consequences are often not understood because the direct measurement of transmission is difficult. However, its different components can be analysed using nonlinear transmission functions, contact matrices and networks. A particular challenge is to develop such functions for spatially extended systems. This is illustrated for vector transmission where a ‘perception kernel’ approach is developed that incorporates vector behaviour in response to host spacing. A major challenge is understanding the relative merits of the large number of approaches to quantifying transmission. The evolution of transmission mode itself has been a rather neglected topic, but is important in the context of understanding disease emergence and genetic variation in pathogens. Disease impacts many biological processes such as community stability, the evolution of sex and speciation, yet the importance of different transmission modes in these processes is not understood. Broader approaches and ideas to disease transmission are important in the public health realm for combating newly emerging infections.
This article is part of the themed issue ‘Opening the black box: re-examining the ecology and evolution of parasite transmission’.
In this article, which is based on my opening talk as a ‘facilitator’ at the British Ecological Society retreat on Transmission in September 2015, I review some of the issues that I think are important when considering the subject of disease transmission. I was specifically asked to provide an overview of aspects of disease transmission that I find interesting, drawing on examples from my own experience, and ‘sowing the seeds’ for subsequent discussions. My focus was on one-host–one-parasite systems, with Jo Webster, the other facilitator, focusing on multispecies systems .
Transmissible diseases are caused by infectious agents, and an imperative of disease control is to determine and interrupt these routes of transmission to reduce pathogen fitness. In humans, this is the province of the public health community, while eliminating the pathogen once it enters the individual is the focus of the medical profession. However, focusing on cure eventually fails, because evolutionary processes nearly always trump pharmacological solutions; population level understanding is essential. There are often other reasons for studying transmission; in biological control and with live vaccines, the goal may be to increase transmission rather than decrease it. For an ecologist or evolutionary biologist, to focus on transmission is to allow that dispersal is as important a fitness component  as the oft-lauded life-history features of reproductive output and survival.
Transmission is more than dispersal and consists of pathogen presentation by the host (=departure), movement between infected and healthy hosts (=dispersal per se), and entry into the new host (=establishment; figure 1). There will always be debates about what to include in each of these steps and how to parse them into meaningful components, but recognizing the steps emphasizes that transmission is a function of both the host and the pathogen. Because the pathogen stands to gain from increased transmission, it is tempting to succumb to ‘adaptive’ thinking and put the onus of transmission ecology and evolution solely in the lap of the pathogen. However, if we parse the transmission process into pathogen presentation, dispersal and arrival, then it is clear that both the host and the pathogen have to be involved.
Most disease biologists are familiar with the famous ‘disease triangle’ of the three factors (host, pathogen and environment) that contribute to disease expression . While this triangle is a tautology (how could these factors not be essential!), it has been useful in emphasizing that if we ignore or are unable to measure one of the factors, then it is erroneous to ascribe the cause of the disease only to the measured factors ; ulcers were happily attributed to genetics and environment, in the absence of any conviction that Helicobacter pylori could be a causative infectious agent . Correspondingly, it is also possible to produce a ‘transmission triangle’ where now the process of transmission is a function of the pathogen, the host and the environment (figure 2). Because all hosts and pathogens necessarily consist of component genotypes, then clearly transmission itself can evolve, and hosts and pathogens can potentially co-evolve in the traits determining their transmission.
2. Multiplicity of transmission modes and routes
In considering transmission, the term ‘mode’ is best thought of as referring to the method that a pathogen uses to move among hosts, whereas the ‘route’ refers to the specific path taken, including the point of presentation of the infective stages, and their point of entry. Investigating the contribution of different modes and routes of transmission is not straightforward. While genomic markers may trace an infection to an individual, they cannot in and of themselves always identify how that infection was transmitted. There is a huge diversity of transmission processes that lead to different epidemiological outcomes, alter conditions for disease increase, and affect control policies . Furthermore, any particular host–pathogen interaction usually involves multiple modes and routes of transmission [7,8]. This raises additional challenges: how to characterize those pathways and how to assess their fitness and dynamical consequences either singly or in combination.
This complexity can be illustrated by our studies on the transmission process in a plant disease, anther smut, caused by the fungus Microbotryum infecting wild species mostly in the carnation family. Anther smut has become a model for studying disease dynamics in natural systems because of its large fitness effects (it completely sterilizes the host plant) and ease of experimental manipulation [9,10]. The fungal spores are produced in the anthers of a flower, and because it is transmitted by pollinators during sexual reproduction of the host (figure 3), it exhibits features in common with many other sexually transmitted diseases in animals [7,11]. The pollinators act as passive vectors, and spore deposition on flowers does not occur if pollinators are experimentally excluded. However, several studies have now shown that this may not be the main mode of transmission [12–14]. Instead, aerial transmission of spores falling on nearby plants may be as important. It is well known that seedlings and plants in the vegetative stage are susceptible to infection, and they are routinely inoculated by this route in the laboratory; experimental studies have also shown that non-flowering plants placed under diseased individuals can become diseased . As emphasized with the ‘transmission triangle’, the mode of transmission may be determined in large measure by the degree to which different stages and sites of entry into the host are susceptible to fungal spores rather than by any difference in the pathogen stage that is involved; obviously the environment, whether this be the density of plants or the composition of the pollinator community, will also play a role.
Anther smut spores also land on the soil, but infection via this environmental route has never been detected. However, there are other, poorly studied, transmission pathways in this system. For example, pollinators can carry spores to flowers of other species . When the spores germinate, they undergo meiosis and produce a yeast-like haploid stage that can multiply asexually in nectar, not only of conspecifics, but also of other species; flowers of these other species can therefore potentially act as asymptomatic carriers.
I am not sure that there is any great message here for other host–pathogen systems, other than to say that there is probably no disease for which all the modes and routes of transmission have been characterized, let alone quantified in terms of their contribution to disease spread; perhaps HIV comes closest. Certainly, even diseases that are quite host-specific may show multiple transmission modes and routes. Research into multiple transmission modes is important, because even minority routes may be critical for determining disease thresholds and dynamics [9,16].
3. Transmission dynamics
Even though transmission is a complex process, in simple models, it is often encapsulated using one parameter, β, the transmission coefficient (figure 1). We are reminded of Anderson and May's [17, p. 63] warning that ‘direct measurement of β is essentially impossible for most infections’. It is true that transmission is to all intents and purposes invisible: we cannot place a camera on every microorganism in every individual at every location and watch a virus or even tapeworm move between hosts. However, it is perhaps better to see Anderson and May's ‘impossible’ more as a challenge than a fact: the goal is to face this multifaceted complexity of transmission, and distil from it useful understanding that can be applied to diseases in nature, agriculture and humans .
One way of distilling the complexity of the transmission coefficient, β, is to consider how the per capita rate at which healthy individuals become infected F, or ‘the force of infection’, is a function of the number of susceptible and infected individuals, S and I, respectively. If F = βI, the force of infection increases linearly with number of contacts, and transmission is said to be ‘density-dependent’. The simplest alternative is to assume that transmission depends on the fraction of individuals that are diseased, in which case the force of infection, F = βI/(S + I), and transmission is said to be ‘frequency-dependent’ (table 1; ). The latter scenario is considered to be likely in sexually transmitted infections because the per-individual rate of sexual contacts does not usually increase as population density increases. Frequency-dependent transmission is also considered to occur in vector transmitted diseases, provided that vectors actively move further if their hosts are further apart . This is likely to be the case for flying vectors such as mosquitoes, but perhaps less likely for fleas or ticks. Another circumstance engendering frequency-dependent transmission would be if the population was subdivided into groups of similar size, regardless of overall population size, and within which most of the transmission occurred. Transmission functions may therefore subsume several transmission modes.
Frequency- versus density-dependent transmission predicts contrasting thresholds and dynamics, and such functions are useful for making predictions about disease spread and disease characteristics (table 1). For example, while in practice, the distinction may not be clear cut or may be scale dependent, the recognition of the differences between them has huge policy implications. If the transmission of a disease (such as a sexually transmitted infection) is indeed purely frequency dependent, then herd immunity is not operative, and can no longer be proposed as a tenable reason for policies of compulsory vaccination. A number of other transmission functions have been proposed which take into account decreasing per capita rates of contact with increasing density either with other hosts and vectors  or with environmentally transmitted infectious stages .
A particular challenge is to develop such functions for spatially extended systems. Individuals will likely have more contacts with their neighbours, and the spread of a disease will itself change the relative positions of susceptible and infectious individuals. For example, Best et al.  examined the dynamics that result from three different local transmission mechanisms: density-dependent, frequency-dependent and active host searching. They showed that when frequency-dependent transmission is local, extinction is less likely than when it is global. However, when hosts actively search for contacts, the conditions for population extinction approach those of global frequency-dependence.
Much effort has been put into estimating ‘vectorial capacity’, essentially a measure of rate of pathogen increase where vectors both take up and deliver infectious stages [23,24], but such a measure cannot be used to study vector transmission in a spatial context. A standard way to model and study spatial spread of disease is to estimate and use dispersal distributions (or kernels), which effectively show how transmission is expected to decline with distance . However, such kernels are inappropriate for modelling disease spread by actively flying vectors because they are likely to adjust their flight behaviour depending on the spacing among hosts, moving and searching further when hosts are further apart. It is difficult to observe individual vectors, especially over large distances and over substantial periods of time; even when they can be observed, their transmission efficiency is hard to estimate . I therefore developed a simple agent-based model capturing essential features of vector behaviour, and which can be applied to field data and used to predict disease dynamics in new spatial contexts. This model uses a ‘perception kernel’, rather than a fixed dispersal kernel, to model vector behaviour. For another approach that takes animal movement processes into account see Fofana & Hurford .
The model in its simplest form is as follows. The vector arrives at a point and ‘perceives’ the hosts around it; hosts further from the point of arrival are given less weight according to a simple power function, where the perceived density d = k∑(xi)−p, where k and p are constants, and xi is distance. Whether the vector remains or leaves is dependent on this perceived host density; the vector stays with probability 1 − exp (− d). The number of vector visits, v, can also be varied. If the vector stays then it moves to the host with a probability proportional to its contribution to perceived density, and the process is iterated. Using randomly generated spatial arrays at different densities, and parameter values close to those observed by fitting the model to field data, it can be shown that the relationship between population density and disease transmission (spore deposition in the case of anther smut) follows theoretical expectations [20,28] for a vector transmitted disease (figure 4), thus supporting the ‘perception model’ concept. At low densities, hosts are far apart and not found/perceived by the vector; at intermediate densities, pollinators adjust their flight distances to compensate for changes in host density, whereas at very high host densities the dilution effect becomes important such that the per host visitation rate again falls. All of this assumes that vector numerical dynamics is independent of host density.
In addition, the results show that measuring only vector movement from diseased to healthy individuals cannot accurately assess vector impacts, as many vectors simply do not visit hosts in areas of low density. As an example, when density was 0.1 hosts m−2 (average spacing 3.16 m), vectors visited hosts only 24.3% of the time, whereas when it was 2 m−2 (spacing 0.71 m) they visited 99.7% of the time. However, the difference in the overall dispersal distances was much less (mean: 1.56 versus 1.02, median: 0.82 versus 0.45, for 10 000 visits) even though there was an increase in the number of short distance visits at the higher density (figure 5). Importantly, this shows that observations of vector movement between extant hosts, in and of itself, does not provide a complete picture, because ‘non-contacts’ are invisible; thus, studies of the actual transmission process (pick-up, transport and deposition) and not just vector dispersal distances are required to understand spatial dynamics of vector transmission.
4. Heterogeneity in contact rates and the transmission process
Every contact is not the same. In a real-world situation, healthy individuals making multiple contacts with a diseased individual may already have become infected by an earlier contact; in that case the force of infection is best represented by F = 1 − (1 − δ)cI/N, or 1 minus the probability of not getting diseased after c contacts, where δ is the per contact infection probability. If contacts increase linearly with host density, with a proportionality constant k, i.e. c = kN, then F reduces to 1 − (1 − δ)kI. This immediately introduces a nonlinearity in the transmission function. If δ is small, this can be further approximated by 1 − exp (− lβ'), where now β' = δk. The beta in this function can be termed the ‘exponential transmission coefficient’  and is more appropriate for difference equation models where there are multiple contacts (cf. the Nicholson–Bailey model of host–parasitoid interactions ).
Nonlinearities arise in many other ways. It has long been appreciated that there is often extreme heterogeneity in the contribution of different individuals to disease spread [17,30]. A major challenge in the field of disease epidemiology is to decide on an approach for assessing transmission while accounting for heterogeneity in contact rates among individuals; these can arise from differences in age, spatial position, genetics, or social position. Several types of approaches have been used, and their merits may depend on the specific disease and the question being asked. One approach is to take simple measures of the heterogeneity and re-calibrate the transmission parameter accordingly. For example, Anderson & May [17, p. 233] showed that in sexually transmitted diseases with individual variation in the number of partners, the ‘effective contact rate’ for a population was equal to the mean plus the coefficient of variation in the number of partners. This has led to a focus on the importance of super-spreaders and mechanisms of identifying them to increase the efficacy of disease control . Another approach is to use ‘contact matrices’ which assign contact rates between different subpopulations (social classes, sexes, ages), and whose implementation into models (analytically or by simulation) can be used to predict disease dynamics .
Contact matrices can also be presented as networks where each element in the matrix is a function or quantity describing the properties of the ‘edge’, or line representing the connections between the ‘nodes’ (i.e. the row–column identities); depending on the situation, the nodes can be individuals or groups, such as social categories or cities, characterized by their interactions or distances from other groups. The edges can be differentially weighted to take into account host behaviour, directional transmission, distance and other factors affecting the interactions between each pair of nodes. For example, in anther smut disease, the spatial arrangement of plants can be represented as a network, with lines representing all possible combinations, nearest neighbour combinations or some intermediate level of connectedness . The application of network theory to epidemiology is a rapidly developing field [34–36]. Most of the focus of this approach has been on human diseases where social contact patterns are often known or can be inferred from airline schedules, phone calls, proximity sensors  or even (in the case of Hanta virus) from the sales statistics for mouse traps (Kurt Vandegrift 2016, personal communication).
There have been some notable insights from this approach, as for example in predicting efficient vaccination strategies especially where vaccine supply may be limited [38,39]. Directed networks (where transmission is asymmetrical depending on the characteristics of the individuals involved in the contact) were also useful for predicting the impact on healthcare workers of control of hospital infections .
I see the major challenge here as integrating these different approaches to contact structures and assessing their relative merits. It is difficult to evaluate any one such model against another especially with regard to what could be termed ‘eco-statistical reality’; detailed models that break processes into their many component parts may actually be worse at prediction than more phenomenological approaches that allow for better estimation of fewer parameters [41,42]. Network approaches are more reductionist, but are they always therefore better, especially when judged against alternatives and especially in situations where the connectedness measures themselves are subject to error? It is also a question of deciding what predictions one wants to make: for example, a mean field model may be reasonably adequate at predicting changes in overall disease prevalence, but it cannot predict the likelihood that a particular individual will get infected in relation to its connectedness to other individuals in the population.
5. Evolution of transmission mode
Evolutionary studies related to transmission mode have largely focused on the consequences of transmission modes for the evolution of virulence [43–45] and evolution of disease characteristics [8,46] rather than on the evolution of transmission mode itself. However, except in the case of transitions between horizontal and vertical transmission [9,47] and transitions between sexual and non-sexual transmission , the study of the evolution of different horizontal transmission modes is a surprisingly neglected topic .
There has also been very little work examining what factors select for particular transmission modes. Theoretical studies on the evolution of sexual transmission [50,51] confirmed that low-density populations should favour sexual transmission; here, evolution of transmission was under ‘pathogen control’ (i.e. genetic variation in the pathogen affected transmission mode), but I know of no studies of evolution of transmission mode when it is under ‘host control’. For example, transmission mode may evolve by selection on genetic variation in host resistance to pathogen entry at different sites or at different ages. In addition, there has been no examination of selection on transmission mode in a spatial context, even though spatial extensions of evolutionary models show that spatial structure greatly affects the evolution of infectivity and virulence [52,53].
Concern about the emergence of ‘new’ diseases has focused on pathogen transmission from wildlife reservoirs or increases in their virulence [54,55] but changes in transmission mode may be equally important in driving disease emergence. For example, dourine in domesticated horses is caused by a trypanosome that has shifted from vector to sexual transmission . HIV is another potential example, even though the transmission mode of simian immunodeficiency virus in primates remains uncertain . However, it is not known whether such emergence resulted from altered contact structure (suggested for early spread of HIV ) or was contingent on the presence of pathogen genetic variants.
Multiple modes of transmission also present a challenge. Are multiple modes directly adaptive to the pathogen, or are some routes dead-ends (e.g. maternal transmission of HIV)? How are different routes of transmission affected by host or pathogen genotype, and can different transmission routes in one population be the result of genetic variants each with their own singular dynamics and virulence? Do such genetic variants ‘presage’ an evolutionary shift to an alternative mode? These and other questions are more fully addressed in the article on evolution of transmission mode in this special issue .
6. The disease and non-disease consequences of transmission mode
As mentioned above, there has been substantial research on the adaptations of both hosts and pathogens to different transmission modes. For example, the co-transmission ‘interests’ of genes and endosymbionts should be expected to lead to a low virulence of vertically transmitted pathogens; and parasite manipulation of the behaviour and appearance of their intermediate hosts is readily interpretable as an adaptation of the pathogen to increase its trophic transmission to definitive hosts . In this context, it is often difficult to distinguish features that are ‘adaptive’ (i.e. the product of natural selection for traits increasing fitness) from traits that promote persistence in a community and determine ‘assembly rules’ [60–63]. Thus, in the case of sexually transmitted diseases, sterility has been interpreted as a pathogen trait that has evolved to increase opportunities for transmission by preventing pregnancy and encouraging repeated mating . Similarly, the low virulence of such diseases could be interpreted as a pathogen trait that allows repeated mating over successive seasons. However, an analysis of a suite of population dynamics models  showed that in sexually transmitted diseases, host and pathogen coexistence is also more likely if the pathogen is sterilizing and causes low mortality; sexually transmitted pathogens causing only mortality would simply be less likely to stably persist with their hosts. Distinguishing ‘assembly rules’ from adaptations is important in understanding disease emergence.
A subject that I think has received little attention is how transmission mode, as distinct from disease per se, may impact on the multiplicity of ecological and evolutionary processes affected by pathogens and parasites. These processes include aspects such as maintenance of community diversity , the evolution of sex  or mating systems , and speciation . Pathogen risk has also been implemented in determining traits such as sleep  and sexual dimorphism . The usual presumption, in both verbal and theoretical arguments, has been that the pathogen is directly transmitted in a density-dependent manner and the disease causes mortality. A question rarely raised in all these discussions is what happens if such ‘canonical’ assumptions are relaxed: does transmission mode matter to the generalizations that emerge, or is it irrelevant? It has been shown  that arguments about the evolution of sex hinge critically on epidemiological feedbacks and virulence, features also likely to be affected by transmission mode. Are some transmission modes more likely than others to result in genetic isolation and speciation (of the host and/or the pathogen)? If transmission is age specific, do different transmission modes lead to different host and pathogen life histories? Do our ideas about disease and the evolution of sex need to take transmission mode into account? How do different transmission modes likely affect the genetic structure of host and pathogen populations? There are many questions of this kind.
The investigation of pathways and mechanisms of transmission is a major undertaking in the public health realm, and takes on especial urgency in the case of newly emerging infections. As with the discovery of the Ebola virus in seminal fluid of ‘cured’ patients , new potential routes of transmission bring new concerns. In the more academic realm of disease ecology and evolution, transmission has been rather ‘taken for granted’ perhaps, because in ecological and evolutionary thinking, dispersal as a fitness trait has played second fiddle to death and reproduction. I have argued here that there are still major areas where both theoretical and empirical studies of transmission mode are needed, and many problems wait to be resolved. This article has only illustrated some of these, and then with a bias towards my own experiences and interests. Many others are illustrated in the series of papers that follow.
This work involved no human subjects.
No unpublished data are presented.
I have no competing interests.
NSF grant no. DEB1115895 and NIH R01GM122061.
I thank Mike Boots, Emme Bruns and Michael Hood for extensive discussions that contributed to the ideas presented here.
One contribution of 16 to a theme issue ‘Opening the black box: re-examining the ecology and evolution of parasite transmission’.
- Accepted August 25, 2016.
- © 2017 The Author(s)
Published by the Royal Society. All rights reserved.