Quantifying Transmission

ABSTRACT

Transmissibility is the defining characteristic of infectious diseases. Quantifying transmission matters for understanding infectious disease epidemiology and designing evidence-based disease control programs. Tracing individual transmission events can be achieved by epidemiological investigation coupled with pathogen typing or genome sequencing. Individual infectiousness can be estimated by measuring pathogen loads, but few studies have directly estimated the ability of infected hosts to transmit to uninfected hosts. Individuals’ opportunities to transmit infection are dependent on behavioral and other risk factors relevant given the transmission route of the pathogen concerned. Transmission at the population level can be quantified through knowledge of risk factors in the population or phylogeographic analysis of pathogen sequence data. Mathematical model-based approaches require estimation of the per capita transmission rate and basic reproduction number, obtained by fitting models to case data and/or analysis of pathogen sequence data. Heterogeneities in infectiousness, contact behavior, and susceptibility can have substantial effects on the epidemiology of an infectious disease, so estimates of only mean values may be insufficient. For some pathogens, super-shedders (infected individuals who are highly infectious) and super-spreaders (individuals with more opportunities to transmit infection) may be important. Future work on quantifying transmission should involve integrated analyses of multiple data sources.

View related correspondence here.

INTRODUCTION

Transmissibility is the defining attribute of infectious diseases, and it has profound consequences for their epidemiology. In contrast to noncommunicable diseases, the risk of an individual contracting an infectious disease increases with the number of infected and infectious individuals present in the population. This is positive feedback, and it makes the epidemiology of infectious diseases considerably more complex and often hard to understand intuitively. For example, reducing the per capita transmission rate is expected to decrease the size of an epidemic, but it is difficult to estimate by how much; because of the positive feedback, there is not a proportional (or linear) relationship between epidemic size and transmission rate. Less obvious still is the expectation that decreasing transmission rate may increase rather than decrease the duration of an outbreak (1).

A quantitative understanding of transmission is therefore central to infectious disease epidemiology and to evidence-based decisions on prevention and control strategies. Nonetheless, measuring transmission either retrospectively (estimating how many transmission events have occurred) or prospectively (estimating transmission risk) is often a formidable technical challenge. In this chapter, I review some of the various approaches used to quantify transmissibility at both the individual and population levels.

TRANSMISSION EVENTS

Retrospective investigation of transmission events is a well-established activity that contributes to standard public health procedures such as epidemiological tracing, outbreak investigation, and forensic epidemiology (2). These are usually empirical exercises based on knowledge of transmission routes, contact histories (i.e., transmission opportunities), epidemiological risk factors, and the so-called natural history of infection, which indicates the possible relative timings of key events such as exposure, the onset of infectiousness, and the onset of clinical signs (Fig. 1). These techniques are widely used for a range of infectious diseases such as measles (3) and foot-and-mouth disease (FMD) (4). Epidemiological data may be supplemented by pathogen typing data, preferably as detailed as possible to maximize the ability to discriminate between dissimilar strains in two or more hosts, thus ruling out a transmission event. The outputs of epidemiological tracing studies typically take the form of a (sometimes subjective) assessment of the likelihood that individual X infected individual Y.

FIGURE 1.

Time line of exposure, infectiousness, and clinical signs. Following exposure to infection, there is a period when the host is infected but not yet infectious—the latent period (yellow)—and a period when the host is infected but not yet showing clinical signs—the incubation period (yellow and orange). In this example, there is a (brief) period when the host is infectious but asymptomatic (orange), as occurs for infections such as influenza or FMD.

Much greater levels of confidence may be achieved where pathogen sequence data are available. The analysis of sequence data to establish transmission pathways—“who infected whom”—is known as forensic phylogenetics. Forensic phylogenetics takes advantage of the high nucleotide substitution rates in fast-evolving RNA viruses (of the order of 1 × 10⁻³ to 5 × 10⁻³ per site per year), making it possible to use sequences isolated from different individuals at different times in order to estimate time-resolved phylogenetic trees. Forensic phylogenetics has been used, for example, in suspected cases of HIV/AIDS transmission and can confirm or rule out transmission events with a high level of certainty (5).

INDIVIDUAL TRANSMISSIBILITY

Empirical studies of individual transmissibility can be considered under two subheadings: (i) infectiousness, i.e., the potential of an infected individual to infect others given the opportunity to do so; and (ii) opportunities to transmit, as determined by some measure of the behavior or other attributes of the infected individual relevant to a pathogen’s route of transmission.

Infectiousness may be most straightforwardly measured by quantifying pathogens exiting from the host body in feces (e.g., Escherichia coli bacteria counts in stool samples) or urine (e.g., egg counts for Schistosoma haematobium), as aerosols (e.g., influenza virus particles in droplets), or as the successful infection of vectors (e.g., tsetse vectors of trypanosomes). More indirect measures are also used (e.g., density of malaria gametocytes in host blood). Simple assays of viremia or bacteremia in the blood are the most widely used as measures of infectiousness, but these are less satisfactory if transmission is not via the blood (e.g., influenza virus).

The gold standard determination of infectiousness is experimental exposure of susceptible hosts to infected hosts, though this is far less frequently attempted, especially for natural hosts (e.g., humans, cattle, and pigs) as opposed to model systems. Importantly, such studies have the ability to distinguish between pathogen detection and sufficient levels of pathogen excretion to infect other hosts. For example, an experimental study of FMD virus (FMDV) transmission between cattle (6) suggested that the period for which infected cattle could infect in-contact cattle was substantially less than the period for which virus could be detected (often at very low levels) in the blood, and that cattle were typically infectious for only a short period before clinical signs appeared (Fig. 2). This has important implications for what are termed reactive control measures, i.e., implementing preventive measures once clinical disease is detected, since if clinical cases are detected and removed early enough, then transmission rates can be greatly reduced (6).

FIGURE 2.

Infectiousness of FMDV in experimental infections of cattle. Distribution of the incubation period minus the latent period, predicted using a Bayesian analysis, where a negative value indicates when clinical signs appear before an animal is infectious. The plot shows that when infectiousness is measured directly by the exposure of in-contact susceptible cattle, the analysis indicates that only a small fraction of infectiousness is found to occur before the appearance of clinical signs (black line). In contrast, if infectiousness is measured indirectly using virus isolation from blood (red) or nasal fluid (green), the bulk of infectiousness is estimated to occur well before clinical signs appear. Data from reference 6; figure kindly supplied by Simon Gubbins.

Estimating an individual’s opportunities to transmit infection requires information on behaviors associated with a risk of transmission. A straightforward example is commercial sex workers and the transmission of sexually transmitted infections. Identification of sex workers and their sexual contacts enables the provision of health interventions that would benefit the individuals concerned and also be beneficial in public health terms by reducing the risk of onward transmission.

More generally, contact tracing is a standard public health tool that can be used not only retrospectively (as described above) but also prospectively to identify at-risk individuals who have been exposed to an infected individual and might require preventive interventions (e.g., quarantine or vaccination) or therapy. Contact tracing is widely used during infectious disease outbreaks, such as the 2014–2015 ebolavirus epidemic in West Africa (7). This kind of approach is useful for pathogens transmitted by direct contact or close proximity of individuals (e.g., HIV or influenza) but usually not for those transmitted indirectly, such as via the fecal-oral route (e.g., cholera) or by vectors (e.g., malaria or Zika virus).

Factors affecting individual transmissibility (infectiousness and transmission opportunities) can, in principle, be investigated and their effects quantified using standard epidemiological risk analyses. However, in marked contrast to the vast number of empirical studies of risk factors for becoming infected (susceptibility and exposure), few studies of transmissibility of this kind have been published. There are some obvious reasons for this lack of attention. First, it is often much harder to establish that an individual has transmitted infection than that it has acquired infection. Second, the sample size available is not the total population but the infected population (each of whom may or may not have transmitted infection onwards), typically a much smaller number with a corresponding loss of statistical power to identify risk factors. Examples of quantitative analysis of the risk of onward transmission include farms infected with FMD (8) and E. coli O157 on cattle farms (9).

POPULATION-LEVEL TRANSMISSIBILITY

Contact tracing can, in principle, be scaled up from the individual to the population level if the distribution of the key risk factors across the population is known. An example is the reconstruction of transmission “trees” for the spread of FMD between livestock farms in the United Kingdom in 2001 based on the dates on which FMD was detected and the distances between farms, given that interfarm distance was known to be a major risk factor (10). Applied in real time, with the incorporation of information on additional risk factors where available, such methods enable estimation of the case reproduction number (the average number of cases generated per case) and therefore projections of epidemic trajectory (11). In general, population-level contact tracing is likely to be less accurate than individual-level contact tracing since many of the detailed risk factors, e.g., movement of people from one household to another or sexual contacts, are not knowable for the entire population. Even so, demographic and geographic variables may represent useful proxies for individual risk behaviors and thus be used to generate good approximations of transmission patterns at the population level.

In recent years, the availability of pathogen genome sequences coupled with advances in bioinformatics analysis have led to the increasing use of phylogeographic approaches to understanding transmission patterns at the population level. As an early example, phylogenetic analyses of FMDV genome sequence data from a subset of affected farms from the 2001 U.K. epidemic largely supported the results of contact tracing studies, but did suggest some revisions to those assessments (12). More recently, ebolavirus genome sequences from West Africa in 2014-15 were analyzed to obtain estimates of the case reproduction rate, infectious period, and sampling fraction, and provided important supporting data for projections of epidemic trajectory based on case reports (13).

A potentially powerful application of phylogeographic methods is to quantify the frequency with which a pathogen moves between populations, representing different locations, e.g., cities, or different host species. Given that only a fraction, often a very small fraction, of cases provide sequence data, these methods do not provide estimates of absolute rates of transmission but can show whether transmission has occurred and, in principle, indicate the relative importance of different routes. Examples include the transmission of the SAT2 topotype of FMDV between different ungulate species in Africa (14) and the transmission of the CC398 clade of methicillin-resistant Staphylococcus aureus between humans and livestock (15).

These two studies covered time spans of several decades; using sequence data to resolve epidemiological questions is challenging due to the short time scales, and therefore few nucleotide substitutions, involved. However, phylogeographic techniques have been used during epidemics, for example, to investigate the geographic origins and spread of H1N1 influenza A in 2009 (16). Similarly, this approach has been used to determine the source of outbreaks. For example, Middle East respiratory syndrome outbreaks tend to occur as genetically distant lineages persisting for only a few months each, suggesting multiple introductions from an animal reservoir with limited human-to-human transmission (17). In contrast, both the 2009 H1N1 influenza pandemic and 2014 West Africa ebolavirus disease epidemic consisted of single rapidly expanding lineages, suggesting single introductions followed by sustained human-to-human transmission.

A key parameter in interpreting sequence data is the time to most recent common ancestor (TMRCA) of the cases. From sequences obtained during an outbreak, however sparsely sampled, a TMRCA much longer ago than the first reported case suggests an unobserved epidemic, e.g., in a reservoir population, and multiple origins for the current outbreak. For outbreaks that spread entirely within the host population, the TMRCA of the sequenced cases will be closer to the date of the first infection (whether sampled or not) and provides an estimate of when the pathogen was introduced into that population.

MODELING

Mathematical models have been used in infectious disease epidemiology for more than 100 years (18). A key parameter in such models is the per capita transmission rate, often designated as β. β is a composite parameter, encompassing infectiousness, opportunities to transmit the infection, and susceptibility. It is also a component of the basic reproduction number, R₀, the average number of infections generated by a single infection introduced into a large population of previously unexposed hosts. The threshold R₀ > 1 is a condition for a large outbreak or epidemic to be possible.

Rapid and accurate estimation of β and R₀ are therefore extremely important for predicting the trajectory of an infectious disease outbreak. Neither parameter is likely to be known precisely in advance of an outbreak since they vary with the characteristics of the pathogen (e.g., strain differences) and the host population (demography, contact patterns, and risk behavior). Comparative assessments may be possible; e.g., for pathogens transmitted by direct contact, such as measles or influenza A, transmission rates may be higher in higher-density host populations. However, even for these kinds of pathogens the common assumption that β scales linearly with host density—so-called density-dependent transmission—may be overly simplistic, for example, in spatially structured populations (19). Often, quantitative estimates for a specific pathogen in a specific host population are only possible once an outbreak is occurring.

The standard approach to obtaining quantitative estimates of β and R₀ is to fit an appropriate epidemiological model to time series data on epidemic progression, usually based on clinical cases but sometimes on diagnosis of infection or of exposure (e.g., by serology). This exercise requires additional information on the generation time, i.e., the average interval between the time of infection of a host and onward transmission of infection by that host. It also requires accurate data, which may be problematic. For example, data collection was poor during the early stages of the West African ebolavirus epidemic, and the majority of H1N1 cases were subclinical and unreported during the 2009 pandemic. Model assumptions may also be critical, especially whether or not the host population can be regarded as homogeneous from the perspective of pathogen transmission (see next section).

Recently, methods have been developed for estimating population transmission rates using pathogen genome sequence data. These methods are based on estimates of changes in the effective population size of the pathogen over time. They were used for both the 2009 influenza A pandemic and the 2014–2015 ebolavirus epidemic (17) and were helpful in supporting or challenging estimates made using epidemiological data. In order to inform public health responses during an infectious disease outbreak, pathogen sequences need to be obtained and made available for analysis in real time. This has recently become technically feasible, and is likely to become a more widely used epidemiological tool for outbreak management (17). In the future, the most accurate estimates of transmission parameters, requiring the minimum of data, are likely to come from the integrated analysis of combinations of epidemiological and pathogen sequence data (20).

HETEROGENEITIES

Individual variation in infectiousness, contact behavior, and susceptibility can have consequences for infectious disease epidemiology at the population level (21, 22). These include potentially substantial effects on the likelihood that an outbreak will take off, the initial rate of growth, and the scale and duration of the outbreak. Such variation may also favor targeted intervention strategies that not only protect those most at risk of infection but also prevent the onward transmission of infection from those most likely to do so.

Heterogeneities in infectiousness may involve a phenomenon termed “super-shedding,” meaning that a small proportion of individuals are substantially more infectious than the median (23). Super-shedding has been reported for a number of different infections, including severe acute respiratory syndrome coronavirus, bovine tuberculosis, paratuberculosis, norovirus, and influenza (24). Super-shedding is particularly well characterized for E. coli O157 in cattle. E. coli O157 is fecally transmitted, and bacterial counts in feces demonstrate marked heterogeneities (Fig. 3A). The mechanism underlying super-shedding is known (23): super-shedding infections involve bacterial colonization at the rectal-anal junction—these infections are more productive and more persistent than transient infections of the gut lumen. Model-based studies have suggested that super-shedders are associated with much higher herd prevalences, and in the absence of super-shedding R₀ for E. coli O157 in cattle is <1 (25).

FIGURE 3.

Transmission heterogeneities. (A) Heterogeneous infectiousness. Frequency distribution of bacterial counts for E. coli O157 in cattle fecal samples (horizontal axis, log scale). Raw data (histogram) are compared with a fitted mixture distribution log normal model that identified two distributions (red lines) and their sum (green). Arrowheads indicate the mean for each distribution. Reproduced with permission from reference 23. (B) Heterogeneous contact rates. The graph shows the cumulative, fractional contribution to the value of R₀ of individuals arranged in order (highest to lowest along the horizontal axis) of their observed contact rates. For a range of infectious diseases (multiple examples covering HIV/AIDS, malaria, schistosomiasis, and leishmaniasis), 20% of the population contribute 80% of the basic reproduction number, R₀, as estimated given observed heterogeneities in contact behavior (sexual contacts, vector biting rates, water contact, as appropriate). Data from reference 21.

Heterogeneities in contact behavior may promote “super-spreading,” meaning that a small proportion of individuals have substantially more opportunities to infect other hosts than the median (23). Super-spreading is a property of individual hosts, whereas super-shedding is a property of individual infections, as determined by the host-pathogen interaction. Super-spreading has been widely reported for many different kinds of infection, particularly those transmitted sexually or by vectors (21), but may be less apparent for those transmitted by direct contact (22). For infectious diseases in the former category, e.g., HIV/AIDS, malaria, and schistosomiasis, a useful rule of thumb is that 20% of individuals are responsible for at least 80% of R₀, the so-called 20–80 rule (Fig. 3B).

Heterogeneities in host susceptibility to infection are commonly studied and are commonly found; note that here we are concerned only with heterogeneity in susceptibility to infection, not disease, since it is this that influences the population-level transmission rate. Heterogeneities in susceptibility may be due to multiple causes including host genetics, physiology, and immune status (19), but I do not review these in depth here.

Heterogeneities in infectiousness, contact behavior, and susceptibility clearly all have the potential to influence the ways in which a pathogen spreads through a host population. Often these heterogeneities are ignored in estimating transmission parameters; however, in some circumstances, estimation of R₀ requires knowledge of not only the mean but also the variance of the transmission rate (21). This situation arises when there is a correlation between the propensity of a host to infect and the propensity of a host to be infected. Often there will not be an a priori reason to suspect that a highly susceptible individual will also be highly infectious if infected (a super-shedder), although this is certainly conceivable, for example, with immune-compromised patients. However, for contact behavior there may be circumstances when a correlation is expected between behavior that increases onward transmission and behavior that increases exposure to infection. This is the case, for example, with sexually transmitted or vector-borne infections, although it is not necessarily so, for example, with fecal-oral transmission.

In circumstances in which the variance in transmission rate is high and there is a strong positive correlation between propensity to infect and propensity to be infected, transmission heterogeneities can have a very substantial impact on the absolute value of R₀ (21). A corollary is that the variance in transmission rates contributes more to the absolute value of R₀ than does the mean. Moreover, in addition to the second-order effects captured by the variance, there may be higher-order effects on R₀ captured only by the full matrix of rates of (direct or indirect) transmission between subsets of the population (26, 27).

One study of these effects concerned the potential for infectious disease transmission between cattle farms as a result of the movement of cattle between farms (28). Here, β was broken down into the number of farms per unit time from which cattle are moved onto a given farm, designated β₁, and the number of farms per unit time to which cattle are moved from a given farm, designated β₂ (so β = β₁β₂). R₀ is given by the expression

$$R_0\propto \frac{1}{N}{{\displaystyle \sum }}^{\text{}}{\beta }_1{\beta }_2=\overline{{\beta }_1}\overline{{\beta }_2}+\sigma ({\beta }_1)\sigma ({\beta }_2)r_{\beta 1\beta 2}$$

where σ(•) represents the standard deviation, r is the linear correlation coefficient, N is the number of farms, and the right-hand term represents the average of the cross-products over all farms. For cattle farms in the United Kingdom, β₁ and β₂ had high standard deviations but were not correlated, so there was little impact on the absolute value of R₀, although because of high variance in the value of the product β₁β₂ across farms, the population still followed the 20–80 rule (28).

In general, quantifying these effects requires estimation of the distribution of the components of transmission across individuals in the population and knowledge of the extent that transmission rates from and to subpopulations or individuals are correlated. This information is, in principle, relatively straightforward to collect where contact behaviors are observable, e.g., movements between locations, sexual contacts, or vector biting rates. There has also been progress in methodologies to observe patterns of proximity between individuals that are relevant to transmission by direct contact such as influenza (29). Another approach is to fit models explicitly incorporating transmission heterogeneities to outbreak data (22).

CONCLUDING REMARKS

Four aspects of infectious disease transmission have been reviewed here: tracing transmission events, phylogenetics, mathematical modeling, and heterogeneities in transmission rates. Each of these is an important topic in its own right, but I anticipate that the most significant future developments in quantifying transmissibility will involve integrating these components. This will require both the integration of data—case data, demographic and behavioral data, and pathogen sequence data—and methods for integrated data analysis. Some progress has already been made. There has been recent work on ways of analyzing sequence data using a framework based explicitly on epidemiological models (30). Estimates of the transmission chain from temporal sequence data can be improved by incorporating additional information on the date of onset of individual cases, duration of latent and infectious periods, and overall prevalence (31), and there has also been work on integrating sequence analysis with contact tracing (20). Although we still have some way to go before a truly integrated analysis of multiple data types is available as an epidemiological tool, this does look to be an achievable goal, and one which would be a powerful aid to understanding and controlling infectious disease outbreaks of all kinds.