Show Summary Details

p. 112. Transmission at different scalesfree

  • Marta L. Wayne
  •  and Benjamin M. Bolker


The term ‘transmission’ defines infectious disease. Respiratory viruses such as influenza are airborne; diseases such as HIV and hepatitis are transmitted through direct, usually sexual, exchange of bodily fluids; water-borne diseases such as cholera can survive in the environment; and vector-borne pathogens have evolved to use other organisms, especially blood-sucking insects and mites, to travel from one host to another. ‘Transmission at different scales’ considers the filters for encounter and compatibility, mathematical modelling of epidemic dynamics, and the key factors of virulence, resistance, and tolerance.

Transmission defines infectious disease. Transmission occurs when someone passes a disease to someone else: technically speaking, when a pathogen that was established in one host organism’s body succeeds in moving into another host’s body and establishing itself there.

Transmission occurs in a huge variety of ways. For example, in transmission of influenza (a respiratory disease), virus particles produced by the cells in an infected person’s lungs would first be coughed or sneezed into the surrounding atmosphere. The infectious particles can survive briefly in the air or on surfaces in the environment, and thus be directly transmitted from person to person with minimal contact. The receiving person could either inhale them directly, or could pick them up by touching a surface shortly after virus-containing droplets landed there. The receiver would then transfer virus particles to their nose by touching their face; from there, the natural movement of air within their nose would move the virus into their respiratory tract. In the respiratory tract, the virus particles would enter vulnerable cells and resume their cycle of spreading from one cell to another within the host’s body.

Many viruses, including influenza and diarrhoea-causing viruses such as rotavirus, can survive for days in the environment, p. 12building up on particular kinds of objects known as fomites. Have you noticed a sudden increase in male physicians sporting bow ties? This fashion statement is a response to health researchers’ identification of standard ties as fomites. Influenza viruses can even survive for several days on banknotes, especially if they are first mixed with ‘nasopharyngeal secretions’ (snot), although we don’t actually know whether this transmission pathway is important in real epidemics.

Pathogens whose infectious particles die almost instantaneously outside the warm, wet environment of the human body often rely on bodily fluids being directly transferred from person to person, as in the case of sexually transmitted diseases such as HIV (see Chapter 4) and gonorrhoea. While sexual contact was the most common form of fluid exchange throughout most of human evolutionary history, these pathogens can also be transmitted by more modern modes of fluid exchange such as blood transfusions or the sharing of syringes by drug users.

Other pathogens that cannot survive in the environment have evolved to use other organisms, especially blood-sucking insects and mites, as vectors to travel from one host to another. This strategy requires considerably more biological machinery than direct transfer between the bodies of two hosts of the same species. In the extreme case of pathogens with complex life cycles such as malaria (see Chapter 6), the pathogen goes through major transformations within the body of the mosquito vector. In fact, from the perspective of a mosquito-inhabiting malaria parasite, a human is just a convenient way to transmit itself to another mosquito.

Other infectious diseases can persist much better outside of the hosts’ bodies. Diseases such as cholera (see Chapter 5), typhoid, and Legionnaires’ disease can survive in water, making their way from one host to another through drinking water or air conditioning systems. Anthrax—which kills its hosts quickly, p. 13reducing the potential for direct transmission from one animal host to another—produces long-lasting spores that survive for years in the environment, infecting grazing animals years later when they ingest spores attached to soil particles. Many fungi, such as certain species of Aspergillus, live primarily as free-living organisms, but can sometimes grow within human hosts if they find themselves there, especially if the host has its immune system weakened by stress or infection with other diseases. (These are called opportunistic infectious diseases, in contrast to the obligate dependence of most pathogens. Opportunistic infections can live in a host if one is available, but do not require a host in order to complete their life cycles.) The amphibian fungus Batrachochytrium dendrobatidis (Chapter 7) is closely related to non-pathogenic soil-dwelling fungi, but is itself an obligate parasite—as far as we know it can only persist in the environment for a few weeks.

  • Top of page

Filters for encounter and compatibility

Following the work of Claude Combes, we can break the process of transmission down into three stages: (1) transfer of infectious particles from inside the original host’s body to the environment; (2) transfer of infectious particles through the environment, or through the bodies of intermediary vectors or hosts, to the receiving host; (3) transfer of particles from the environment into parts of the receiving host’s body such as the blood, lungs, or liver where the pathogen can reproduce. These three stages collectively comprise the encounter filter.

Having made it into a new host’s body, the travelling pathogen must overcome physical, biochemical, and immunological barriers in order to grow in the body of the new host. In other words, even if the pathogen can pass the encounter filter, it must also be biologically compatible with the new host; this final stage is called the compatibility filter. A host could close its compatibility filter by having a disease-resistant genetic mutation, such as the p. 14sickle-cell variant of the haemoglobin gene that protects against malaria. Opportunistic fungal infections are usually blocked as long as the host has a properly functioning immune system. In order to block most viral diseases, however, the host’s immune system needs to have encountered the pathogen before, either naturally or through vaccination.

Both the encounter and compatibility filters must be open in order for successful transmission to occur. Public health measures can close the encounter filter and are especially important in the early stages of an epidemic. Drugs or vaccines can close the compatibility filter, but they are not always available.

Methods for closing the encounter filter include simple preventive strategies such as quarantine (see Chapter 1). They also include environmental strategies such as improved sanitation to control water-borne disease, or mosquito and tick control to stop vector-borne disease. Another class of strategies tries to convince people to modify their behaviour. These include the US Centers for Disease Control and Prevention’s advice to ‘Cover Your Cough’ to stop influenza, as well as their suggestions for avoiding mosquito-borne diseases such as West Nile virus: stay indoors at dusk, wear long pants and long-sleeved shirts, and use insect repellent. Though changing people’s behaviour is difficult, it is usually the cheapest way to control disease. You don’t need to inject or swallow substances that may have harmful side effects, and behavioural changes can even protect against unknown pathogens. Avoiding exchanging bodily fluids with strangers is a good idea, even if they have been screened for all currently known diseases.

  • Top of page

Epidemic dynamics

It’s easy to understand the encounter and compatibility filters at the individual level: if you can prevent the transfer of infectious particles from the environment into your body, or if you immunize p. 15yourself to prevent the infection from taking hold in your body, you can stay safe. In order to understand the effects of these filters at the population level—for example, to decide whether an immunization programme or a quarantine will stop an epidemic—we need mathematical models. Almost as soon as biologists began to understand the mechanics of disease transmission, mathematicians started to develop models to describe the effects of the encounter and compatibility filters at the population level. As early as 1760, Daniel Bernoulli, a member of an eminent Swiss family of mathematicians and scientists, used a mathematical model to describe to what extent smallpox immunization (i.e. closing the compatibility filter for some individuals) could improve public health. Bernoulli concluded that immunization could increase the expected lifespan at birth by 10 per cent, from about twenty-seven to thirty years (the expected lifespan at birth was very short in the 18th century because of the high rate of infant and childhood mortality).

Bernoulli’s model only took into account the direct benefits of immunization, thus missing the key insight of herd immunity. Immunization protects the people who are immunized, but it also reduces the prevalence of the disease and thus provides an indirect benefit to non-immunized people. To eradicate disease, you don’t need to close the compatibility and encounter filters entirely (i.e. immunize 100 per cent of the people, or prevent transmission 100 per cent of the time); you just need to reduce transmission enough so that each infectious case gives rise to less than one new case. In technical terms, you need to reduce the reproductive number—the average number of new cases generated by a single case—to less than 1. If you succeed, then the disease will die out in the population as a whole, even if a few unlucky people still get infected.

The reproductive number depends on the biology of the disease: how quickly can it produce new infectious particles? How well do they survive in the environment? It also depends on the ecology p. 16and behaviour of the host, which controls the encounter filter: how dense is the population, how do hosts interact with each other, and how often do they interact? Finally, it depends on the fraction of the population that remains susceptible to the disease, which declines over the course of an epidemic as individuals first get infected and then recover (typically becoming immune, at least temporarily) or die. To ignore this last complication, epidemiologists focus on the intrinsic reproductive number, R0 (pronounced ‘R-zero’ or ‘R-nought’), which is the number of cases that would be generated by the first case in a new outbreak. R0 is a basic measure of disease biology and community structure; it doesn’t depend on how far the epidemic has spread through the population. If you can close the compatibility and encounter filters far enough to reduce the intrinsic reproductive number to less than 1, then you can not only control an epidemic in progress, but prevent the disease from getting started in the first place.

The importance of this kind of average-centred, population-level thinking in disease control was first appreciated by Ronald Ross, who built mathematical models of malaria transmission to prove that malaria could be eradicated without completely eliminating mosquitoes, by reducing mosquito populations below a threshold level—so that on average each infected human led to less than one new human case. (As we will see in Chapter 6, mosquito control and other methods for closing the encounter and compatibility filters have successfully eradicated malaria in some places, but not worldwide.) Ross won the Nobel Prize in 1902 for elucidating the life cycle of malaria, but his biography at the Nobel Foundation’s website states that ‘perhaps his greatest [contribution] was the development of mathematical models for the study of [malaria] epidemiology’.

Ross’s model was one of the first compartmental models, which divide the population into compartments according to their disease status and track the rates at which individuals change p. 17from one disease status to another. The most common, simplest compartmental model is called the SIR model because it divides the population up into Susceptible, Infective, and Recovered people. Susceptibles are people who could get infected, but are not currently infected (i.e. their compatibility filter is open); infectives have the disease and can transmit it (i.e. they are infectious as well as infected); recovered people have had the disease and are at least temporarily immune.

The original compartmental models spawned many variations: for example, SIS models represent diseases such as gonorrhoea where individuals go straight back into the susceptible compartment once they have been cured of disease (say by taking antibiotics), because there is no effective immunity. Dozens of books and thousands of scientific papers have been written about compartmental models. Although the original versions were very simple, researchers have since added all kinds of complexity, accounting for the effects of genetics, age, and nutrition on the compatibility filter, and constructing various representations of social and spatial networks to model the encounter filter. Compartmental models also form the basic structure of huge computer models that track the behaviour and infection status of every individual in the US population in order to understand the spatial spread of influenza epidemics.

While realism and faithfulness to the biological facts of a given disease are important, compartmental models have remained the workhorse of epidemiological modelling because, even in their simpler forms, they capture most of the important characteristics of the spread of disease through a population. Especially when we are ignorant of important information about a disease—a situation painfully familiar to epidemiologists—an oversimplified model can be more useful than an overcomplicated one, as long as we interpret its conclusions cautiously.

Compartmental models typically assume that everyone in the population starts out equally susceptible to a particular disease p. 18(at birth, or in the case of sexually transmitted diseases, once they become sexually active). Susceptibles get infected by mixing with infected people in some way—for example, being coughed or sneezed on or exchanging bodily fluids. In general the infection rate increases with the proportion of infected people in the population, but the details vary enormously among models. After an infectious period during which they spread disease, infected people recover; they move into the recovered compartment and gain effective immunity to the disease. As we have seen, a huge number of variations on this model are possible, including subdividing the population by age, sex, or geographic location; allowing people to return to the susceptible class from the recovered class after some time period; or allowing for variation in the rate at which different individuals transmit disease.

Even without going into any of the underlying mathematics, the structure of the SIR model (Figure 1) helps categorize the ways we can control epidemics. The most common control strategy—closing the compatibility filter by immunization or prophylactic drug treatment (i.e. giving people drugs to prevent rather than cure disease)—moves individuals directly from the susceptible to the recovered compartment without passing through the infected compartment on the way. Almost all other epidemic control measures affect the encounter filter in one way or another. For epidemics in wildlife or domestic animals and plants, killing susceptible or infected individuals (culling) removes these individuals from the population entirely, hopefully reducing R0 below 1. Culling is one of the few available strategies, albeit a very controversial one, for controlling the foot and mouth disease virus in cattle. Post-exposure treatment increases the rate at which individuals move into the recovered compartment, importantly shortening their infectious period and reducing the number of susceptibles they can infect. Finally, transmission controls such as quarantines block infection without moving individuals between compartments.

1. The SIR model describes the progression of people through disease stages from susceptible to infectious to recovered. Interventions such as culling, treatment, or quarantine can speed up or prevent transition among compartments.

p. 19As well as a conceptual framework for thinking about disease control measures, the SIR model also provides a quantitative framework for calculating exactly how much control is necessary to eradicate a disease, or how much a given level of control will reduce the level of disease in the population. Suppose we can eliminate some fraction of effective contacts, by a control fraction (p), by closing either the compatibility filter (e.g. by vaccination) or the encounter filter (e.g. by providing condoms or clean needles). Then the value of R0 will be reduced by a factor 1 − p; if R0 is initially equal to 4 and we can achieve a control fraction of 0.75 or 75 per cent, then we will reduce R0 to (1 − 0.75) × 4 = 1.

A little bit of algebra shows that in order to reduce R0 to less than 1 we need to increase the control above a critical value of pcrit = 1 − 1/R0 (Figure 2). This tells us immediately why it was much easier to eliminate smallpox (R0 ≈ 6, pcrit ≈ 0.8) than it has been to eliminate measles (R0 ≈ 15, pcrit ≈ 0.95), despite the fact that cheap and effective vaccines are available for both diseases, p. 20and why it will be extremely difficult to eradicate malaria, even once we have an effective vaccine: R0 is estimated to be greater than 100 in some areas, so the critical control fraction will be greater than 99 per cent. In fact, the only way to eradicate malaria in high-disease areas will likely be to combine several different strategies (e.g. vaccine and mosquito control), each of which could have (say) 90 per cent effectiveness, so that their combined efficacy could reach the 99 per cent level that might be required.

2. Critical control level required (proportion immunized or treated to prevent transmission) to eradicate an infectious disease, based on its R0 value.

In principle, if disease control measures can reduce R0 below 1, they will not only terminate any existing epidemic, but will prevent recurrence of the epidemic as long as the control measures are maintained. Eradicating a disease within a given region, such as the UK or Europe, reduces the local burden of infectious disease, but does not eliminate the need for disease control unless public health authorities can somehow be 100 per cent sure that they can prevent the importation of disease from outside the eradication zone. Only if we can eradicate a disease globally, as has so far been p. 21done only for smallpox and rinderpest (a lethal cattle disease closely related to measles), can control measures safely be discontinued. This makes eradicating a disease, rather than simply controlling it, an attractive policy option—once the disease is completely gone, any resources that went into managing it can be freed for other disease control efforts, or for other societal goals.

Of course, knowing R0 does not tell us everything about controlling disease—diseases such as influenza (R0 ≈ 2 − 3) and HIV (R0 ≈ 2 − 5) are harder to control than their relatively low R0 values would suggest. Sometimes treatments are unavailable, or too expensive. In other cases, treatment or control measures are only partly effective. With a vaccine that is only 50 per cent effective, comparable to the experimental malaria vaccines currently being tested, and better than the best HIV vaccines available (≈ 30 per cent effective), twice as many people need to be treated (if R0 > 2 it would be impossible to eradicate the disease with this vaccine). Another problem is that infections may be hard to detect, and thus be out of reach of disease control efforts, for either biological or cultural reasons. Biologically, some individuals (carriers) can be infected and spread a disease while showing no symptoms; culturally, many diseases carry a stigma that makes people hide the fact that they are infected. During the ongoing West African Ebola epidemic, one of the major concerns about imposing harsh control measures is that they may simply encourage people exposed to Ebola to hide from authorities.

Compartmental models tell us much more than the level of control necessary to eradicate disease locally or globally. They also give a simple formula for the number of people who will be affected by a disease outbreak in the absence of control, or the size of the susceptible population at equilibrium for a disease that becomes established in the population. Compartmental models have also helped epidemiologists to think about the dynamics of disease—the ways that the infected population changes over time.

p. 22For example, one of the first applications of compartmental models explained that observed multi-year cycles of measles epidemics did not necessarily mean that a new genetic type was invading every few years; rather, disease spread so fast that the susceptible population was exhausted and required several years to build up to the point where it could support another major outbreak. Similarly, mathematicians have pointed out that vaccination campaigns that fail to eradicate a disease allow the number of susceptibles in the population to build up. Even if vaccination coverage stays high, these build-ups may lead to large outbreaks several years after the beginning of the campaign. Without this dynamical insight, the outbreak could easily be interpreted as a sudden change in the effectiveness of the vaccine or the transmissibility of the disease, rather than as a straightforward consequence of a sub-critical level of control.

  • Top of page

Within-host disease dynamics

One of the many biological details that compartmental models omit in their quest for simplicity is any description of the way that disease plays out within an individual host. In compartmental models, hosts are either infected or not; we don’t keep track of the level of infection within an individual (e.g. the number of virus-infected cells or the density of the virus in the bloodstream), nor of the response of the individual’s immune system to the disease.

Standard compartmental models are best for understanding small pathogens (microparasites) such as viruses, bacteria, and fungi; because these types of pathogens tend to build up very quickly within a host, and trigger similar immune responses in most hosts, characterizing hosts as either infected or uninfected is a reasonable simplification. In populations infected with macroparasites—larger parasites such as tapeworms or ticks—the number of parasites per host varies greatly among individuals.

p. 23To account for this variation, mathematicians have had to design more complex models. Within the last decade or so, however, these distinctions have begun to blur as researchers build more elaborate microparasite models that track changes in the numbers of infected particles or cells and the level of activation of the immune system within an individual. For example, a large fraction of HIV transmission occurs within the first month of infection. If we want to understand and predict HIV epidemics, we obviously need to use models that distinguish between recently- and not-so-recently-infected people; we might even want to track the precise level of virus in the blood and other bodily fluids of an infected person.

Nested models, which track both changes in the number of infected people and changes in the number of infected cells within individuals, are mathematically complex—one can imagine the difficulty of keeping track of all of the virus particles within every individual in a population! Somewhat more manageable are within-host models, which focus on the progress of disease within a typical person, ignoring how the disease is spreading among individuals. Where epidemiological models represent the progress of disease in a population, and give insight into the impact and control of disease at the population level, within-host models can help understand how disease works within a single individual.

Despite this difference in scope, however, epidemiological models and within-host models have striking similarities (Figure 3). The compartmental model can easily be adapted for within-host models, especially for parasites such as viruses that must invade host cells in order to reproduce. Instead of assuming that infection builds up quickly and characteristically within individual hosts so that we can practically treat them as either uninfected or infected, we now assume that the level of infection (e.g. the number of virus particles) builds up quickly and characteristically within host cells. The concepts of encounter and compatibility filters are just as useful on the within-host as the within-population levels, p. 24describing how infection gets from one cell to another and what prevents or allows infection of a cell by a disease particle.

3. A within-host compartmental model showing: the infection of cells and death of infected cells; triggering of the immune response by infected cells and by treatment; killing of infected cells by the immune response and by treatment; and blocking of between-cell transmission by treatment.

Within-host models often add a new compartment to keep track of free-floating infectious particles outside of cells, and they often include a separate term for the level of immune defences activated within a host. Within-host models usually assume that the strength of immune defences increases as the number of infected cells increases. If the immune response is rapid enough and strong enough, these models show how the immune system can naturally overwhelm an infection, although not necessarily before the infection has had time to proliferate temporarily and infect another host. Within-host models can also show how drug treatments can slow down disease spread within the host sufficiently for the immune response to eradicate the disease. In viruses such as HIV and the human T-lymphotropic virus that attack immune cells, within-host models show exactly how these diseases pervert the normal immune strategy; the immune system responds to the presence of virus infection by activating more p. 25immune cells, which in turn provide more resources for virus growth. This is like finding out that you’re trying to put out a fire with gasoline instead of water.

  • Top of page

Virulence, resistance, and tolerance

Compartmental models have been used most often for widespread diseases where nearly everyone in the population is equally susceptible, such as measles, polio, or smallpox. Humans do vary in their susceptibility to infection: because they have different genotypes (i.e. complete sets of genetic material), or are better or worse nourished, or are more or less stressed. They also vary in infectiousness, how badly they suffer, and how likely they are to die from the disease. However, for the purposes of epidemiological planning it’s often wise to ignore these details, at least initially.

When we turn to thinking about evolution, this variation becomes not just dangerous to ignore, but central to the questions we are asking. In the last few decades, epidemiological modellers have turned from just trying to understand how diseases spread in populations over timescales from days to years, to trying to understand how diseases evolve over timescales from years to thousands of years. What is it about the combination of a particular host, a particular parasite, and a particular environment that allows the parasite to infect a host? What determines whether the host is badly harmed by the infection or only has mild symptoms?

We have to make several important distinctions about the characteristics of parasites. The first is between infectiousness (how easily the parasite can infect the host) and virulence (how severely it affects the host if it succeeds). We often treat infectiousness and virulence as fixed properties of a parasite. Smallpox has much more horrible symptoms than measles, and a much higher chance of killing the host, regardless of the particular genetic makeup of the parasite or of the host it infects. Measles is p. 26always more infectious than smallpox, which is more infectious than HIV or Ebola. In principle, however, we can imagine two parasite strains and two kinds of hosts that ‘cross over’ in their effects, with one parasite having higher virulence on the first host genotype than the second and the other having higher virulence on the second genotype.

Hosts could control the infectivity and virulence of the pathogens attacking them in two ways. If the host is able to close the compatibility filter partially or completely, we say that it resists the parasite. As a result the parasite might not be able to infect the host at all, or it might not be able to build up its population within the host to very high levels, so that the host suffers few ill effects. Alternatively, the host might allow the parasite to infect it (or more precisely it might not invest energy in defending itself), but it could evolve mechanisms so that it was not badly harmed by infection: in this case, we would call the host tolerant rather than resistant.

Tolerance and resistance have similar outcomes at the level of the individual host (the host isn’t harmed by the parasite), but very different outcomes at the level of the population. If some individuals are highly susceptible (neither resistant nor tolerant), then the presence of resistant individuals will help them by lowering the overall chances of infection, while tolerant individuals will increase the chance of infection. This is one reason that epidemiologists worry about the introduction of partially effective vaccines. If pathogens evolved to replicate more quickly within the host in order to overcome partial resistance in vaccinated people, they might increase their virulence in non-vaccinated people; if vaccination makes people tolerant rather than resistant to disease, they could still spread infection to unvaccinated people.