Disease Transmission Primer

Stages of an Infection Transmission Probability Basic Reproductive Number (R0)

Knowing the clinical appearance of influenza and the details about the virus is only part of the picture. We also need to know something about how the virus spreads through the population and how quickly. For this we need some basic information on infectious disease epidemiology.

As discussed in the Influenza Primer I and II, the ability to cause disease (pathogenicity) and the severity of the disease (virulence) are not properties of the virus alone but of the complicated relationship of the virus, the host (say a human or a bird) and the environment they all live in. This relationship itself isn’t constant but is constantly changing as the three parts (host - agent - environment) change. This is clear when we talk about how the disease spreads. The immune status of the host or its state of health, the specific strain of the virus and how it changes as it multiplies in the host, and how close together people are and how often they are in contact with each other are all critical factors to how influenza spreads. In order to bring some order into this we need some basic terms and ideas.

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Stages of an infection

Infection begins when an intact virus (sometimes called a viral particle or a virion) enters a host cell and begins to replicate. For a time, called the latent period, the host has no symptoms nor is he (we’ll fix the victim to be male) infectious because he hasn’t yet started to shed virus into his environment. The point where this starts to happen is the end of the latent period and the beginning of the infectious period. Also at some point after infection the subject may start to have symptoms of infection (sore throat, aching or fever). This is the start of the symptomatic period. The time from the start of the latent period to the start of the symptomatic period is called the incubation period and may or may not include some of the period of infectiousness.

What makes this scheme more complicated and also very important from the public health point of view is that the order in which the infectious period and the symptomatic periods happen is not fixed for different diseases. Thus in SARS people became sick (symptomatic) before they were maximally infective, so health care workers rather than the general population were most likely to be exposed. It was thus also easier to control the disease because apparently well people were not infectious. With influenza, on the other hand, the infectious period begins about 24 hours before the symptomatic period. This gives influenza a head start in infecting people, before the person knows he is sick and thus more likely to have contact with others.

People can also become infected and sick but never infectious (although this would be rare for influenza), but more importantly they can become infected and infectious but not sick (inapparent or silent infection). These people are “healthy carriers.” There are estimates as high as 30% to 60% for infected people who are infectious for influenza but otherwise healthy. Until recently most aquatic wildfowl were also healthy carriers, although now migratory birds in China have been reported to be sickened by the virus, not just carriers. One concern about the use of vaccination in domestic poultry is that it might convert birds who would otherwise obviously be sick to normal-looking healthy carriers.

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Transmission probability

The thing most people want to know about the risk of getting influenza is how likely they are to become infected if exposed. This is called the transmission probability and is one of the key numbers to consider in disease spread. Technically, it is the probability (the chance) of the disease being transmitted from one person to another or from a bird or other animal to a person, given that there has been contact between them. While this definition seems fairly clear at first, it has a lot of “interior” parts because it depends on characteristics of the host (for example how much virus he is shedding and how he is shedding it), the particular viral strain (for example, how well does it survive in various environments and how easily does it infect various hosts), the possible new host (e.g., what her immune status is or her age) and what we mean by “contact” (being in the same household? The same room? Having touched the infected person? Etc.) Thus this is not either a single number or even one that is easy to estimate in a given situation. In order to understand what any given figure for transmission probability means you need to know quite a bit about how it was measured and importantly what definition of “contact” was used.

One frequently encountered indicator of transmission probability is the Secondary Attack Rate (SAR) (which technically is not a rate but a proportion). The SAR is the probability of disease among known (or presumed) susceptible people following contact with a known primary case (often called the index case). It is often measured in some convenient population like a household, classroom or airplane. It measures only the “first level” of infections, not any secondary infections that occur later from those infected by the index case.

SAR has been the subject of some discussion in trying to decide whether H5N1 has gone “human-to-human” in southeast asia. To understand what this is about we need to consider the definitions we just gave for latent period, infectious period and incubation period. These times are not the same for everyone so we need to consider both a minimum and maximum latent period, a minimum and maximum infectious period, and a minimum and maximum incubation period.

Consider someone who is exposed to an infected chicken on day one. The minimum and maximum latent times tell when the earliest and the latest they will be infective. The minimum and maximum incubation period tells the earliest and latest that an exposed person would come down with disease. So if you take the shortest time that a person can first become infectious together with the shortest incubation time, that will tell you the shortest interval between two cases you could have for person to person transmission. Any shorter time interval and you would consider two cases in the same family to be co-primaries (to have gotten it from the same or different sources but not from each other). A time interval longer than the combined maximum latent interval, maximum infectious period and maximum incubation period tell you how far apart two cases might be before you would consider them not to have been transmitted one to another. This is the basis for the famous “bimodal” family clusters (i.e., cases that are separated by an interval that could possibly, but not necessarily, indicate transmission from one person to another).

For influenza H5N1 these intervals are not known with any precision but generally the latent period is thought to be 24 to 48 hours and an average of 2 days for the incubation period (but a range of 1 to 4 days), with infectiousness lasting several days to a week for adults but sometimes up to 2 weeks for children. The immunocompromised patients can shed virus for months. In most instances, this means that a secondary case (one acquired from the first, or index case) would have to be one that first experiences symptoms more than 24 hours and perhaps less than two weeks after the first person. A second case that occurs inside that window is a good candidate for a human to human case but not proof of one. Cases outside that window (especially less than 48 hours) would not be likely human-to-human cases, but because children and the immunocompromised can continue to shed virus outside the usual five day window, fixing an upper limit needs to be done on a case-by-case basis.

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Basic reproductive number (R0)

The other “number” that is frequently mentioned in the influenza case and infectious disease epidemiology is called the Basic Reproductive Number, usually designated by the symbol R0 (pronounced ‘R naught”). It is the expected (average) number of new infectious cases in a completely susceptible population produced by a single case during its entire period of infectiousness. Like transmission probability, this simple definition hides some subtleties.

The number of cases produced does not include any additional cases caused by the secondary cases (that is, further down the chain) and it does not count any new non-infectious cases. The reason for this is that R0 is meant to measure how likely is the disease to spread. If all the cases produced by the original case were non-infectious the disease couldn’t spread. Also, if the number of cases, on average were less than one, then eventually the disease would die out. (This assumes the disease is of some limited duration, either because of recovery or death. Clearly if a case lasted for a lifetime, eventually it would spread to the entire population, as long as R0 were greater than zero.) When R0 = 1.0, each case just reproduces itself so the number of cases stays steady, neither growing nor shrinking. Thus a higher R0 represents a more transmissible the disease and the more broadly it can spread in the population. R0 for some diseases like measles is up around 10. For influenza there have been various estimates but it is generally thought to be below 4, perhaps in the 1.5 to 3 range.

But R0 is not the whole story. It, too, has “component” parts not visible in the single summary number. First, it is an average, so in some cases R0 will be greater than one and spread locally, producing a cluster, and others less than one and not go anywhere. But more importantly, R0 has four components built into it: how long the infectious period is; how many contacts an infectious person makes in a period of time; the transmission probability (above); and the probability that someone who gets infected is themselves infectious. You can see from this that R0 is not actually a characteristic of the virus or the disease (although it is sometimes spoken of in this way) but of the virus in a specific population at a specific time and place. By altering some or all of the components you can also alter R0.

This strategy of altering R0 is behind many of the public health interventions suggested for controlling influenza. For example, consider the contact rate. By quarantine, self-isolation or canceling school or public events this is reduced, thus reducing R0. Similarly, treatment with antivirals may both reduce the infectious period by a day or two and also the amount of viral shedding, both of which will reduce R0.

Because it is a composite number, R0 is not as good for comparing infectious diseases as would seem at first. Halloran, in her chapter on Infectious Disease Epidemiology in Rothman and Greenland’s Modern Epidemiology (second edition) gives an instructive example. R0s for measles and HIV are both about 9, but measles has high probability of transmission and a short infectious period, measured in days, while HIV has low probability of transmission but a very long infectious period, measure in years. Both produce major epidemics but over vastly different time scales. R0 does not tell the whole story.

Moreoever R0 is the average number of new infectious cases in the susceptible population. But we know that not everyone may be susceptible, say, because they were treated prophylactically with antivirals or (if available) a vaccine. Thus the effective reproductive number will be less than R0 and is just designated R. This illustrates another fact, that the underlying assumptions about R0 usually don’t hold: not everyone is susceptible, not everyone is equally likely to be in contact with the index case, not everyone has the same duration of infectiousness, etc. Various sophisticated methods have been devised to account for some of these departures from the ideal case.

Finally, it is sometimes said that the “natural” evolution of a virulent virus is toward a state of more mild disease. However considering the components of R0 one can see this is not necessarily true. On the one hand, if the disease is so virulent it kills its host quickly, less time is spent in the infectious state and R0 decreases. This is not good for the virus and one might then expect it to adapt by becoming less virulent. However it might also be true that increased virulence increases the transmission probability, say because there is more violent coughing, or bleeding that soils bedsheets and contaminates care-givers more readily. Positive and negative selective pressures on the virus will be a balance of the various components of R0. As one increases, another may decrease and the relative amounts will be related to virulence in a complicated way that will probably also depend on the setting (contact rate, environmental conditions) and the host status.

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Page last modified on December 05, 2008, at 07:31 AM by pogge