Transmission risks and rates
Encyclopedia
Transmission
of an infection
requires three conditions:
An effective contact is defined as any kind of contact between two individuals such that, if one individual is infectious and the other susceptible, then the first individual infects the second. Whether or not a particular kind of contact will be effective depends on the infectious agent and its route of transmission
.
The effective contact rate (denoted β) in a given population
for a given infectious disease
is measured in effective contacts per unit time. This may be expressed as the total contact rate (the total number of contacts, effective or not, per unit time, denoted γ), multiplied by the risk of infection, given contact between an infectious and a susceptible individual. This risk is called the transmission risk and is denoted p. Thus:
The total contact rate, γ, will generally be greater than the effective contact rate, β, since not all contacts result in infection. That is to say, p is almost always less than 1 and it can never be greater than 1, since it is effectively the probability
of transmission occurring.
This relation formalises the fact that the effective contact rate depends not only on the social patterns of contact in a particular society (γ) but also on the specific types of contact and the pathology of the infectious organism (p). For example, it has been shown that a concurrent sexually transmitted infection
can substantially increase the probability (p) of infecting a susceptible with HIV
. Therefore, one way to reduce the value of p (and hence lower HIV transmission rates) might be to treat other sexually transmitted infections.
There are a number of difficulties in using this relation. The first is that it is very difficult to measure contact rates because they vary widely between individuals and groups, and within the same group at different times. For sexually transmitted infections, large scale studies of sexual behaviour
have been set up to estimate the contact rate. In developed countries for serious diseases such as AIDS
or tuberculosis
, contact tracing is often carried out when a patient is diagnosed (the patient and medical authorities try to inform every possible contact the patient may have made since infection). This, however, is not so much a research tool and more to alert the contacts to the possibility that they may be infected and so can seek medical treatment and avoiding passing on the disease if they have contracted it.
A second consideration is that it is generally thought unethical
to carry out direct experiments to establish per-contact infection risks as this would require the deliberate exposure of individuals to infectious agents. The Common Cold Unit
that researched cold transmission in the UK between 1946 and 1989 was a notable exception. It is also possible to estimate the transmission risk in certain circumstances where exposures to infection have been documented, for example the rate of infection among nurses who have accidentally pricked their fingers with a needle that had previously been used with contaminated blood.
A more direct assessment of transmission risks can be provided by a contact study, which is often carried out because of an outbreak (such a study was carried out during the SARS outbreak of 2002–3). The first (or primary) case within a defined group (such as a school or family) is identified and people infected by this individual (called secondary cases) are documented. If the number of susceptibles in the group is n and the number of secondary cases is x, then an estimation of the transmission risk is
Here, p is the same parameter
as before but it has been calculated in a different way. To reflect this, it is called the secondary attack rate (it is really a risk, of course, and not a rate, but the term is still commonly used).
Even if the whole group in question is susceptible, x is generally smaller than the basic reproduction number
for the disease. That is defined as the number of individuals each infected individual will go on to infect themselves, in a population with no resistance to the disease. The basic reproduction number includes all secondary cases infected by a primary case, while x is only the number of secondary cases within the group in question.
Secondary attack rates are useful for comparisons between vaccinated
and unvaccinated groups and hence assessing the efficacy of vaccinations against the disease under inspection. However, there are inevitably complications with such contact studies. It is not always obvious which members of the group are susceptible and distinguishing between secondary and subsequent cases (for example, those infected by the secondary cases are tertiary cases and so on) can be difficult. Also, the possibility of infection from an outsider must be ignored.
Despite these problems, the parameters p and β are powerful tools in the mathematical modelling of epidemics. But it should always be remembered that a model is only as good as the assumptions on which it is based and the data from which its parameters are calculated.
Transmission (medicine)
In medicine and biology, transmission is the passing of a communicable disease from an infected host individual or group to a conspecific individual or group, regardless of whether the other individual was previously infected...
of an infection
Infection
An infection is the colonization of a host organism by parasite species. Infecting parasites seek to use the host's resources to reproduce, often resulting in disease...
requires three conditions:
- an infectiousInfectious diseaseInfectious diseases, also known as communicable diseases, contagious diseases or transmissible diseases comprise clinically evident illness resulting from the infection, presence and growth of pathogenic biological agents in an individual host organism...
individual - a susceptible individual
- an effective contact between them
An effective contact is defined as any kind of contact between two individuals such that, if one individual is infectious and the other susceptible, then the first individual infects the second. Whether or not a particular kind of contact will be effective depends on the infectious agent and its route of transmission
Transmission (medicine)
In medicine and biology, transmission is the passing of a communicable disease from an infected host individual or group to a conspecific individual or group, regardless of whether the other individual was previously infected...
.
The effective contact rate (denoted β) in a given population
Population
A population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than cross-breeding with individuals...
for a given infectious disease
Infectious disease
Infectious diseases, also known as communicable diseases, contagious diseases or transmissible diseases comprise clinically evident illness resulting from the infection, presence and growth of pathogenic biological agents in an individual host organism...
is measured in effective contacts per unit time. This may be expressed as the total contact rate (the total number of contacts, effective or not, per unit time, denoted γ), multiplied by the risk of infection, given contact between an infectious and a susceptible individual. This risk is called the transmission risk and is denoted p. Thus:
The total contact rate, γ, will generally be greater than the effective contact rate, β, since not all contacts result in infection. That is to say, p is almost always less than 1 and it can never be greater than 1, since it is effectively the probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
of transmission occurring.
This relation formalises the fact that the effective contact rate depends not only on the social patterns of contact in a particular society (γ) but also on the specific types of contact and the pathology of the infectious organism (p). For example, it has been shown that a concurrent sexually transmitted infection
Sexually transmitted disease
Sexually transmitted disease , also known as a sexually transmitted infection or venereal disease , is an illness that has a significant probability of transmission between humans by means of human sexual behavior, including vaginal intercourse, oral sex, and anal sex...
can substantially increase the probability (p) of infecting a susceptible with HIV
HIV
Human immunodeficiency virus is a lentivirus that causes acquired immunodeficiency syndrome , a condition in humans in which progressive failure of the immune system allows life-threatening opportunistic infections and cancers to thrive...
. Therefore, one way to reduce the value of p (and hence lower HIV transmission rates) might be to treat other sexually transmitted infections.
There are a number of difficulties in using this relation. The first is that it is very difficult to measure contact rates because they vary widely between individuals and groups, and within the same group at different times. For sexually transmitted infections, large scale studies of sexual behaviour
Sexual network
A sexual network is a social network that is defined by the sexual relationships within a set of individuals.-Studies and discoveries:Like other forms of social networks, sexual networks can be formally studied using the mathematics of graph theory and network theory.Recent epidemiological studies ...
have been set up to estimate the contact rate. In developed countries for serious diseases such as AIDS
AIDS
Acquired immune deficiency syndrome or acquired immunodeficiency syndrome is a disease of the human immune system caused by the human immunodeficiency virus...
or tuberculosis
Tuberculosis
Tuberculosis, MTB, or TB is a common, and in many cases lethal, infectious disease caused by various strains of mycobacteria, usually Mycobacterium tuberculosis. Tuberculosis usually attacks the lungs but can also affect other parts of the body...
, contact tracing is often carried out when a patient is diagnosed (the patient and medical authorities try to inform every possible contact the patient may have made since infection). This, however, is not so much a research tool and more to alert the contacts to the possibility that they may be infected and so can seek medical treatment and avoiding passing on the disease if they have contracted it.
A second consideration is that it is generally thought unethical
Medical ethics
Medical ethics is a system of moral principles that apply values and judgments to the practice of medicine. As a scholarly discipline, medical ethics encompasses its practical application in clinical settings as well as work on its history, philosophy, theology, and sociology.-History:Historically,...
to carry out direct experiments to establish per-contact infection risks as this would require the deliberate exposure of individuals to infectious agents. The Common Cold Unit
Common Cold Unit
In Britain, the Common Cold Unit , also known as the Common Cold Research Unit , was set up by the civilian Medical Research Council in 1946 on the site of a former military hospital, the Harvard Hospital, at Harnham Down near Salisbury in Wiltshire...
that researched cold transmission in the UK between 1946 and 1989 was a notable exception. It is also possible to estimate the transmission risk in certain circumstances where exposures to infection have been documented, for example the rate of infection among nurses who have accidentally pricked their fingers with a needle that had previously been used with contaminated blood.
A more direct assessment of transmission risks can be provided by a contact study, which is often carried out because of an outbreak (such a study was carried out during the SARS outbreak of 2002–3). The first (or primary) case within a defined group (such as a school or family) is identified and people infected by this individual (called secondary cases) are documented. If the number of susceptibles in the group is n and the number of secondary cases is x, then an estimation of the transmission risk is
Here, p is the same parameter
Parameter
Parameter from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”, can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines....
as before but it has been calculated in a different way. To reflect this, it is called the secondary attack rate (it is really a risk, of course, and not a rate, but the term is still commonly used).
Even if the whole group in question is susceptible, x is generally smaller than the basic reproduction number
Basic reproduction number
In epidemiology, the basic reproduction number of an infection is the mean number of secondary cases caused by an individual infected soon after disease introduction into a population with no pre-existing immunity to the disease in the absence of interventions to control...
for the disease. That is defined as the number of individuals each infected individual will go on to infect themselves, in a population with no resistance to the disease. The basic reproduction number includes all secondary cases infected by a primary case, while x is only the number of secondary cases within the group in question.
Secondary attack rates are useful for comparisons between vaccinated
Vaccination
Vaccination is the administration of antigenic material to stimulate the immune system of an individual to develop adaptive immunity to a disease. Vaccines can prevent or ameliorate the effects of infection by many pathogens...
and unvaccinated groups and hence assessing the efficacy of vaccinations against the disease under inspection. However, there are inevitably complications with such contact studies. It is not always obvious which members of the group are susceptible and distinguishing between secondary and subsequent cases (for example, those infected by the secondary cases are tertiary cases and so on) can be difficult. Also, the possibility of infection from an outsider must be ignored.
Despite these problems, the parameters p and β are powerful tools in the mathematical modelling of epidemics. But it should always be remembered that a model is only as good as the assumptions on which it is based and the data from which its parameters are calculated.
See also
- Mathematical modelling in epidemiologyMathematical modelling in epidemiologyIt is possible to mathematically model the progress of most infectious diseases to discover the likely outcome of an epidemic or to help manage them by vaccination...
- Risk factorRisk factorIn epidemiology, a risk factor is a variable associated with an increased risk of disease or infection. Sometimes, determinant is also used, being a variable associated with either increased or decreased risk.-Correlation vs causation:...
- Transmission (medicine)Transmission (medicine)In medicine and biology, transmission is the passing of a communicable disease from an infected host individual or group to a conspecific individual or group, regardless of whether the other individual was previously infected...
- Bugchasing and giftgiving
- Epidemic modelEpidemic modelAn Epidemic model is a simplified means of describing the transmission of communicable disease through individuals.-Introduction:The outbreak and spread of disease has been questioned and studied for many years...