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A population comprises a large number of individuals, all of whom are different in various fields. In order to model the progress of an epidemic in such a population this diversity must be reduced to a few key characteristics which are relevant to the infection under consideration. For example, for most common childhood diseases which confer long-lasting immunity it makes sense to divide the population into those who are susceptible to the disease, those who are infected and those who have recovered and are immune. These subdivisions of the population are called compartments. It 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. ...
In epidemiology a susceptible individual (sometimes known simply as a susceptible) is a member of a population who is at risk of becoming infected by a disease, if they are exposed to the infectious agent. ...
In medicine, infectious disease or communicable disease is disease caused by a biological agent (e. ...
The immune system is the organ system that protects an organism from outside biological influences. ...
The SIR model
Standard convention labels these three compartments S (for susceptible), I (for infectious) and R (for recovered). Therefore, this model is called the SIR model.
This is a good, simple, model for many infectious diseases including measles, mumps and rubella. Rubella (also known as epidemic roseola, German measles or three-day measles) is a disease caused by the Rubella virus. ...
The letters also represent the number of people in each compartment at a particular time. To indicate that the numbers might vary over time (even if the total population size remains constant), we make the precise numbers a function of t (time): S(t), I(t) and R(t). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.
The SIR model is dynamic in two senses As implied by the variable function of t, the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an endemic disease with a short infectious period, such as measles in the UK prior to the introduction of a vaccine in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(t)) over time. During an epidemic, the number of susceptibles falls rapidly as more of them are infected and thus enter the infectious and recovered compartments. The disease cannot break out again until the number of susceptibles has built back up as a result of babies being born into the compartment. In epidemiology, an infection is said to be endemic in a population when that infection is maintained in the population without the need for external inputs. ...
Vaccination is a term coined by Edward Jenner for the process of administering a weakened form of a disease to patients as a means of giving them immunity to a more serious form of the disease. ...
1968 was a leap year starting on Monday (the link is to a full 1968 calendar). ...
An epidemic disease is a disease that appears as new cases in the population in a period of time at a rate (the number of new cases in the population during a specified period of time is called the incidence rate) that substantially exceeds what is expected, based on recent...
The SIR is also dynamic in the sense that individuals are born susceptible, then may acquire the infection (move into the infectious compartment) and finally recover (move into the recovered compartment). Thus each member of the population typically progresses from susceptible to infectious to recovered. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments.
Image File history File links SIR compartment model (epidemiology) for article on models, diagram by Viki Male File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
Transition rates For the full specification of the model, the arrows should be labelled with the transition rates between compartments.
Between S and I, the transition rate is λ, the force of infection, which is simply the rate at which susceptible individuals become infected by an infectious disease. In epidemiology, force of infection (denoted λ) is the rate at which susceptible individuals become infected by an infectious disease. ...
Between I and R, the transition rate is δ (simply the rate of recovery). If the duration of the infection is denoted D, then δ = 1/D, since an individual experiences one recovery in D units of time.
Elaborations on the basic SIR model
The SEIR model For many infections there is a period of time during which the individual has been infected but is not yet infectious himself. During this latent period the individual is in compartment E (for exposed). Image File history File links Download high resolution version (887x99, 4 KB)SEIR compartment model (epidemiology) for article on models, diagram by Viki Male File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
The MSIR model For many infections, including measles, babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the placenta or through colostrum). This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model. Human placenta shown a few minutes after birth. ...
Colostrum (occasionally known as beestings) is a form of milk produced by the mammary glands in late pregnancy and the first hours after giving birth. ...
Image File history File links Download high resolution version (887x99, 4 KB)MSIR compartment model (epidemiology) for article on models, diagram by Viki Male File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
Carrier state Some people who have had an infectious disease such as tuberculosis never completely recover and continue to carry the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably Mary Mallon, who infected 22 people with typhoid fever. The carrier compartment is labelled C. Tuberculous lungs show up on an X-ray image Tuberculosis is an infection with the bacterium Mycobacterium tuberculosis, which most commonly affects the lungs (pulmonary TB) but can also affect the central nervous system (meningitis), lymphatic system, circulatory system (miliary TB), genitourinary system, bones and joints. ...
An asymptomatic carrier (or carrier), is a person who is infected with the agent of an infectious disease, or carries the abnormal gene of a recessive genetic disorder. ...
For the comicbook character Typhoid Mary, see Typhoid Mary (comics) Mary Mallon (September 23, 1869 – November 11, 1938), also known as Typhoid Mary, was an Irish immigrant who was the first known healthy carrier of typhoid fever in the United States. ...
This is about the disease typhoid fever. ...
Image File history File links SIR compartment model with carrier class (epidemiology) for article on models, diagram by Viki Male File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
The SIS model Some infections, for example the group of those responsible for the common cold, do not confer any long lasting immunity. Such infections do not have a recovered state and individuals become susceptible again after infection. The Common Cold The Common Cold is a fictional character and a villain in Codename: Kids Next Door. ...
Image File history File links SIS compartment model (epidemiology) for article on models, diagram by Viki Male File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
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