Susceptible-Infected-Recovered (SIR) Model
A Susceptible-Infected-Recovered (SIR) Model is a epidemiological compartmental model used for the mathematical modelling of infectious disease that consists of three compartments: S for the number of susceptible, I for the number of infectious, and R for the number of recovered or deceased (or immune) individuals.
- Context:
- It can be a Predictive Explanatory Model.
- It assumes the disease is transmitted directly from infected individuals to susceptible individuals.
- It assumes that there is no latent period between infection and becoming infectious.
- Example(s):
- Counter-Example(s):
- See: Kermack–McKendrick Theory, Expected Fatality, Basic Reproduction Number, Explanatory Model.
References
2023
- (ChatGPT-OpenAi, 2023) ⇒ https://chat.openai.com Retrieved 2023-4-16.
- Q: What is a Susceptible-Infected-Recovered (SIR) Model?
- A: The Susceptible-Infected-Recovered (SIR) model is a mathematical model used to describe the spread of an infectious disease within a population. The model divides the population into three compartments:
- 1. Susceptible (S): individuals who are not infected and can potentially contract the disease
- 2. Infected (I): individuals who are currently infected and can spread the disease to susceptible individuals
- 3. Recovered (R): individuals who have recovered from the disease and are now immune to further infection
- The SIR model assumes that individuals who recover from the disease are immune and cannot be re-infected. The model also assumes that the disease is transmitted directly from infected individuals to susceptible individuals, and that there is no latent period between infection and becoming infectious.
- The model is based on a set of differential equations that describe the rate of change of each compartment over time. The equations take into account the rate of transmission of the disease, the rate of recovery, and the size of the susceptible population.
- The SIR model is often used to study diseases that confer long-lasting immunity, such as measles or chickenpox. It can be used to predict the course of an outbreak, assess the impact of different interventions, and inform public health policy decisions.
2020
- (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SIR_model Retrieved:2020-4-6.
- The SIR model is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: S for the number of susceptible, I for the number of infectious, and R for the number of recovered or deceased (or immune) individuals. This model is reasonably predictive for infectious diseases which are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella.
These variables (S, I, and R) represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infected and recovered individuals may 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. ...
... 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 susceptible individuals 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, e.g. as a result of offspring being born into the susceptible compartment.
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, ...
- The SIR model is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments: S for the number of susceptible, I for the number of infectious, and R for the number of recovered or deceased (or immune) individuals. This model is reasonably predictive for infectious diseases which are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella.