= SIR model
{c}
{title2=$s+i+r=1$}
The <SIR model> is a <mathematical model> of an <epidemic> that follows three groups: a <susceptible compartment> whose members can acquire <infection>, an <infectious compartment> whose members can pass it on, and a <removed compartment> whose members neither acquire nor pass on <infection>. The letters stand for susceptible, infectious and recovered or removed. Here we study the simplest closed, constant-parameter version, with <homogeneous mixing> and no births, deaths, migration or waning <immunity>. A person who leaves the <infectious compartment> never returns to the <susceptible compartment> in this version.https://ocw.mit.edu/courses/1-022-introduction-to-network-models-fall-2018/fe3c864fd7d2d45ed7fe65e601d9c69e_MIT1_022F18_lec20.pdf[Amir Ajorlou, MIT Lecture 20: Epidemics, slides 18 and 24]{ref}
The appeal of the <SIR model> is that one can explain a rise and fall in the <infectious compartment> without changing anyone's behavior: fewer opportunities for new <infection> eventually reverse the growth. The <SIR first integral> even determines the <SIR infection peak> without computing its time. These are useful deductions from explicit assumptions. The stipulated numbers below illustrate the <mathematical model>; they are neither estimates for an actual disease nor a forecast or medical advice.
Kermack and McKendrick's 1927 paper, "A contribution to the mathematical theory of epidemics", in Proceedings of the Royal Society A, is an early foundation for the <SIR model>. Its DOI is `10.1098/rspa.1927.0118`, also recorded in the Royal Society's archive of contemporary referee reports.https://doi.org/10.1098/rspa.1927.0118[Kermack and McKendrick, original 1927 paper]{ref}https://catalogues.royalsociety.org/CalmView/Record.aspx?id=RR%2F35%2F131&src=CalmView.Catalog[Royal Society archive: contemporary referee report and publication record]{ref}
\Image[/sir-compartment-transfer.png]
{title=Transfers between the three compartments of the <SIR model>}
{description=The <SIR model equations> transfer a <fraction> $\beta si$ per day from the <susceptible compartment> to the <infectious compartment>, and a <fraction> $\gamma i$ per day from the <infectious compartment> to the <removed compartment>. Each arrow contributes a loss to one group and an equal gain to another, giving <conservation of population>.}
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