| Abstract: |
| In epidemiological models such as the SIR model
\begin{align*}
\dot S &= -\beta S I, \
\dot I &= \beta S I - \gamma I, \
\dot R &= \gamma I,
\end{align*}
the effective contact rate $\beta$ is treated as a constant. In fact we know from experience that $\beta$ behaves more like a state variable: due to fear, contact rates often fall as infection rates rise. We shall discuss a simple extension of SIR due to Piero Poletti and collaborators in which a single equation models how response to a changing infection rate spreads through a population by contact, much like the epidemic itself. We show how the model can be analyzed using geometric singular perturbation theory. Unlike the usual SIR model, the extended model can produce successive ``waves of infection. |
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