SIR project
For a closed population \(N=S+I+R\), a standard frequency-dependent SIR model is
\[\frac{dS}{dt}=-\beta\frac{SI}{N},\quad \frac{dI}{dt}=\beta\frac{SI}{N}-\gamma I,\quad \frac{dR}{dt}=\gamma I.\]The basic reproduction number is
\[R_0=\frac{\beta}{\gamma}.\]Worked experiment
Start with one or a few infectious individuals and numerically solve the system. Compare trajectories for \(R_0<1\) and \(R_0>1\). The infectious population initially grows when \(\beta S/N>\gamma\).
Intervention
Represent reduced effective contact by lowering \(\beta\) at a chosen time and compare epidemic peak size and timing.
Project outcome. Connect transmission and recovery mechanisms to epidemic growth, peak formation and intervention effects.