This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking (RKF45) to approximate the solution to the SIR equations with the \(\delta\) parameter to account for quarantine effects: \[ \begin{aligned} \dfrac{dS}{dt} &= -\dfrac{\beta I (1-\delta)S}{N} \\ \dfrac{dI}{dt} &= \dfrac{\beta I(1-\delta)S}{N} - \gamma I \\ \dfrac{dR}{dt} &= \gamma I. \end{aligned} \] Where \(S\) is the number of susceptible persons, \(I\) is the number of infected persons and \(R\) is the number of recovered persons. \(\beta\) is a parameter that pertains to the average number of contacts per person per time and the rate of transmission for the disease. \(\gamma\) is the inverse of the average time a person is infected with the disease. \(N\) is the total population. My original model had \(\gamma I\) multiplied by \(1-\delta\), but as quarantine should not affect how long it takes for people to recover, it should not affect this term.