SIR equations solver

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.
Parameter Value Explanation
A parameter that pertains to how many contacts there are per person and how easily the disease spreads from an infected person to an infected person.
A parameter that is a measure of how quickly people recover from the disease.
A parameter with values from 0 to 1 pertaining to how effective quarantine measures are at slowing the disease outbreak. If \(\delta = 0\), the measures are either non-existent or completely ineffective. If \(\delta = 1\), all infected persons are immediately, as soon as they become infected, quarantined.
Starting time for the simulation in days.
End time for the simulation in days. Default is \(14\times 7 = 98\), which is the number of days in 14 weeks.
Value of \(S\) at \(t_0\).
Value of \(I\) at \(t_0\).
Value of \(R\) at \(t_0\).
Error tolerance. \(\epsilon \lt\) 1e-12 usually freezes the webpage up.
Initial guess for step size.