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 $t$ is time and is usually in units of days. $S$ 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. Consequently, the basic reproduction number, which is typically represented as $R_0$ (not to be confused with the initial population of recovered individuals), is given by:

\begin{aligned} R_0 = \dfrac{\beta(1-\delta)}{\gamma} \end{aligned}

(Ridenhour et al., 2014). $N$ is the total population.

If you would like to examine a more realistic model, with birth and death rates, loss of immunity, and incubation periods, then check out the SEIRS model solver webpage.

Simulation parameter form.
Parameter	Value	Explanation
$\beta$ :		A parameter that pertains to how many contacts there are per person and how easily the disease spreads from an infected person to an uninfected person.
$\gamma$ :		A parameter that is a measure of how quickly people recover from the disease.
$\delta$ :		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.
$t_f$ :		End time of simulation.
$S_0$ :		Initial number of susceptible individuals.
$I_0$ :		Initial number of infected individuals.
$R_0$ :		Initial number of recovered individuals.
$\epsilon$ :		Error tolerance for our numerical solution to the SIR equations.
$\mathrm{Tol}_{\mathrm{type}}$ :		Tolerance type, can be either absolute (0) or relative (1).
$h_{\mathrm{Initial}}$ :		Initial step size.
$h_{\mathrm{Min}}$ :		Minimum allowed step size.
$\Delta t$ :		Time increment for skipping ahead in animation.
$t_1$ :		Time you want to skip ahead to in animation when you press the skip button.
$\mathrm{Width}$ :		Width (in px) of Plotly windows used for plotting and animation below.
$\mathrm{Height}$ :		Height (in px) of Plotly windows used for plotting and animation below.
$t_\mathrm{Scale}$ :		Proportion of animation time passed per real time. $t_{\mathrm{Scale}}=1.0$ means animation and real time match. $t_{\mathrm{Scale}}<1.0$ means the animation is going more slowly than real time. $t_{\mathrm{Scale}}>1.0$ means it is going more rapidly.
$\mathrm{Opacity}$ :		Opacity of the lines in the 3D phase space animation. Customizable in case you need to tweak it in order to see the red dot marker.

Reference list

Ridenhour, B; Kowalik, JM; & Shay, DK (2014). Unraveling $R_0$ : Considerations for Public Health Applications. American Journal of Public Health, 104(2): e32–e41. doi: 10.2105/AJPH.2013.301704. PMID 24328646. PMC 3935673.

© Brenton Horne. I do not claim to be infallible, so feel free to open issues or pull requests on GitHub if you notice flaws or things that can be improved.
I favour Oxford spelling, so if you notice I generally use different spelling to Australian spelling, that is probably why.
Homepage. Source code: https://github.com/fusion809/fusion809.github.io.
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