SEIR solver

This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking RKF45 to approximate the solution to the SEIR equations with the $\delta$ parameter to account for quarantine effects:

\begin{aligned} \frac{dS}{dt} & = \Lambda N - \mu S - \frac{\beta I (1-\delta)S}{N} \\ \frac{dE}{dt} & = \frac{\beta I (1-\delta) S}{N} - (\mu +a ) E \\ \frac{dI}{dt} & = a E - (\gamma +\mu ) I \\ \frac{dR}{dt} & = \gamma I - \mu R. \end{aligned}

Where $S$ is the number of susceptible persons, $E$ is the number of exposed persons, $I$ is the number of infectious persons and $R$ is the number of recovered persons. $a$ is the inverse of the average incubation period. $\beta$ 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. $\Lambda$ is the birth rate. $\mu$ is the overall population death rate (not only including the disease death rate). $N$ 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.

Simulation parameter form.
Parameter	Value	Explanation
$a$ :		Inverse of the average incubation period.
$\beta$ :		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.
$\Lambda$ :		Birth rate.
$\mu$ :		Death rate.
$t_f$ :		End time for the simulation in seconds (s)
$S_0$ :		Initial $S$ coordinate.
$E_0$ :		Initial $E$ coordinate.
$I_0$ :		Initial $I$ coordinate.
$R_0$ :		Initial $R$ coordinate.
$\epsilon$ :		Error tolerance.
$\mathrm{Tol}_{\mathrm{type}}$ :		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.

© 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.
Website built with Franklin.jl.

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