The Mathematical Storytelling that's like what I need Linguistic Leaps and Bounds because this is some effective pedagogy that eases the transition for students from high-school to college-level, the QA forms that give us the language of the discipline of mathematical epidemiologists as they examine the effects of these parameters, of infectious disease spread. @Lybrya Kebreab.
ClearAll[s, e, i, t, \[Lambda], \[Beta], \[Mu], \[Alpha], \[Gamma], \
\[Delta]]
sliderRow[label_, dynamicVar_, {min_, max_}] := Row[{
label,
Spacer[5],
Dynamic[dynamicVar],
Spacer[20],
Slider[
Dynamic[dynamicVar],
{min, max},
Appearance -> "Labeled"
]}];
DynamicModule[{s0 = 0.6, e0 = 0.7, i0 = 0.5, ttime = 5},
Column[{
sliderRow["\[Lambda] =", \[Lambda], {0, 2}],
sliderRow["\[Beta] =", \[Beta], {0, 1}],
sliderRow["\[Mu] =", \[Mu], {0, 1}],
sliderRow["\[Alpha] =", \[Alpha], {0, 1}],
sliderRow["\[Gamma] =", \[Gamma], {0, 1}],
sliderRow["\[Delta] =", \[Delta], {0, 1}],
Row[{Dynamic[
sol = NDSolve[{
s'[t] == \[Lambda] - \[Beta] s[t] - \[Mu] s[t] + \[Alpha] i[
t], e'[t] == \[Beta] s[t] - (\[Gamma] + \[Mu]) e[t],
i'[t] == \[Gamma] e[t] - (\[Alpha] + \[Mu] + \[Delta]) i[t],
s[0] == s0, e[0] == e0, i[0] == i0}, {s, e, i}, {t, -ttime,
ttime}];
Plot[Evaluate[
{s[t], e[t], i[t]} /. sol],
{t, -ttime, ttime},
PlotLegends -> {"s[t]", "e[t]", "i[t]"},
PlotStyle -> ColorData["DarkRainbow"] /@ Range[0, 1, 1/3],
ImageSize -> 400,
BaseStyle -> {FontColor -> Yellow}
]
],
Dynamic[
ParametricPlot3D[
Evaluate[{s[t], e[t], i[t]} /. sol],
{t, -ttime, ttime},
BoxRatios -> {1, 1, 1},
AxesLabel -> {"s", "e", "i"},
PlotRange -> All,
ImageSize -> 400,
BaseStyle -> {FontColor -> Yellow}
]]},
Background -> RGBColor[0.2, 0.1, 0.2]
]
}]]
The Wolfram Language vector fields and linear transformations absolutely show what we're looking for. I developed a positive mathematics identity. It begs the question of the good meta-model for the observer, abstracting away the computer system. @Lybrya Kebreab that was the best instructional experience that I have ever had. That was more than I could have ever deserved. It was like showing a three year old everything there is to know about the elements of a Turing Machine. Because I learned so much just from making connections within & among dynamic representations of the differential equations and the dynamics of infectious disease spread.
But now these prompts give us this structural transport between these different areas of Mathematics, the authentic historical context that allows us to engage in and build methods to understand how a Supernova spreads out.
