Table 3.

Differential Equations Used for Each Epidemic Model, Other than the Previously Stated SIR Model.

SEIR	One-path SAIR	Two-path SAIR
$\begin{array}{c}\frac{dS(t)}{dt}=-c\mathit{\beta }S(t)P_{SI}\hfill \\ \frac{dE(t)}{dt}=-c\mathit{\beta }S(t)P_{SI}-\mathit{\kappa }E(t)\hfill \\ \frac{dI(t)}{dt}=\mathit{\kappa }E(t)-\mathit{\gamma }I(t)\hfill \\ \frac{dR(t)}{dt}=\mathit{\gamma }I(t)\hfill \end{array}$	$\begin{array}{c}\frac{dS(t)}{dt}=-cS(t)({\mathit{\beta }}_A{P}_{SA}+{\mathit{\beta }}_I{P}_{SI})\hfill \\ \frac{dA(t)}{dt}=-cS(t)({\mathit{\beta }}_A{P}_{SA}+{\mathit{\beta }}_I{P}_{SI})-{\mathit{\gamma }}_{A}A(t)\hfill \\ \frac{dI(t)}{dt}={\mathit{\gamma }}_{A}A(t)-{\mathit{\gamma }}_{I}I(t)\hfill \\ \frac{dR(t)}{dt}={\mathit{\gamma }}_{I}I(t)\hfill \end{array}$	$\begin{array}{c}\frac{dS(t)}{dt}=-cS(t)({\mathit{\beta }}_A{P}_{SA}+{\mathit{\beta }}_I{P}_{SI})\hfill \\ \frac{dA(t)}{dt}=-cS(t)({\mathit{\beta }}_A{P}_{SA}{p}_{AA}+{\mathit{\beta }}_I{P}_{SI}(1-p_{II}))-{\mathit{\gamma }}_{A}A(t)\hfill \\ \frac{dI(t)}{dt}=-cS(t)({\mathit{\beta }}_A{P}_{SA}(1-p_{AA})+{\mathit{\beta }}_I{P}_{SI}{p}_{II})-{\mathit{\gamma }}_{A}A(t)\hfill \\ \frac{d{R}_A(t)}{dt}={\mathit{\gamma }}_{A}I(t)\hfill \\ \frac{d{R}_I(t)}{dt}={\mathit{\gamma }}_{I}I(t)\hfill \end{array}$