ODE SEIR Model

Available identifiers

ordinary differential equations SEIR Model

List of mathematical expressions with quantities

Initial Number Of SEIR Condition	$\begin{aligned} s_{2} (0) = \frac{S_{2} (0)}{N_{2}} \\ e_{2} (0) = \frac{E_{2} (0)}{N_{2}} \\ i_{2} (0) = \frac{I_{2} (0)}{N_{2}} \\ r_{2} (0) = \frac{R_{2} (0)}{N_{2}} \end{aligned}$
$E_{2}$ symbol represents Number of Exposed Individuals
$I_{2}$ symbol represents Number of Infectious Individuals
$N_{2}$ symbol represents Total Population Size
$R_{2}$ symbol represents Number of Removed Individuals
$S_{2}$ symbol represents Number of Susceptible Individuals
${\bar{e}}_{2}$ symbol represents Fraction Of Population Density Of Exposed In The ODE Region (Mean)
${\bar{i}}_{2}$ symbol represents Fraction Of Population Density Of Infectious In The ODE Region (Mean)
${\bar{r}}_{2}$ symbol represents Fraction Of Population Density Of Removed In The ODE Region (Mean)
${\bar{s}}_{2}$ symbol represents Fraction Of Population Density Of Susceptibles In The ODE Region (Mean)

Rate Of Change Of Population Density Fraction Of Exposed Mean ODE	${\dot{\bar{e}}}_{2} \approx (1 - \frac{A}{{\bar{n}}_{2} + n_{0}}) {\bar{s}}_{2} (β_{e} {\bar{e}}_{2} + β_{i} {\bar{i}}_{2}) - σ {\bar{e}}_{2} - ϕ_{e} {\bar{e}}_{2} - \frac{1}{\| Ω_{2} \|} \int_{Γ} ν_{1}^{T} D \nabla e_{1} d o$
$A$ symbol represents Allee Threshold
$D$ symbol represents Diffusion Coefficient for SEIR Model
${\bar{e}}_{2}$ symbol represents Fraction Of Population Density Of Exposed In The ODE Region (Mean)
${\bar{i}}_{2}$ symbol represents Fraction Of Population Density Of Infectious In The ODE Region (Mean)
${\bar{s}}_{2}$ symbol represents Fraction Of Population Density Of Susceptibles In The ODE Region (Mean)
$β_{e}$ symbol represents Asymptomatic Infection Rate
$β_{i}$ symbol represents Symptomatic Infection Rate
$ν_{1}^{T}$ symbol represents Unit Normal Vector
$ϕ_{e}$ symbol represents Asymptomatic Recovery Rate
$σ$ symbol represents Rate of Becoming Infectious
$e_{1}$ symbol represents Fraction Of Population Density Of Exposed In The PDE Region
$n$ symbol represents Population Density

Rate Of Change Of Population Density Fraction Of Infectious Mean ODE	${\dot{\bar{i}}}_{2} \approx σ {\bar{e}}_{2} - ϕ_{i} {\bar{i}}_{2} - \frac{1}{\| Ω_{2} \|} \int_{Γ} ν_{1}^{T} D \nabla i_{1} d o$
$D$ symbol represents Diffusion Coefficient for SEIR Model
${\bar{e}}_{2}$ symbol represents Fraction Of Population Density Of Exposed In The ODE Region (Mean)
${\bar{i}}_{2}$ symbol represents Fraction Of Population Density Of Infectious In The ODE Region (Mean)
$ν_{1}^{T}$ symbol represents Unit Normal Vector
$ϕ_{i}$ symbol represents Infected Recovery Rate
$σ$ symbol represents Rate of Becoming Infectious
$i_{1}$ symbol represents Fraction Of Population Density Of Infectious In The PDE Region

Rate Of Change Of Population Density Fraction Of Removed Mean ODE	${\dot{\bar{r}}}_{2} \approx ϕ_{i} {\bar{i}}_{2} + ϕ_{e} {\bar{e}}_{2} - \frac{1}{\| Ω_{2} \|} \int_{Γ} ν_{1}^{T} D \nabla r_{1} d o$
$D$ symbol represents Diffusion Coefficient for SEIR Model
${\bar{e}}_{2}$ symbol represents Fraction Of Population Density Of Exposed In The ODE Region (Mean)
${\bar{i}}_{2}$ symbol represents Fraction Of Population Density Of Infectious In The ODE Region (Mean)
${\bar{r}}_{2}$ symbol represents Fraction Of Population Density Of Removed In The ODE Region (Mean)
$ν_{1}^{T}$ symbol represents Unit Normal Vector
$ϕ_{e}$ symbol represents Asymptomatic Recovery Rate
$ϕ_{i}$ symbol represents Infected Recovery Rate
$r_{1}$ symbol represents Fraction Of Population Density Of Removed In The PDE Region

Rate Of Change Of Population Density Fraction Of Susceptibles Mean ODE	${\dot{\bar{s}}}_{2} \approx - (1 - \frac{A}{{\bar{n}}_{2} + n_{0}}) {\bar{s}}_{2} (β_{e} {\bar{e}}_{2} + β_{i} {\bar{i}}_{2}) - \frac{1}{\| Ω_{2} \|} \int_{Γ} ν_{1}^{T} D \nabla s_{1} d o$
$A$ symbol represents Allee Threshold
$D$ symbol represents Diffusion Coefficient for SEIR Model
${\bar{e}}_{2}$ symbol represents Fraction Of Population Density Of Exposed In The ODE Region (Mean)
${\bar{i}}_{2}$ symbol represents Fraction Of Population Density Of Infectious In The ODE Region (Mean)
${\bar{s}}_{2}$ symbol represents Fraction Of Population Density Of Susceptibles In The ODE Region (Mean)
$β_{e}$ symbol represents Asymptomatic Infection Rate
$β_{i}$ symbol represents Symptomatic Infection Rate
$ν_{1}^{T}$ symbol represents Unit Normal Vector
$n$ symbol represents Population Density
$s_{1}$ symbol represents Fraction Of Population Density Of Susceptibles In The PDE Region

Decomposition Of Population Density Fractions In The ODE Region Into Spatially Constant And Fluctuating Part	$\begin{aligned} s_{2} = \bar{s_{2}} + \tilde{s_{2}} \\ e_{2} = \bar{e_{2}} + \tilde{e_{2}} \\ i_{2} = \bar{i_{2}} + \tilde{i_{2}} \\ r_{2} = \bar{r_{2}} + \tilde{r_{2}} \end{aligned}$
$\tilde{e_{2}}$ symbol represents Fraction Of Population Density Of Exposed In The ODE Region (Fluctuating Part)
$\tilde{i_{2}}$ symbol represents Fraction Of Population Density Of Infectious In The ODE Region (Fluctuating Part)
$\tilde{r_{2}}$ symbol represents Fraction Of Population Density Of Removed In The ODE Region (Fluctuating Part)
$\tilde{s_{2}}$ symbol represents Fraction Of Population Density Of Susceptibles In The ODE Region (Fluctuating Part)
$\bar{e_{2}}$ symbol represents Fraction Of Population Density Of Exposed In The ODE Region (Mean)
$\bar{i_{2}}$ symbol represents Fraction Of Population Density Of Infectious In The ODE Region (Mean)
$\bar{r_{2}}$ symbol represents Fraction Of Population Density Of Removed In The ODE Region (Mean)
$\bar{s_{2}}$ symbol represents Fraction Of Population Density Of Susceptibles In The ODE Region (Mean)
$e_{2}$ symbol represents Fraction Of Population Density Of Exposed In The ODE Region
$i_{2}$ symbol represents Fraction Of Population Density Of Infectious In The ODE Region
$r_{2}$ symbol represents Fraction Of Population Density Of Removed In The ODE Region
$s_{2}$ symbol represents Fraction Of Population Density Of Susceptibles In The ODE Region