MathepiaModels

SEIAR(du,u,p,t)

Define classic SEIR(suspected-exposed-infected-asymptomatic-recovered) model.

Parameters: (birth rate, natural death rate, disaese induced death rate, population, infection rate, recovery rate, incubation period, exposed decreasing infection ratio, asymptomatic infection decreasing infection ratio, asymptomatic rate,recovery rate of asymptomatic)

\[\begin{aligned} & \frac{\rm{d}S}{\rm{dt}} = \Lambda -\beta S (I+k_{E}E+k_{A}A)/N - d S,\\ &\frac{\rm{d}E}{\rm{dt}} = \beta S (I+k_{E}E++k_{A}A)/N - \sigma E -d E,\\ &\frac{\rm{d}I}{\rm{dt}} =(1-\rho)\sigma E - \gamma I - d I - \alpha I,\\ &\frac{\rm{d}A}{\rm{dt}} =\rho\sigma E - \gamma_{A} A - d A,\\ &\frac{\rm{d}R}{\rm{dt}} = \gamma I +\gamma_{A} A - d R,\\ \end{aligned}\]

SEIR(du,u,p,t)

Define classic SEIR(suspected-exposed-infected-recovered) model.

Parameters: (birth rate, natural death rate, disaese induced death rate, population, infection rate, recovery rate, incubation period, exposed decreasing infection ratio)

\[\begin{aligned} & \frac{\rm{d}S}{\rm{dt}} = \Lambda -\beta S (I+k_{E}E)/N - d S,\\ &\frac{\rm{d}E}{\rm{dt}} = \beta S (I+k_{E}E)/N - \sigma E -d E,\\ &\frac{\rm{d}I}{\rm{dt}} =\sigma E - \gamma I - d I - \alpha I,\\ &\frac{\rm{d}R}{\rm{dt}} = \gamma I - d R,\\ \end{aligned}\]

SIR(du,u,p,t)

Define classic SIR(suspected-infected-recovered) model.

Parameters: (birth rate, natural death rate, disaese induced death rate, population, infection rate, recovery rate)

\[\begin{aligned} & \frac{\rm{d}S}{\rm{dt}} = \Lambda -\beta S I/N - d S,\\ &\frac{\rm{d}I}{\rm{dt}} = \beta S I/N - \gamma I - d I - \alpha I,\\ &\frac{\rm{d}R}{\rm{dt}} = \gamma I - d R,\\ \end{aligned}\]

SIS(du,u,p,t)

Define classic SIR(suspected-infected-suspected) model.

Parameters: (population, infection rate, recovery rate)

\[\begin{aligned} & \frac{\rm{d}S}{\rm{dt}} = -\beta S I/N + \gamma I,\\ &\frac{\rm{d}I}{\rm{dt}} = \beta S I/N - \gamma I,\\ \end{aligned}\]