Variables and parameters

Variable

Description

$S_i\left(t\right)$

Population of susceptible individuals of group i

$E_i\left(t\right)$

Population of exposed individuals of group i

$I_i\left(t\right)$

Population of infected individuals of group i

$R_i\left(t\right)$

Population of recovered individuals of group i

Parameter

Description

${\pi }_i$

Recruitment rates for individuals

${\beta }_i$

Effective contact rates for individuals

${\mu }_i$

Natural death rate for individuals

${\tau }_e$

Modification parameter for infectiousness of exposed

individuals in the $E_i$ class relative to those in the $I_i$ class

$m_{i\left(3-i\right)}$

Rate at which susceptible individuals migrate from group i

to group (3-i)

$a_{i\left(3-i\right)}$

Rate at which exposed individuals migrate from group i

to group (3-i)

${\alpha }_i$

Symptoms rate for exposed individuals

${\kappa }_i$

Recovery rate for symptomatic individuals

$n_{i\left(3-i\right)}$

Rate at which recovered individuals migrate from group i

to group (3-i)