Stochastic SEIRD model
The model is SEIRD model, where infected individuals can survive or die at different rates, with waning immunity. The full model specification is:
- $S$: susceptibles
- $E$: exposed, i.e. infected but not yet contagious
- $I_R$: infectious who will survive
- $I_D$: infectious who will die
- $R$: recovered
- $D$: dead
There are no birth of natural death processes in this model. Parameters are:
- $\beta$: rate of infection
- $\delta$: rate at which symptoms appear (i.e inverse of mean incubation period)
- $\gamma_R$: recovery rate
- $\gamma_D$: death rate
- $\mu$: case fatality ratio (proportion of cases who die)
- $\epsilon$: import rate of infected individuals (applies to $E$ and $I$)
- $\omega$: rate waning immunity
The model will be written as: