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: