### Susceptible – Exposed – Infectious – Recovered

The SIER model is similar to the SIR model, but adds and extra category ‘Exposed’ for those who have caught the disease, but are not yet infectious giving three groups (or compartments):

- Susceptible – Those who do not have the disease and thus can be infected.
- Exposed – Those who have caught the disease but are not yet infectious.
- Infectious – Those where the disease as developed and potentially may infect others
- Recovered – Those who have had the disease and are now recovered and thus not able to re-catch the disease (at least for a period).

As with the SIR model, be aware that ‘R’ can also refer to the ‘reproduction number’. Also note that the Infectious group is sometimes simply called ‘Infected’ as in SIR.

The SIR model has the same *alpha* and *beta* parameters as SIR, but also has a third parameter *gamma* to control the rate at which the disease progresses from E to I:

*alpha*– the transmission rate, that is the number of people per day that potentially catch the disease from an infected person, assuming they are susceptible.*beta*– the proportion of infected people who recover each day. For the purposes of this model deaths are treated the same as recovery, someone who cannot catch the disease again.*gamma*– the proportion of exposed people each day where the disease progress to be infectious.

For these we can calculate:

- The average time a person stays exposed before becoming infectious is days.
- The average time a person stays infectious is days.
- The average time a person stays infected (from first exposure to recovery) is days.
- The reproduction number (also called R), “the average number of secondary infections produced by a single infected person” (gov.uk) is the reproduction rate the average number of people who catch the disease.

We’ll start with a total population of and initially exposed people.