Reed–Frost SIR/SEIR are discrete-time versions of infection transmission in a host population with standard (Susceptible, Exposed, Infectious, Recovered) compartments with the usual transition patterns:

.

The transition rate from each strata to the next is determined by a survival probability per unit time step (e.g. day). It measures what fraction of a given compartment will stay within the compartment. For instance, the fraction

of latent group

* *would remain latent over one time step, while the complementary

* *would advance to the next level

. The force of infection

depends on the resistance level of the

group (probability to survive an infectious contact)

, the contact rate

(per day), and the infected population fraction

(the product

gives the average number of infective contacts per day). Model parameters include:

The basic reproduction number (BRN) is

, which determines whether an infection outbreak occurs

or dies out

. It also controls the endemic level (provided

. In our setup, the total population

stays constant and the variables

represent population fractions (or prevalences) relative to

.

[1] Ohio Supercomputer Center Summer Institute. "Reed–Frost Epidemic Model." (May 22, 2012).