Reed-Frost SEIR Model

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The Reed–Frost model for infection transmission is a discrete time-step version of a standard SIR/SEIR system: Susceptible, Exposed, Infectious, Recovered prevalences ( is blue, is purple, is olive/shaded, is green). This Demonstration lets you explore infection history for different choices of parameters, duration periods, and initial fraction.

Contributed by: David Gurarie (May 2012)
Open content licensed under CC BY-NC-SA



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).

[2] Animal Population Health Institute, Colorado State University. "Deterministic and Stochastic Reed–Frost Epidemic Modeling Software." (May 22, 2012)

[3] G. Davis. "Simple Reed–Frost Equation." (May 22, 2012).

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