*! version 1.0.0 02apr2020
help epi_seir

Title

epi_seir -- Implementation of SEIR epidemiological model and simulations.

Syntax

epi_seir ,
options

Model parameters (if any of the options below is not specified, value 0 is assumed)

beta(#) The model parameter controlling how often a
susceptible-infected contact results in a new infection

gamma(#) The model parameter controlling for the rate of recovery

sigma(#) The model parameter controlling the rate
at which an exposed individual becomes infected

mu(#) The model parameter reflecting natural mortality
rate unrelated to the epidemic. The model assumes constant population
size, so mortality is compensated by the equivalent fertility
replenishing the susceptible population.

nu(#) The model parameter controlling vaccination rate
transferring a susceptible individual directly to recovered state.

Initial conditions (if any of the options below is not specified, value 0 is assumed)
susceptible(#) Number of susceptible individuals at t0

exposed(#) Number of exposed individuals at t0

infected(#) Number of infected individuals at t0

recovered(#) Number of recovered individuals at t0

Description

epi_seir calculates the deterministic SEIR model (susceptible-exposed-
infected-recovered), which is a theoretical model of the number of infected
individuals in a closed population over time. The model is commonly used for
modeling the development of directly transmitted infectious diseases (spread
through contacts between individuals). The model differs from SIR by the
introduction of another state (Exposed). The persons in this state have
had a contact with an infected person, but are not infectious themselves.

The initial conditions must be specified in absolute numbers, (not as shares, or in percent).

The output can be produced in absolute numbers, or in percentages.

The model is solved numerically by applying the fourth-order Runge-Kutta algorithm.

Examples

Simulation

. epi_seir , days(15) beta(0.9) gamma(0.2) sigma(0.5) susceptible(10) infected(1)

Perform SEIR model simulation for a population of 10 susceptible and 1
infected individuals over 15 days, and with specified values of the model
parameters. Then draw a graph of the number of individuals in each state.

. epi_seir , days(15) beta(0.9) gamma(0.2) sigma(0.5) susceptible(10) infected(1) recovered(2) clear

Same as above, but start also with 2 recovered individuals, and clear the
data in memory (if any).

. epi_seir , days(15) beta(0.9) gamma(0.2) sigma(0.5) susceptible(10) infected(1) recovered(2) clear nograph

Same as above, but without plotting any graph.

. epi_seir , days(15) day0("2020-02-29") beta(0.9) gamma(0.2) sigma(0.5) susceptible(10) infected(1) recovered(2) clear

Same as above, but with plotting of the graph and indicating that day zero
of the simulation corresponds to February 29, 2020.

Authors

Sergiy Radyakin, The World Bank

Paolo Verme, The World Bank

Also see

Online: epimodels homepage