*! version 1.0.0 02apr2020
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Title

epi_sir -- Implementation of SIR epidemiological model and simulations.

Syntax

epi_sir ,
options

Model parameters (optional, assumed to be zero if not specified)
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.

Initial conditions (optional, assumed to be zero if not specified)
susceptible(#) Number of susceptible individuals at t0

infected(#) Number of infected individuals at t0

recovered(#) Number of recovered individuals at t0

Description

epi_sir calculates the deterministic SIR model
(susceptible-infected-recovered), which is a theoretical model of the number of
infected individuals in a closed population over time.

"The SIR (susceptible-infected-removed) model was developed by Ronald Ross, William Hamer, and others in the early twentieth century." online

The model is commonly
used for modeling the development of directly transmitted infectious disease
(spread through contacts between individuals). See Kermack-McKendrick (1927)
for the model description and assumptions.

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

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

Examples

Simulation

. epi_sir , days(100) beta(0.9) gamma(0.3) susceptible(10) infected(1)

Perform SIR model simulation for a population of 10 susceptible and 1
infected individuals, with infection rate 0.9 and recovery rate 0.3 over 100
days, and display graph

. epi_sir , days(100) beta(0.9) gamma(0.3) 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_sir , days(100) beta(0.9) gamma(0.3) susceptible(10) infected(1) recovered(2) clear day0(2020-02-29)

Same as above, but indicate dates on the graph starting from
Feb.29, 2020 corresponding to day0 of the simulation.

. epi_sir , days(100) beta(0.9) gamma(0.3) susceptible(10) infected(1) recovered(2) clear nograph

Same as above, but without plotting any graph.

References

Carlos Castillo-Chavez, Fred Brauer, Zhilan Feng (2019). Mathematical Models in Epidemiology. New York: Springer.

Kermack, W. O. and McKendrick, A. G. (1927). Contributions to the mathematical
theory of epidemics, part i. Proceedings of the Royal Society of Edinburgh. Section A. Mathematics. 115 700-721
online

The SIR Model for Spread of Disease. Mathematical Association of America. online

Authors

Sergiy Radyakin, The World Bank

Paolo Verme, The World Bank

Also see

Online: epimodels homepage