Modeling Infectious Diseases in Humans and Animals
Matt J. Keeling & Pejman Rohani

SIR model with corrected term-time forcing (page 171)

An alternative model of seasonal forcing, based very much on the behaviour of measles and other childhood-diseases, is to include term-time forcing. As such the transmission rate is higher during school terms and lower during school holidays. The equations become:

Where Term is +1 during the school terms and -1 during the holidays.
β0 is the mean transmission rate
b1 is the amplitude of term-time forcing
μ is the per capita death rate, and the population level birth rate.
γ is called the removal or recovery rate, though often we are more interested in its reciprocal (1/γ) which determines the average infectious period.
S(0) is the initial proportion of the population that are susceptible.
I(0) is the initial proportion of the population that are infectious.
All rates are specified in days.

The programs can return either standard time-series, or bifurcation plots. Bifurcation plots are achieved by setting b1 to be a vector in the Matlab code, or by setting Num_Bif_Steps in the parameter file for the C and Fortran code.

All parameters must be positive, b1 ≤ 1, and S(0)+I(0) ≤ 1

C++ ProgramPython ProgramFortran ProgramParametersMATLAB Code.

Questions and comments to: or
Princeton University Press
Our research web pages:
Matt Keeling      Pejman Rohani