An alternative model of
seasonal forcing, based very much on the behaviour of measles and other
childhooddiseases, is to include termtime 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.
Parameters
β_{0} 
is
the mean transmission
rate 
b_{1} 
is
the amplitude of termtime 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 timeseries, or bifurcation
plots. Bifurcation plots are achieved by setting b_{1} to be a vector in the
Matlab code, or by setting Num_Bif_Steps in the parameter file for the
C and Fortran code.
Requirements.
All parameters must be positive, b_{1}
≤ 1, and S(0)+I(0) ≤ 1
Files
C++ Program, Python Program, Fortran Program, Parameters, MATLAB Code.
