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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.
Parameters
| 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.
Requirements.
All parameters must be positive, b1 ≤ 1, and S(0)+I(0) ≤ 1.
Files
MATLAB Code, Python Program, R Code, C++ Program, Fortran Program, Parameters.
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