Program 6.4 - SIR model with demographic stochasticity
We now expand the approach used in program 6.3 to implement event-driven stochasticity into the standard SIR equations. There are now six different possible events which we have to consider:
Once again we assume that the population size N is constant which prevents the permanent extinction of the host population.
Note that we are using numbers (X,Y,Z) throughout this chapter for greater clarity.
Note that we are using numbers (X,Y,Z) throughout this chapter for greater clarity.
Parameters
| β | is the transmission rate and incorporates the encounter rate between susceptible and infectious individuals together with the probability of transmission |
| 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 |
| μ | is the per capita death rate |
| X(0) | is the initial number or density of susceptible individuals |
| Y(0) | is the initial number or density of infectious individuals |
| N | is the population size -- assumed to be constant. We assume Z(0)=N-X(0)-Y(0) |
All rates are specified in days.
Requirements.
All parameters must be positive. Remember, X, Y, Z and N all refer to integer numbers.
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