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.
|| is the transmission
rate and incorporates the encounter rate between susceptible and
infectious individuals together with the probability of transmission.
called the removal
or recovery rate, though often we are more interested in its reciprocal
(1/γ) which determines the average infectious period.
the per capita death
the initial number or density of susceptible individuals.
the initial number or density of infectious individuals.
size -- assumed to be constant. We assume Z(0)=N-X(0)-Y(0)
All parameters must be positive. Remember, X, Y, Z and N all refer to integer
Python Program, MATLAB Code.