We now expand the approach used in
program 6.3 to implement eventdriven 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.
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)=NX(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.
Files
Python Program, MATLAB Code.
