Modeling Infectious Diseases in Humans and Animals
Matt J. Keeling & Pejman Rohani

SIR model with demographic stochasticity (page 203)

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.

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.
is the population size -- assumed to be constant. We assume Z(0)=N-X(0)-Y(0)
All rates are specified in days.

All parameters must be positive. Remember, X, Y, Z and N all refer to integer numbers.

Python ProgramMATLAB Code.

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