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

SIR model with partial immunity (page 118)

We start Chapter 4 by considering a relatively simple complete but simple version of a model for two competing SIR disease strains. In this formulation NAB refers to the proportion of the population who are A with respect to disease 1 and B with respect to disease 2. The two diseases have differing basic epidemiological characteristics, hence β and γ are strain specific parameters. In addition, previous exposure to the one strain leads to differential levels of susceptiblity (controlled by α) and transmissibility (controlled by a) for the other strain. The basic equations are:

βi is the basic transmission rate for strain i.
γi is the recovery rate for strain i.
is the birth rate, which is set equal to μ
is the per capita death rate.
is the modified susceptiblity to strain i for those individuals recovered from the other strain.
is the modified transmission rate of strain i from those individuals that have recovered from the other strain.
NAB(0) is the initial proportion of the population in each group is set within the program.
All rates are specified in days.

All parameters must be positive.

Python ProgramMATLAB Code.

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