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:
All rates are
is the basic transmission
rate for strain i.
recovery rate for strain i.
the birth rate, which is set equal to μ
|is the per capita death rate.
the modified susceptiblity to strain i
for those individuals recovered from the other strain.
|is the modified
rate of strain i from those individuals that have recovered from the
proportion of the population in each group is set within the program.
All parameters must be positive.
Python Program, MATLAB Code.