THE COMPUTATION OF R(0) FOR DISCRETE-TIME EPIDEMIC MODELS WITH DYNAMIC HETEROGENEITY

An explicit algorithm is given for the computation of the basic reprod uction ratio R(0) (or the net reproduction ratio R in the case of a no t wholly susceptible population) for a class of discrete-time epidemic models. These models allow for a finite number of different individua l types, type changes at fixed type-dependent intervals, arbitrary con tact intensity between individuals of the various types, and variable infectivity. The models reflect the situation where an infectious dise ase spreads in a population of animals that are reared in different st ables on farms. In addition, it is shown analytically that the reprodu ction ratio depends, for any given type, on the product of the suscept ibility and the total infectivity of that type and not on these factor s separately. We call this product the transmission weight of the type . The maximum overall transmission weight gives an upper bound for the reproduction ratio, irrespective of the particular submodels for type change and contact structure. Reduction of all transmission weights b elow 1, by vaccination or some other control measure, will result in R < 1 and will hence lead to eradication of the disease.