The Computation of R(0) for Discrete-time Epidemic Models with Dynamic Heterogeneity

An explicit algorithm is given for the computation of the basic reproduction ratio R(0) (or the net reproduction ratio R in the case of a not wholly susceptible population) for a class of discrete-time epidemic models. These models allow for a finite number of different individual types, type changes at fixed type-dependent intervals, arbitrary contact intensity between individuals of the various types, and variable infectivity. The models reflect the situation where an infectious disease spreads in a population of animals that are reared in different stables on farms.In addition, it is shown analytically that the reproduction ratio depends, for any given type, on the product of the susceptibility and the total infectivity of that type and not on these factors 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 below 1, by vaccination or some other control measure, will result in R < 1 and will hence lead to eradication of the disease.