Abstract

The SIR (susceptible-infected-recovered) differential equations model for the spread of infectious diseases is very prominent in mathematical literature. The key interest of investigations is often to 1nd and analyse extensions of the basic model structure in order to introduce a more detailed and supposedly realistic representation of the underlying disease and population dynamics. It is however true that problems and solutions in healthcare and health economics actually tend to require more and more sophisticated modelling approaches which are also capable of incorporating larger data sets as parametrisation in an effective way. This makes the comparison and combination of different modelling techniques and results an important research topic. This paper investigates a probabilistic drift formulation of the basic differential equations model which allows a very 1ne-grained parametrisation of the progression of diseases. It is shown that this formulation is capable of reproducing results from models with delay. Aggregation leads directly back to the traditional compartment approach and, in the heterogeneous case, a discrete representation can be interpreted as a system of local Markov processes. Furthermore some preliminary results on epidemiological measures like the basic reproduction number are presented.