On the formulation of discrete-time epidemic models

Jacquez constructed a properly posed, more general model for the Reed-Frost epidemic process by assuming independent behaviors for the susceptibles and introducing the generating function for the number of contacts per person. An alternative approach is proposed here that relies on similar hypotheses for the infectives and allows the usual chain-binomial structure of the infection process to be extended. For this new model, the derivation of the final size and the threshold phenomenon becomes much simpler. A detailed analysis and its generalization to heterogeneous populations and continuous-time models will be the subject of a forthcoming paper.