Applications of martingale theory to some epidemic models, II

We consider Weiss's and Downton's models with parametersπ, αandβdepending oninumber of susceptibles andjnumber of carriers. A martingale argument is performed when πandα /βonly depend onior, in Weiss's case, whenα /βis the product of a function ofiby a function ofj.In these cases the martingale approach proves very valuable and gives explicit results quite easily. In particular it shows that well-known relations between moments and integrals along a trajectory are still true for any stopping time and for more general models than the classic ones.