Distribution of the final state and severity of epidemics with fatal risk

This paper considers a Markovian epidemic process for the spread of an infectious disease with fatal risk. The model includes as extreme cases two classical models, the general epidemic (for those diseases that confer immunity after infection) and the fatal epidemic (for those diseases that lead inevitably to death). Our purpose is to derive the joint exact distribution of the final state and severity of the disease process. These statistics provide a measure of the total damage caused by the epidemic. The approach followed relies on the construction of a family of martingales and then the use of a nonstandard family of polynomials. The two special models above are discussed separately.