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...

The paper is concerned with the first meeting or crossing problem between two independent trajectories for some basic counting processes. Our interest is focused on the exact distribution of the level and the time of this first meeting or crossing. The question is examined for a renewal process...

The collective epidemic model is a quite flexible model that describes the spread of an infectious disease of the Susceptible-Infected-Removed type in a closed population. A statistic of great interest is the final number of susceptibles who survive the disease. In the present paper, a necessary...