The maximum number of infected individuals in SIS epidemic models: Computational techniques and quasi-stationary distributions

We study the maximum number of infected individuals observed during an epidemic for a Susceptible–Infected–Susceptible (SIS) model which corresponds to a birth–death process with an absorbing state. We develop computational schemes for the corresponding distributions in a transient regime and till absorption. Moreover, we study the distribution of the current number of infected individuals given that the maximum number during the epidemic has not exceeded a given threshold. In this sense, some quasi-stationary distributions of a related process are also discussed.