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

Authors:
J. R. Artalejo;A. Economou;M. J. Lopez-Herrero
Affiliations:
Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, 28040 Madrid, Spain;Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece;School of Statistics, Complutense University of Madrid, 28040 Madrid, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

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.