The number of inspections until the extinction of an epidemic in a discrete-time stochastic SIS-type model with some applications

Abstract

This talk deals with an infective process of type SIS, taking place in a closed population of moderate size that is inspected periodically. Our purpose is to study the extinction time counterpart in discrete-time, that is the random variable that counts the total number of inspections that find an active epidemic process. As the underlying mathematical model involves a discrete-time Markov chain (DTMC) with a single absorbing state, the number of inspections in an outbreak is a first-passage time into this absorbing state. Cumulative probabilities are numerically determined from a recursive algorithm and expected values came from explicit expressions. Additionally, I provide several applications derived from the theoretical results. The talk is based on the paper: Gamboa M. and López-Herrero M.J. (2018). On the number of periodic inspections during outbreaks of discrete-time stochastic SIS epidemic models. Mathematics 6, article 128.DOI: 10.1007/s11538-013- 9836-3