A Markovian epidemic model in a resource-limited environment

Abstract

In this paper, we present a Markov chain model to study infectious disease outbreaks assuming that healthcare facilities, specifically the number of hospital beds for infected individuals, are limited. Therefore, only a restricted number of infected individuals can be admitted to a hospital ward and receive medical care at the same time. Since the pathogen spreads both inside and outside the ward, modeling the dynamics of the epidemic involves SIS- and SI-type models that are inherently linked to each other, in such a way that the potential transmission of the pathogen outside the ward is only possible when the hospital ward is working functionally full. Our goal is to study the influence of the resource-limited environment on performance measures related to hospital operations, such as the time until the ward reaches its maximum capacity, the number of critical events —occurring when the hospital ward reaches its maximum capacity—, the time that limited healthcare facilities should be continuously active, or the economic impact of administering therapeutic treatments, which could be evaluated in terms of the number of admissions and the number of treatments provided in the case of reinfection.