A stochastic Markov-based modeling framework with demography

Stochastic epidemic modeling has become increasingly crucial for assessing the severity of infectious diseases, attracting considerable attention in recent years. In this paper, we present three Markov-based epidemic models that incorporate demographic dynamics, including births, deaths, and migration. The inclusion of transition rates associated with these factors defines open-population systems, leading to a time-dependent transition pattern from the susceptible to the infectious phase. Notably, this work is the first to investigate epidemic models with time-varying population sizes within a Markovian framework. Furthermore, we introduce novel computational approaches for estimating stochastic features related to the number of secondary infections originating from an index case and the onset of a hazard (hitting) time associated with the number of susceptible cases in the system. Through extensive sensitivity analysis, we assess the impact of demographic dynamics on these descriptors and, consequently, on the severity of epidemic outbreaks. To validate the effectiveness of the introduced models, we utilize data from the 2022 mpox outbreak in Greece and examine the effect of interventions such as lockdowns on disease severity. This analysis helps health authorities identify optimal initiation periods and more effectively adjust the stringency of restrictive measures.