An Enhanced Epidemic Susceptible-Infected-Hospitalized-Recovered-Deceased (SIHRD) Stochastic Model with Emphasis on the Impact of Hospitalizations on Epidemic Evolution

In this paper, we focus on a novel stochastic epidemiological Susceptible-Infected-Hospitalized-Recovered-Deceased (SIHRD) model with emphasis on the impact of hospital admissions on epidemic evolution. The proposed stochastic model offers an advanced and effective method to evaluate an epidemic because it considers both hospitalized and deceased cases at the same time, which are the most informative indicators for assessing the severity of an outbreak. Several stochastic quantities are estimated, such as the maximum number of hospitalized cases, the total number of hospitalizations until epidemic extinction, the time of reaching a critical number of hospitalizations and the joint distribution of total infections and hospitalizations until the extinction of the disease. We underline that this analysis focuses not only on time-related characteristics, but especially on the introduction of size-related features, such as the total, maximum sizes and joint distributions. Formulas are provided for the computation of the distributions and moments of interest, leading to additional information beyond the average trend of the stochastic characteristics. Illustrative examples and a detailed sensitivity analysis shed light on the influence of the system’s parameters on the tendencies of the features studied. Additionally, important remarks regarding efficient computational techniques for high-dimensional matrix equations and reduced storage requirements are presented. The state of hospitalized cases can also be considered as a quarantine or isolation state without imposing changes to the epidemic scheme, thus increasing the generalizability of the proposed model. Finally, knowing the maximum number of hospitalized cases along with the time required to reach this critical level can facilitate timely hospital coordination.