Novel stochastic descriptors of a Markovian SIRD model for the assessment of the severity behind epidemic outbreaks

• Published in: Journal of the Franklin Institute Vol. 361; no. 12; p. 107022
• Main Author: Papageorgiou, Vasileios E.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.08.2024
• Subjects: Continuous-time Markov chains; Epidemiology; Final size; First-passage time; Stochastic processes; Stochastic SIRD model; Stochastic SIRD model; First-passage time; Final size; Epidemiology; Stochastic processes; Continuous-time Markov chains
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/j.jfranklin.2024.107022

•Novel stochastic descriptors according to a Markov-based SIRD model are proposed.•We examine size-related stochastic features like the maximum infective cases, the total numbers of infections, and deaths.•We investigate the time until an alarming threshold of infective or deceased cases is reached.•New formulae for the computation of the distributions and moments of the studied stochastic features are presented.•The proposed descriptors can assist health authorities in making decisions that will reduce the mortality risk. In contemporary epidemiology, it is of paramount importance to effectively evaluate epidemic occurrences by employing novel approaches that yield dependable predictions for the progression of widespread outbreaks. The present paper focuses on proposing novel stochastic descriptors based on a Markovian SIRD (susceptible-infected-recovered-deceased) epidemiological scheme that accounts for multiple re-infections. A continuous-time, three-dimensional Markovian process is employed tailored to the characteristics of the presented SIRD model. Our study examines several new time- and especially size-related characteristics, including the final size of infections and deaths, the maximum number of concurrent infectious cases, and the alarm time associated with escalating numbers of infections or deaths. We present theorems and algorithms for the determination of the distributions and moments of key statistical measures. Additionally, we share further insights on effective computational techniques designed to enhance the efficiency of employing the suggested algorithms. Moreover, numerous illustrative instances, coupled with a thorough sensitivity analysis, demonstrate how system parameters affect the severity of epidemics. This not only bolsters the credibility of the outcomes, but also underscores the significance of the suggested stochastic descriptors when assessing real-life epidemics. At the same time, we examine the applicability of the proposed methodology to real Marburg fever data in Angola. Unlike other approaches that mainly concentrate on using mathematical models to fit the evolution of a disease, our goal is to complement these studies by emphasizing significant aspects that play an important role in assessing the seriousness of epidemics. The introduced epidemiological quantities can aid public health authorities in making well-informed choices, potentially leading to a substantial decrease in both mortality rates and socio-economic repercussions. 62G30, 60G10, 62P10, 62G32