A Novel Technology-Based Stochastic Epidemic Model

Annual Meeting in Mathematics 2023

Abstract

In this article, we propose a new discrete-time stochastic epidemic compartment model to study and analyze the spread of disease. The SUQIHR model consists of six compartments; Susceptible (S), Unsafe (U), Quarantined (Q), Infected (I), Hospitalized (H) and Recovered (R). The Unsafe class (U) comprises individuals who are at higher risk of infection compared to the general susceptible population, such as those with close contact to infected individuals. Transitions between compartments are assumed to follow certain probability distributions that capture the movement of individuals. The advancement of tracking technologies enables the differentiation of unsafe individuals from susceptible ones through the use of tracking equipment or mobile applications. Therefore, this model finds relevance in technology-ready societies. In this study, we utilize the SUQIHR model to forecast the future spread of diseases. The model incorporates both the transmission dynamics of epidemics and measures to control their spread. We examine the mathematical analysis of the model such as long-term behavior, the basic reproduction number and sensitivity analysis. Moreover, the Monte Carlo simulation can be employed to study the survival distribution of the outbreak, the final size of infected individuals, and the expected duration of the epidemic. By this comprehensive approach, our model provides valuable insights for understanding and managing disease outbreaks in various scenarios.