Quarantine and Vaccination in Hierarchical Epidemic Model

Elena Gubar (), Vladislav Taynitskiy (), Denis Fedyanin and Ilya Petrov
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Elena Gubar: Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg 198504, Russia
Vladislav Taynitskiy: Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg 198504, Russia
Denis Fedyanin: V. A. Trapeznikov Institute of Control Sciences of RAS, Moscow 117997, Russia
Ilya Petrov: V. A. Trapeznikov Institute of Control Sciences of RAS, Moscow 117997, Russia

Mathematics, 2023, vol. 11, issue 6, 1-17

Abstract: The analysis of global epidemics, such as SARS, MERS, and COVID-19, suggests a hierarchical structure of the epidemic process. The pandemic wave starts locally and accelerates through human-to-human interactions, eventually spreading globally after achieving an efficient and sustained transmission. In this paper, we propose a hierarchical model for the virus spread that divides the spreading process into three levels: a city, a region, and a country. We define the virus spread at each level using a modified susceptible–exposed–infected–recovery–dead (SEIRD) model, which assumes migration between levels. Our proposed controlled hierarchical epidemic model incorporates quarantine and vaccination as complementary optimal control strategies. We analyze the balance between the cost of the active virus spread and the implementation of appropriate quarantine measures. Furthermore, we differentiate the levels of the hierarchy by their contribution to the cost of controlling the epidemic. Finally, we present a series of numerical experiments to support the theoretical results obtained.

Keywords: epidemic process; compartment epidemic models; SEIRD model; optimal control; vaccination (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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