TY - JOUR

T1 - Quarantine and Vaccination in Hierarchical Epidemic Model

AU - Gubar , Elena

AU - Taynitskiy , Vladislav

AU - Fedyanin, Denis

AU - Petrov, Ilya

N1 - Gubar, E.; Taynitskiy, V.; Fedyanin, D.; Petrov, I. Quarantine and Vaccination in Hierarchical Epidemic Model. Mathematics 2023, 11, 1450. https://doi.org/10.3390/math11061450

PY - 2023/3/16

Y1 - 2023/3/16

N2 - 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.

AB - 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.

KW - epidemic process

KW - compartment epidemic models

KW - SEIRD model

KW - optimal control

KW - vaccination

UR - https://www.mendeley.com/catalogue/27257790-abfe-3a34-a94f-e34f1eda7fc7/

U2 - 10.3390/math11061450

DO - 10.3390/math11061450

M3 - Article

VL - 11

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 6

M1 - 1450

ER -