Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic
Document Type
Article
Publication Date
5-1-2024
Abstract
The coronavirus disease 2019 (COVID-19) remains serious around the world and causes huge deaths and economic losses. Understanding the transmission dynamics of diseases and providing effective control strategies play important roles in the prevention of epidemic diseases. In this paper, to investigate the effect of delays on the transmission of COVID-19, we propose a delayed SEIR model to describe COVID-19 virus transmission, where two delays indicating the incubation and recovery periods are introduced. For this system, we prove its solutions are nonnegative and ultimately bounded with the nonnegative initial conditions. Furthermore, we calculate the disease-free and endemic equilibrium points and analyze the asymptotical stability and the existence of Hopf bifurcations at these equilibrium points. Then, by taking the weighted sum of the opposite number of recovered individuals at the terminal time, the number of exposed and infected individuals during the time horizon, and the system cost of control measures as the cost function, we present a delay optimal control problem, where two controls represent the social contact and the pharmaceutical intervention. Necessary optimality conditions of this optimal control problem are exploited to characterize the optimal control strategies. Finally, numerical simulations are performed to verify the theoretical analysis of the stability and Hopf bifurcations at the equilibrium points and to illustrate the effectiveness of the obtained optimal strategies in controlling the COVID-19 epidemic.
Keywords
Delayed SEIR, Stability, Hopf bifurcation, Optimal control, Necessary optimality conditions, Numerical simulation
Divisions
sch_ecs
Funders
National Natural Science Foundation of China (NSFC),Shandong Province Natural Science Foundation of China (ZR2023MA054) ; (12271307)
Publication Title
Journal of Inequalities and Applications
Volume
2024
Issue
1
Publisher
Springer
Publisher Location
ONE NEW YORK PLAZA, SUITE 4600, NEW YORK, NY, UNITED STATES