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Bifurcation analysis and optimal control of COVID-19 with exogenous reinfection and media coverages

International Journal of Biomathematics 2023年第3期16卷 83-118页

作者： Jiajia Zhang Yuanhua Qiao Yan Zhang Faculty of Science Beijing University of Technology Beijing 100124P.R.China

In this paper,a SEIR epidemic model related to media coverage and exogenous reinfections is established to explore the transmission dynamics of COVID-19.The basic reproduction number is calculated using the next generation matrix method.First,the existence of equilibrium points is investigated,and different kinds of equilibrium points indicate that the disease may disappear,or exist that result in different quantity of susceptible individuals,pre-symptomatic infected individuals and symptomatic infected individuals.The stability of the equilibria is discussed by a geometric approach,and it is found that controlling reproduction number to be lower than 1 is not suficient for eradication of COVID-19.Second,transcritical bifurcation is explored,and it is found that improving the ratio of exogenous reinfection may lead to backward bifurcation under poor medical conditions,which indicates that two endemic equilibrium points appear.Third,to investigate the infuence of parameters on the basic reproduction,sensitivity analysis is done to choose relatively sensitive parameters,and the parameters for treatment and media coverage are selected.An optimal control model is established to balance the treatment and media awareness.By exploring the existence and the uniqueness of the optimal control solution,the optimal control strategies are given.Finally,we run numerical simulations to verify the theoretical analysis on actual data of China,and the data from the four different states of India is used for forecasting the situation of infected individuals in a short period.It is found by the simulation that the co-function of treatment and media coverage results in the reduced number of infectious individuals.

关键词： COVID-19 backward bifurcation globally stable optimal control

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Global stability of a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment strategy

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International Journal of Biomathematics 2021年第5期14卷 221-238页

作者： Yanjun Zhao Huilai Li Wenxuan Li Yang Wang College of Humanities and Sciences Northeast Normal University Changchun 130117 P.R.China College of Mathematics Jilin University Changchun 130022P.R.China College of Mathematics Jilin Normal University Siping 136000P.R.China

We consider a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment.The treatment rate has at most a finite number of jump discontinuities in every compact interval.By using Lyapunov theory for discontinuous differential equations and other techniques on non-smooth analysis,the basic reproductive number Ro is proved to be a sharp threshold value which completely determines the dynamics of the model.If Roglobally stable.If Ro>1,the disease-free equilibrium becomes unstable and there exists an endemic equilibrium which is globally stable.We discuss that the disease will die out in a finite time which is impossible for the corresponding SEIR model with continuous treatment.Furthermore,the numerical simulations indicate that strengthening treatment measure after infective individuals reach some level is beneficial to disease control.

关键词： Latent period infected period discontinuous treatment globally stable global convergence in finite time

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Discrete Time Optimal Adaptive Control for Linear Stochastic Systems

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Tsinghua Science and Technology 2007年第1期12卷 105-110页

作者：姜睿罗贵明 Department of Computer Science and Technology Tsinghua University School of Software Tsinghua University

The least-squares （LS） algorithm has been used for system modeling for a long time. Without any excitation conditions, only the convergence rate of the common LS algorithm can be obtained. This paper analyzed the weighted least-squares （WLS） algorithm and described the good properties of the WLS algorithm. The WLS algorithm was then used for adaptive control of linear stochastic systems to show that the linear closed-loop system was globally stable and that the system identification was consistent. Compared to the past optimal adaptive controller, this controller does not impose restricted conditions on the coefficients of the system, such as knowing the first coefficient before the controller. Without any persistent excitation conditions, the analysis shows that, with the regulation of the adaptive control, the closed-loop system was globally stable and the adaptive controller converged to the one-step-ahead optimal controller in some sense.

关键词： stochastic system weighted least-squares （WLS） algorithm optimal adaptive control globally stable

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