Application Of Nonlinear Model Predictive Control In The Containment Of Epidemic Processes

Infectious diseases have always been one of the great challenges facing mankind.How to formulate control strategies to take the epidemic under control during an outbreak is a scenario that worthy of study.Mathematical model is an important tool for studying the containment of the epidemic process.However,most of the former studies can only make theoretical analysis and evaluation,which make it inconvenient to practical use.Combining the dynamic model of infectious diseases with nonlinear model predictive control(NMPC),this thesis creates a new method to formulate epidemic control strategy,which can provide feasible control policies based on the feedback from the real epidemic process.The main works of this thesis are as follows:1.A process model(SI_g I_qR model)of epidemic control system with quarantine as the control measure is established by introducing state variable I_q and control variable u in the SIR model.In particular,we take the number of cases under quarantine as the output variable,which can be accurately observed,and can effectively avoid errors caused by inaccurate data.Based on the above model,a state observer is designed to estimate and feedback the states of the system in real time,and its asymptotic stability is proved afterwards.Finally,the NMPC algorithm for epidemic control is constructed by combining online optimization with state feedback.2.We simulate the epidemic process that can be described by the SI_g I_qR model.And then,quarantine policy is obtained by running the algorithm we proposed.The simulation results show that the control strategy calculated by our algorithm can take the epidemic under control effectively,and can eradicate the infection from the population quickly.3.For practical application,we study the NMPC of Ebola Virus Disease(EVD)in the context of the outbreak in Liberia from 2014 to 2016.Firstly,according to the characteristics and control measures of EVD,we establish an integrated control model(SEI_QI_GI_HFR model)which has seven state variables and four control variables,and estimate the parameters by fitting the uncontrolled model to the data in the early stage of the outbreak.And then,NMPC algorithm for EVD is proposed based on SEI_QI_GI_HFR model,and numerical simulations are carried out to obtain the NMPC strategy for EVD.Driven by the NMPC strategy obtained by our algorithm,the cumulative number of cases and deaths are significantly less than that of official statistics.In addition,7881infectious and 3296 deaths can be averted.The epidemic control method proposed in this thesis can be carried out in real time,which enables us to formulate control strategy according to the feedback from the actual epidemic process.Therefore,it is more flexible and convenient to practical use.