Dynamic Analysis And Optimal Control Of A Class Of Ebola Epidemic Model

Ebola Virus Disease is a rare infectious disease caused by Ebola virus,with a high mortality rate.The devastating effects of several Ebola outbreaks in West Africa in recent years have also renewed public concern over the deadly disease.In order to effectively control the spread of Ebola,it is necessary to establish a suitable mathematical model to study its propagation law.This paper presents a mathematical model of Ebola virus disease composed of susceptible individuals S(t)-exposed individuals E(t)-infected individuals I(t)-recovered individuals R(t)-dead but still infectious individuals D(t)to study the spread of the disease in the population and the corresponding optimal control problem.Chapter 1,we introduce the research background of infectious disease and Ebola virus disease and the current research situation at home and abroad,and point out the main re-search contents of this paper.Chapter 2,we introduce some preparatory knowledge about the dynamics of infectious disease and optimal control.Chapter 3,considering the infectivity of infected bodies and vaccination of susceptible individuals,a new mathematical model SEIRD model on Ebola virus disease is proposed.Firstly,the nonnegative and boundedness of the solution of the infectious disease model is proved.Then the basic regeneration number R₀is obtained by using the classical regen-eration matrix method to predict whether infectious disease will die out or spread.Lastly,the existence and stability of the disease-free equilibrium point and the endemic equilibrium point are proved respectively,that is,when the basic regeneration number R₀<1,the disease-free equilibrium point is globally asymptotically stable in the feasible domain,indi-cating that Ebola virus disease will eventually die out;when the basic regeneration number R₀>1,the endemic equilibrium point is globally asymptotically stable in the feasible region,indicating that Ebola virus disease will eventually spread in the population and form endemic disease.Chapter 4,based on the SEIRD model proposed in chapter 3,two controls(vaccination of susceptible individuals,drug treatment of infected individuals)are introduced to establish the corresponding optimal control model,and the optimal control strategies to control the spread of Ebola virus are studied by using the optimal control theory.Chapter 5,we mainly use the Matlab to explain the proposed SEIRD model numerical-ly.By assigning different parameters,the model is simulated to verify the global asymptotic stability of the equilibrium point and the effectiveness of the optimal control.Chapter 6,we summarize the research contents of this paper,point out the innovation points of this paper,and give out the prospect.Finally,thanks and references.