禽流感模型的动力学行为与最优控制研究

英文摘要AbstractAvian influenza is a zoonotic disease caused by the transmission of the avian influenza A virus.High pathogenic avian influenza has the characteristics of high mortality,and it not only affects thepoultry farming industry but also poses a great threat to human health.Therefore,it is of greattheoretical value and practical significance to study the transmission rule and control strategies ofhighly pathogenic avian influenza.By analyzing the characteristics of avian influenza transmissionand considering the different factors affecting the transmission of avian influenza,five avian influenzamodels are established by using the modeling idea of infectious disease dynamics in this paper.Thedynamic behavior of these models are analyzed and the optimal control of avian influenza are furtherstudied.The details are as follows:(1)Since poultry slaughtering can control the spread of avian influenza in time,a delayed SI-SIRavian influenza model with poultry slaughtering is established.First of all,the local asymptoticstability of the equilibria of the system are studied by using Routh-Hurwitz criterion and relat-ed theory,and the global asymptotic stability of the equilibria are proved through constructingLyapunov function and applying LaSalle invariant principle.Secondly,the corresponding opti-mal control problem is formulated by introducing the control variables,namely the slaughteringfor poultry and education campaign for the susceptible humans.Meanwhile,the existence anduniqueness of the optimal control is investigated.In the end,the accuracy of the analyticalresults are verified by numerical simulations.The numerical results show that slaughtering sus-ceptible(infected)poultry and educating susceptible humans can not only reduce the number ofinfected poultry (humans),but also minimize the cost of implementing these control strategies.(2)On the basis of research content(1),a delayed SI-SIR avian influenza model with Beddington-DeAngelis incidence rate in both poultry and human population is established.Then,threecontrol variables (one with time delay)are introduced to study the optimal control of the mod-el.The conclusions obtained in this part are as follows:implementation of hybrid controlscan significantly reduce the number of infected poultry (humans),and as the delay n or r2increases,the transmission rate of avian influenza will decline.Therefore,in order to preventthe spread of avian influenza,relevant departments should take multiple control strategies at thesame time as soon as possible,which can delay the outbreak of avian influenza and reduce thecost of control the avian influenza.(3)A stochastic delayed SEI-SIR avian influenza model with vaccination and mutation is proposedby considering the avian influenza virus mutates.Firstly,the existence and uniqueness of glob-al positive solutions of the system are studied.Secondly,the thresholds of persistence andextinction for the stochastic avian-only subsystem and the stochastic avian-huma