Alcoholism Models With Media Coverage And Its Optimal

In recent years,alcoholism has become the focus of the community.It has become the third risk cause of disability,as well as the common cause of at least200 diseases.Some studies have shown that many health problems and even global burden of disease are closely related to alcoholism,with about 3.8% of the world's death and 4.6% of disability attributable to alcohol.More and more scholars establish mathematical model to study behavior of alcoholism and seek effective control measures.However,with the highly development of the media industry,the media it can reduce the contact rate of non drinkers and alcoholics and enhance the alcoholics abstinence consciousness.Therefore,alcoholism model with media coverage it is more practical.In view of this,we firstly discuss an alcoholism model with media coverage.Secondly,we present an alcoholism model with media coverage and time delay.In chapter 1,we focus on the introduction of the background,current research situation,and the related theoretical basis and preliminary knowledge are described.In chapter 2,we construct an alcoholism model with media coverage,and both consider the effect of the media on the contact rate and alcoholics.we calculate the basic reproduction number,testify the globally asymptotically stable of alcohol free equilibrium by Lyapunov function method,and analyse locally asymptotically stable of alcoholism equilibrium through the Routh-Hurwitz criterion.Moreover,we use optimal control theory to give the optimal strategy for controlling alcoholism.Further,the conclusion is verified by numerical simulation.In chapter 3,we establish an alcoholism model with media coverage and time delay,which mainly consider the influence on unaware susceptible and alcoholics.When = 0,we demonstrate the locally asymptotically stable of two equilibria;when > 0,it's presented that the condition of stability of the alcoholism equilibrium and existence of the Hopf bifurcation.At last,numerical simulations are also shown to support our results.