Dynamics Of Two Kinds Of Alcoholism Models With Media Reports

With the continuous improvement of the economic level,people’s pressure is also increasing,which is the emergence of drinking problems,which.Therefore,the problem of controlling alcohol abuse will attract great attention.Media reports play a controlling role in the problem of alcoholism to a certain extent.Therefore,two types of alcoholism models with media reports are established in this paper,and theoretical analysis is performed.The numerical results are used to verify and popularize the theoretical results.The first chapter gives the current research status of alcoholism and related preparatory knowledge related to this article.In Chapter two,due to the influence of the media,the ratio of alcoholics to permanent abstinence generally increases.Correcting the influence of alcoholics on the media,theratio from alcoholics to permanent alcoholics is (?),due to the treatment of alcoholics or other factors,some alcoholics become moderate or non-alcoholics.A class of alcoholism models is established.Using the regeneration matrix and constructing the Lyapunov function,the basic regeneration number is obtained R0.By simple computation,it is concluded that when R0<1,the alcohol-free equilibrium point is globally asymptotically stable,and when R0>1,there is uniqueness in the alcoholic equilibrium point.The alcoholic equilibrium point is locally asymptotically stable through simulation.Finally,the theory is verified and generalized by numerical simulations.In Chapter three,based on the model in Chapter two,classifies alcoholics are divided into light drinkers and heavy drinkers.At the same time,by considering the self-control and the influence of external factors,some people will often become easy drinkers Or heavy drinkers.A more complex and realistic new model of alcoholism with recurrence and media coverage is established.The regeneration matrix method is used to calculate the basic regeneration number of the model R0.When R0<1 is true,and certain conditions,are satisfied the alcohol-free equilibrium point of E0 is globally asymptotically stable,and then it is proved that when R0>1,the alcohol-equilibrium equilibrium point of E*exists,and numerical simulation is used to obtain is lead stability.Finally,the optimal principle of prevention and control was obtained by using the Pontryagin maximum value principle.the theoretical results are verified and generalized by numerical simulations.The conclusions can provide some theoretical guidance for controlling alcoholism.