A Class Of SIQRS Infectious Disease Model Of Media Influence,vertical Transmission,isolation And Treatment

Infectious diseases is one of the important conditions,which is harmful to hu-man body health and the development of social survival.Therefore,it is one of the main methods to study the infectious disease control and prevention through the establishment of corresponding mathematical model to study the pathogenesis and spreading rules of infectious diseases and making reasonable control optimization s-trategy,which is crucial.This method is good for experts to find the the popular process of infectious disease,to reveal the development rule of disease,to predict the development trend of disease,the optimal control strategy,to formulate relevant effec-tive for infectious disease control and prevention and to provide important theoretical basis and reasonable guides.However,in the past study of infectious disease control,most results are based on the hypothesis that the population remains the same,but in fact the population and the population mobility input and output factors have a great influence on population change;Most past results failed to consider extensive use of mass media during the course of disease outbreaks.Public health departments and organizations make public outbreak of timely access to relevant information,encouraging people to change their way of life and reducing the severity of disease outbreak significantly.At present,most of the research work is researching the qualitative theory of differential equations,but rarely considering the cost control in practical control problems.Based on this,through reading a large number of literatures,references and the research status of infectious disease control at home and abroad in recent years,this article established a class of SIQRS infectious disease model of media influence,vertical transmission,isolation and treatment to mainly study the following questions:1.According to the H1N1 flu epidemic characteristics and transmission char-acteristics,we can make reasonable assumptions,choos appropriate parameters,and build a class of SIQRS infectious disease model of media influence,vertical transmis-sion,isolation and treatmenta to obtain its dynamic character threshold.This model is obtained by using the method of the next generation of matrix of the basic reproduc-tive number R0,through discussion and analysis of the basic reproductive number,using the method of Liapunov function,LaSalle invariable principle and Hurwitz criterion,proveding the vertical transmission and isolation treatment under the ex-istence of the disease-free equilibrium and the endemic equilibrium and stability.By setting different parameters for the numerical simulation for the model,the result shows that:when the R0<1,disease-free equilibrium global asymptotic stability of the disease will be totally eliminated;When R0>1,endemic equilibrium locally asymptotically stable,the disease will develop for endemic disease.2.On the basis of the first model,assume that the media reports and isolation treatment model changes over time,the disease infection rate and isolation treat-ment as control variables,the objective function is established,using the Pontryagin maximum principle,through introducing the Hamilton function,design method of optimal control law is given to prove the existence of the optimal control,and the forms of expression of the optimal control is given.3.By reference to literature and in combination with the actual statistics,the article uses mathematical software MATLAB to carry on the numerical simulation to verify the rationality of the model and the feasibility and effectiveness of the optimal control.Besides,it points out the realistic guiding significance of the measures,such as the media influence and isolation treatment during outbreaks.