Study On Three Classes Of Infectious Disease Models With Optimal Control

Optimal control is to find the extremum of a multivariate function on a given set,which is widely used.Optimal control has an important influence on the spread of infectious diseases.In this dissertation,three kinds of infectious diseases models with optimal control are proposed,stability analyses and numerical simulations of the models are provided,and the results of numerical simulations are also evaluated.(1)In order to clarify the influence of media coverage on the incidence of cervical cancer,firstly,a HPV epidemic model with optimal control is established.Then,the calculation formula of the control reproduction number is given,and the stability of the disease-free equilibrium is analyzed.After that,the mathematical model is analyzed by using optimal control theory.Furthermore,by the numerical simulation,we verify that media coverage and appropriate isolation measures can reduce the risk of HPV infection,thereby decreasing the number of cervical cancer.(2)In order to investigate the spread rule of influenza,we develop a kind of SVIQR influenza model with optimal control.Then,we calculate the control reproduction number of the model,and prove the stability of the disease-free equilibrium.Moreover,the optimal control strategy is analyzed.Finally,the numerical simulation is carried out with MATLAB to verify that the rational use of medical resources can effectively decrease the number of infected persons,thus effectively reduce the final size of the infected.(3)In order to study the impact of vaccination on the prevention of common infectious diseases,a kind of VSITR model with vaccination and treatment is established.Then,the control reproduction number of the model is given,and the stability of the disease-free equilibrium is proved.What is more,the optimal control strategy is analyzed.Finally,the numerical simulation with MATLAB shows that by reasonable vaccination and medical resources,the number of infections can effectively be reduced.Therefore,the scale of infectious diseases can be effectively reduced.