Deterministic Epidemic Model Of Optimal Vaccination Control Strategy Study

The epidemic, which is one of harmful and terrible diseases to human health, has been received various countries'high attention for a long time. With the continuous development of technology and innovation, the quality and level of human life has been greatly improved, a great many threatening infectious diseases have been eliminated in most parts of the world, but if we wanted to conquer infectious diseases completely, the road is long and tortuously.This paper has established the corresponding dynamic model of infectious diseases, based on the model analysis, and has sought the most effective strategy to control the spread of infectious diseases. The majority infectious diseases control in the research are only to fit the epidemic situation data and to predict disease trends, study the effect of disease prevention through the basic regeneration number analysis, but have not considered the time-variable disease control policy actually. It has been given the dynamic vaccination isolation control law design method based on the optimal control theory principle, which discussed the optimal control strategy and the isolation control strategy for vaccination in the application of spread of SARS. Its main contents are as follows:Firstly, this chapter are discussed the deterministic epidemic model of SIR which based on vaccination, and qualitative analyzed the infectious disease model from the two cases of vaccination whether or not. Paying attention to health and raising the medical level are helpful to control the spread of infectious diseases or deterioration directly when without vaccination; theδ=1is the threshold value which is a measure of the infectious disease withvaccination whether away or not, proved the existence of disease-free equilibrium as well as the stability of the differentδvalue. How obtains to seek an optimal vaccination control strategy through the comparative analysis to be very important.Secondly, a class of deterministic optimal vaccination strategy for epidemic, which is discussed the application of the dynamic isolation and vaccination strategy for SARS epidemics control based on a deterministic epidemic model of SIQR. It has given the dynamic optimal control law design method with the Pontryagin's maximum principle, has proven the optimal control to be existence and uniqueness; the value simulation results illustrated the effectiveness of the optimal strategy for the vaccine inoculation and the isolation treatment control, and the results also demonstrated that the maximum implementations of vaccination in the early stage of the epidemic and isolation strategy in the initial period of epidemic erupts are having the practical significance.