Optiaml Contral And Data Simulation Of An Epidemic Model

Epidemic is one of the major threats to public health of human.It is one of the major methods to study the scientific principle of control strategy by studying the pathogenesis and the law of transmission of epidemic diseases.However,in the past researches of the infectious disease control,most of the propagation coefficient is a constant in the whole epidemic period,that cannot describe the character of some diseases(such as influenza,scarlet fever,etc.)with a long duration and obviously seasonal variations accurately.In this paper,a new class of SEIJAR model is established,which is based on the SEIQINAR model of Qingxia Zhang et al.,and SEAIJRD model of G.et al.,which mainly focus on of class-a and class-b infectious diseases.This paper mainly studies the following problems:1.With the characteristics of the common infectious diseases in daily life,it is considered that the antiviral drug is sufficient and the SEIJAR model is established on this hypothesis.The model has two important characteristics: First,the model takes the mobility of the population into consideration,including the latent and asymptomatic infected ones from the outside.Secondly,the use of the vaccine and quarantine control measures are introduced in the model.When a patients with clinical symptom is found,he receives treatment immediately.Some of the patients with severe symptoms will be isolated.Using the Pontryagin maximum principle,the optimal control problem is transformed into a SEIJAR model with minimum Hamiltonian function,then we prove the existence of the optimal control and the form of optimal control is proved.2.Many epidemics outbroken in temperate regions have strong seasonal fluctuations,so the SEIJAR model takes the factors of seasonal effects into consideration and the seasonal effects in disease performance on transmission speed ?.Based on the analysis of the data of class-a and class-b infectious diseases in Jiangsu province from January 2013 to July 2016,we find out the manifestation of disease transmission speed under the seasonal influence.Using Pontryagin maximum principle,we find the specific form of optimal control of the SEIJAR model with the seasonal effects.Finally,with the help of Runge-Kutta iterative algorithm and the numerical simulation,we test the effectiveness of the optimal control and the sensitivity analysis of several parameters related with seasonal effects.It is proved that after the outbreak of disease with seasonal infectious,the consideration of seasonal factors has great influence on the strategy of optimal control.