Data Simulation And Dynamic Analysis Of The Influenza Model

Influenza is a disease caused by the influenza virus, in China every year more than100,000people hospitalize with influenza infection, and some even die. Establishing Mathematical model has great contributed to our understanding of the occurrence and development of influenza.In this paper, using of ordinary differential equations qualitative and stability theory and computer tools, we establish no vaccine and vaccine model of influenza. According to the Chinese Center for Disease Control data, we simulate parameter using MATLAB to obtain the range of the basic reproduction number of influenza, then we estimate the annual production of vaccines; meanwhile, we calculate the disease-free equilibrium and endemic equilibrium point in the model, lastly we can prove the disease-free equilibrium is globally asymptotically stable.This article is divided into three parts. The first part we first briefly introduce the influenza virus and influenza study of the current situation, then some of the basics; The second part, we first introduce the relationship between the various types of influenza individuals, no vaccine and vaccine differential equations is established. Then according to the CDC from2009to2012influenza data, we estimate those parameters with MATLAB, and fit chi-square test of goodness, finally calculate influenza antigenic relatedness. Through calculating the basic reproduction number of influenza, we can see that the basic reproductive number of influenza in the range of1.1001-1.1561. Then we can estimate the amount of vaccine production is13.50%of the total number of susceptible which has important significance in guidance of vaccine production; In the third part, we analyze of dynamic character of differential equation, firstly we find out the balance point. When Ro<1, using of Hurwitz criterion shows that disease equilibrium is locally asymptotically stable, then through constructed the Lyapunov function and used the LaSalle invariable principle we has proved it is globally asymptotically stable. When Ro>1, the disease-free equilibrium is unstable.