Analysis Of Two Different Dynamic Models Of Infectious Diseases

The dynamic model of infectious diseases is an important part of the biological mathematical model.In recent years,it has been widely concerned by many scholars at home and abroad,and has achieved many results.This article includes two models.The first model studies vaccination and control contact.The impact of the dead infected person on the spread of Ebola virus;the second is a mathematical model for the classification of a group of susceptible people at high risk.First,the Ebola infectious disease model with vaccination and virus transmission after the death of the infected person was established,and the basic reproduction numberR₀ was obtained using the next generation generator matrix method.The Lyapunov function is used to prove the global stability of the disease-free equilibrium point when₀R（27）1,and the disease is finally extinct;when₀R（29）1,the existence and global stability of the endemic disease equilibrium point.Through numerical simulation of the research model,it was found that increasing the vaccine inoculation rate or increasing the reasonable funeral rate shortened the time for the disease to die or stabilized,and effectively controlled the spread of the disease.For the Ebola virus with a very low cure rate,it has important research value and and theoretically has a more accurate prediction for the development of the epidemic.Secondly,when an epidemic breaks out,susceptible people can be divided into high-risk groups and low-risk groups.By classifying susceptible people,we can more accurately understand the spread of outbreaks of infectious diseases and take preventive measures to change human activities In order to shorten the period of disease decay or stability,a type of transmission model with high-risk susceptible population was established and studied and the basic reproduction numberR₀ was obtained.By constructing the Lyapunov function,it is concluded that when the basic reproduction number is less than 1,the disease-free equilibrium point is globally asymptotically stable.When the basic reproduction number is greater than 1,the only endemic disease equilibrium point is obtained,which proves that the disease is consistent and continuous,It is proved that the disease is globally progressively stable at this time,and finally the correctness of the conclusion is verified by the results of numerical simulation.