Three Types Of Vertical Transmission And Isolated Items Of Infectious Disease Model

With the global economic integration, international trade and communication with theacceleration development, but also will promote the frequent contact, thereby increasing thespread of infectious diseases, so the study of the spread of infectious diseases law there is a greatnecessity. In real life, some of the spread of the disease process not only through the populationbetween the contacts, and the disease itself also has inherited, is also the parent to offspringbetween the longitudinal propagation, i.e., vertical transmission, but this mode of transmission ofthe disease continues to play a critical role in the process. With the infectious disease model forthe study of the continuous development, people pay more attention to the mathematical tool tostudy disease prevalence cause as well as in the dissemination process of the key factors, so as toseek for the best method of prevention and control. And control of infectious diseases the mostdirect and effective method is to the sick people were used to isolate and immunization. On thebasis of previous studies to establish a class three with vertical transmission and isolated items ofinfectious disease dynamics model, the mathematical model for the dynamics of infectiousdiseases and stability theory of ordinary differential equation in combination, mainly studies thefollowing content:First introduced the significance of the study of infectious diseases, international developm-ent progress and development trend.Secondly, To establish and analysis of a class of vertical transmission and continuousvaccination and quarantine system SIQR model, the disease-free equilibrium and the endemicequilibrium point,through the Jacobian matrix invariant set principle, constructing Liapunovfunction respectively to prove their stability, obtained favorable conditions to eliminate andcontrol the disease.Then by using impulsive differential inequalities and impulsive differential equationcomparison theorem, put forward a kind of vertical transmission and pulse vaccination andisolation of the SIQR model, proved that the disease-free periodic solution existence and globalstability and the persistence of the disease.Finally,compared with continuous and pulse vaccination inoculation of two differentinoculation methods, gives a real life to choose the optimal inoculation conditions.