Modeling And Research On Dengue Dynamic System With Class-Age Structure

Firstly,according to the characteristics of dengue fever in the treatment and vaccination of the population,we establish a class of dengue fever with infection and vaccination time.By using infinite dimensional eigenvalue theory,theory of disease persistence and constructing Lyapunov functional method,the kinetic properties of this model are analyzed globally,and the basic regeneration number of disease transmission is obtained.When,the basic regeneration number is less than 1,The disease-free equilibrium state is globally asymptotically stable;when the basic regeneration number is greater than 1,the system disease is persistent and the endemic disease state is globally asymptotically stable.Secondly,according to the physiological structure of mosquitoes that reproduce dengue fever and the effect of mosquito egg development time on disease,we establish a dengue dynamics model of mosquito stage structure.Mathematical modeling is used to analyze the e,xistence of the equilibrium state of this kind of system,and obtains the control of the basic regeneration of disease transmission and the global stability of disease-free equilibrium.In particular,we study the dynamics of Aedes population model with age structure,and obtain the threshold conditions for controlling the growth and development of Aedes population:When the threshold R0<1,the local equilibrium state of the system is globally asymptotically stable;When the threshold R0>1,the positive equilibrium of the system is globally asymptotically stable.Finally,combined with the effects of dengue infection,vaccination and the duration of mosquito eggs on the spread of the disease,we further discuss specific measures to control the spread of dengue fever.