Preventive Immunization Strategy Of SIQR Epidemic Model With Constant Input And Nonlinear Occurrence Rate

Communicable disease has threatened the survival of human beingsfor a long time. Due its infectivity and epidemicity, communicable diseasecan transmit between human beings and transmit between human beingsand animals, resulting in serious threat to human health and life. Withimprovement in human living condition and medical level, somecommunicable diseases are already swept away, while new communicablediseases come out, leading to new trial in front of us. As a result, we areforced to look for best method of preventing and controlling communicablediseases. There are2most effective control measures for the popularizationof communicable diseases: immunize susceptible persons; isolate thepatients. Based on previous studies,3types of SIQR epidemic models withconstant input and nonlinear occurrence rate are established in the paper tostudy the following content:Firstly, domestic and foreign development situation of study onepidemic dynamical model is introduced. Relevant concepts, propositions,and lemmas are introduced while main work of the paper is introduced.Secondly, a kind of epidemic model with constant recruitment and ainfectious rate of SI2is discussed. The dynamic behavior of the model isstudied with Differential Stability Theory; the local stability of theequilibrium is proved by using the Jacobian Matrix; the global stability ofthe endemic equilibrium is discussed with Eigenvalue Method. And itshows that, there exist H opfBifurcation Phenomenon in a certain scopeof parameters, and the thresholdR0which shows the prevalence ofdisease is obtained.Then, a constant vaccination of a kind of SIQR epidemic model with constant recruitment and a infectious rate of SI2is studied. Thedisease-free equilibrium and the endemic equilibrium of the system arefound. The local stability and global stability of the equilibrium arediscussed with the Jacobian Matrix and Eigenvalue Method, and thethresholdR0is found. It demonstrates that when R01, the disease willbe completely eliminated.Finally, a pulse vaccination of a kind of SIQR epidemic model withconstant recruitment and a infectious rate of SI2is gave. The existenceand the stability of the disease-free periodic solution about the system isdiscussed, and the conditions of disease-free periodic solution which isglobally asymptotically stable is presented by using the ComparisonTheorem of Impulsive Differential Equation.