The Analysis Of Stuability And Hopf Bifurcation Of Three Types Infectious Disease Models

In addition to the phenomenon of branch, stability is the eternal theme of one ofthe differential equations. This paper studies the dynamic stability of the three types ofinfections diseases.Here the use of a differential equation of stability theory andanalysis system’s existence of the equilibrium point, local stability.Global stabilityobtained the sufficient part and global stable disease condition of free equilibrium andendemic equilibrium. We can attain aim to control the diffusion of epidemic by themeans of vaccinating susceptible and isolating infected.The text’s innovation point, One: Ago simultaneous differential equations wereused to come to biology mathematical models in most articles, we give detaileddescription.Two: The chapter three give Hopf bifurcation and bifurcatieg periodicsolution stability and period computing formula, and then use numerical simulation toobtion a supercritical Hopf bifurcation at balance pointE*. Three: Ordinaly Lyapurovfunction was used to determine the equinoctial point’s global stability. This text make asort of new method of proof: through proof the closed orbit’s existence, the text providea simple easy-run and true method of proof in chapter four. Fort: This text makesinfections rate,birth or death rate, recovery rate and disease rate to spread a functionwith time in chapter five.