Lyapunov functions and global stability analysis for epidemic model with n-infectious

In this paper, an epidemic SI model with n -infectious stages is studied. Lyapunov functions are used to conduct the global stability analysis for equilibrium points. The n -basic reproduction ratios R 1 , R 2 , …, R n are computed, and the basic reproduction number ( R 0 ) is the max value between this ratios is obtained. For, j = 1 , 2 , . . . , n when R j is less than one, all strains die out, and if it is greater than one, then persists. The disease-free and endemic equilibrium points are found, and we studied the global stability for them by using the direct Lyapunov functions. The Maple program is used for carrying a numerical simulations to support the analytically results.