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

Abstract

In this paper, an epidemic $${\text{SI}}$$ SI model with $$n$$ n -infectious stages is studied. Lyapunov functions are used to conduct the global stability analysis for equilibrium points. The $$n$$ n -basic reproduction ratios $$R_{1}$$ R 1 , $$R_{2}$$ R 2 , …, $$R_{n}$$ R n are computed, and the basic reproduction number ($$R_{0}$$ R 0 ) is the max value between this ratios is obtained. For, $$j = 1,2,...,n$$ j = 1 , 2 , . . . , n when $$R_{j}$$ 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.