Abbreviated Journal Title
SIAM J. Appl. Math.
disease model; global stability; Lyapunov function; graph-theoretic; method; EPIDEMIC MODELS; DYNAMICS; TRANSMISSION; CHOLERA; COMPUTATION; NETWORKS; Mathematics, Applied
Two systematic methods are presented to guide the construction of Lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics. Specifically, a matrix-theoretic method using the Perron eigenvector is applied to prove the global stability of the disease-free equilibrium, while a graph-theoretic method based on Kirchhoff's matrix tree theorem and two new combinatorial identities are used to prove the global stability of the endemic equilibrium. Several disease models in the literature and two new cholera models are used to demonstrate the applications of these methods.
Siam Journal on Applied Mathematics
Shuai, Zhisheng and Driessche, P. Van Den, "Global Stability of Infectious Disease Models Using Lyapunov Functions" (2013). Faculty Bibliography 2010s. 4700.