# Zhisheng Shuai

A class of global Lyapunov functions is revisited and used to resolve a long-standing open problem on the uniqueness and global stability of the endemic equilibrium of a class of multi-group models in mathematical epidemiology. We show how the group structure of the models, as manifested in the derivatives of the Lyapunov function, can be completely(More)
• SIAM Journal of Applied Mathematics
• 2013
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(More)
• Mathematical biosciences
• 2011
A general compartmental model for cholera is formulated that incorporates two pathways of transmission, namely direct and indirect via contaminated water. Non-linear incidence, multiple stages of infection and multiple states of the pathogen are included, thus the model includes and extends cholera models in the literature. The model is analyzed by(More)
We investigate an SIR compartmental epidemic model in a patchy environment where individuals in each compartment can travel among n patches. We derive the basic reproduction number R0 and prove that, if R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable. In the case of R0 > 1, we derive sufficient conditions under which the endemic(More)
• Journal of mathematical biology
• 2013
A new quantity called the target reproduction number is defined to measure control strategies for infectious diseases with multiple host types such as waterborne, vector-borne and zoonotic diseases. The target reproduction number includes as a special case and extends the type reproduction number to allow disease control targeting contacts between types.(More)
• Mathematical biosciences
• 2013
A mathematical model for cholera is formulated that incorporates direct and indirect transmission, patch structure, and both water and human movement. The basic reproduction number R0 is defined and shown to give a sharp threshold that determines whether or not the disease dies out. Kirchhoff's Matrix Tree Theorem from graph theory is used to investigate(More)
• Journal of mathematical biology
• 2015
The ability of disease to invade a community network that is connected by environmental pathogen movement is examined. Each community is modeled by a susceptible-infectious-recovered (SIR) framework that includes an environmental pathogen reservoir, and the communities are connected by pathogen movement on a strongly connected, weighted, directed graph.(More)