Zhisheng Shuai

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ABSTRACT. For a class of multigroup SIR epidemic models with varying subpopulation sizes, we establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R0 > 1, then there exists a unique endemic(More)
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)
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)
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)
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)
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)
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)