Mathematical modeling has been increasingly recognized in the public health community as
an important research tool for infectious diseases control. Mathematical models are widely …

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 …

Population dynamics is an important subject in mathematical biology. A central problem is to
study the long-term behavior of modeling systems. Most of these systems are governed by …

The SEIR model with nonlinear incidence rates in epidemiology is studied. Global stability of
the endemic equilibrium is proved using a general criterion for the orbital stability of periodic …

" The mathematical theory of persistence answers questions such as which species, in a
mathematical model of interacting species, will survive over the long term. It applies to …

A SEIR model for the transmission of an infectious disease that spreads in a population
through direct contact of the hosts is studied. The force of infection is of proportionate mixing …

We study a population model for an infectious disease that spreads in the host population
through both horizontal and vertical transmission. The total host population is assumed to …

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 …

A mathematical model that describes HIV infection of CD4+ T cells is analyzed. Global
dynamics of the model is rigorously established. We prove that, if the basic reproduction …

We study the global behavior of a non-linear susceptible-infectious-removed (SIR)-like
epidemic model with a non-bilinear feedback mechanism, which describes the influence of …