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In LaSalle's book "The Stability of Dynamical Systems", the author gives four conditions which imply that the origin of a discrete dynamical system defined on ℝ is a global attractor, and proposes to study the natural extensions of these conditions in ℝⁿ. Although some partial results are obtained in previous papers, as far as we know, the problem is not completely settled. In this work we first study the four conditions and prove that just one of them implies that the origin is a global attractor...
A model of viral infection of monocytes population by the dengue virus is formulated as a system of four ordinary differential equations. The model takes into account the immune response and nonlinear incidence rate of susceptible and free virus particles.
Global stability of the uninfected steady state is investigated. Such a steady state always exists. If it is the only steady state, then it is globally asymptotically stable. If any infected steady state exists, then the uninfected...
In this paper we have considered a nonlinear and nonautonomous stage-structured HIV/AIDS
epidemic model with an imperfect HIV vaccine, varying total population size and
distributed time delay to become infectious due to intracellular delay between initial
infection of a cell by HIV and the release of new virions. Here, we have established some
sufficient conditions on the permanence and extinction of the disease by using inequality
analytical technique....
Tuberculosis (TB) remains a major global health problem. A possible risk factor for TB is
diabetes (DM), which is predicted to increase dramatically over the next two decades,
particularly in low and middle income countries, where TB is widespread. This study aimed
to assess the strength of the association between TB and DM. We present a deterministic
model for TB in a community in order to determine the impact of DM in the spread of the
disease....
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