Invariant Region, Endemic Equilibria and Stability Analysis

Abstract

In this manuscript, the ideas of Lyapunov, Barbalat, Birkhoff and Rota have been explored on the deterministic model A that describes human population, whose state variables and parameters are assumed to be non-negative. This approach is ideally suitable for S.I models where there is no disease induced death rate, for instance chancroid and trichomoniasis. We have put forward and proved three conjectures, that is, the system of equations that describes model A is dissipative, for an endemic equilibrium point Q* of such a system there exist a strict Lyapunov function and that an endemic equilibrium point Q* is both globally and locally asymptotically stable whenever it exists.