TITLE:
A Global Stability Analysis of a Susceptible-Infected-Removed-Prevented-Controlled Epidemic Model
AUTHORS:
Muhammad A. Yau, Hussaini S. Ndakwo, A. M. Umar
KEYWORDS:
Epidemic Model, Stability Analysis, HIV/AIDS, Disease Free Equilibrium Points
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.10,
May
23,
2014
ABSTRACT: A mathematical model of HIV transmission dynamics is proposed and
analysed. The population is partitioned into five compartments of susceptible S(t),
Infected I(t), Removed R(t), Prevented U(t) and the Controlled W(t).
Each of the compartments comprises of cohort of individuals. Five systems of
nonlinear equations are derived to represent each of the compartments. The
general stability of the disease free equilibrium (DFE) and the endemic
equilibrium states of the linearized model are established using the linear
stability analysis (Routh-Hurwitz) method which is found to be locally asymptotically
stable when the infected individuals receive ART and use the condom. The
reproduction number is also derived using the idea of Diekmann and is found to
be strictly less than one. This means that the epidemic will die out.