Abstract :
In this paper, we consider a general bilinear three dimensional ODE system, whose
structure generalizes many mathematical models of biological interest, including many
from epidemics. Our main goal is to find sufficient conditions, expressed in terms of
the parameters of the system, ensuring that the geometric approach to global stability
analysis, due to [M.Y. Li, J.S. Muldowney, A geometric approach to global-stability problems,
SIAM J. Math. Anal. 27 (4) (1996) 1070–1083], may be successfully applied. We completely
determine the dynamics of the general system, including thresholds and global stability of
the nontrivial equilibrium. The obtained result is applied to several epidemic models. We
further show how the role of new parameters on stability of well-established models may
be emphasized
