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. Li and J. Muldowney [SIAM J. Math. Appl., 27 (1996)], may be successfully applied. We completely determine the dynamics of the general system, including thresholds and global stability of the non trivial 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.
On the use of the geometric approach to global stability for three dimensional ODE systems: a bilinear case
LACITIGNOLA, Deborah
2008-01-01
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. Li and J. Muldowney [SIAM J. Math. Appl., 27 (1996)], may be successfully applied. We completely determine the dynamics of the general system, including thresholds and global stability of the non trivial 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
