On the use of the geometric approach to global stability for three dimensional ODE systems: A bilinear case |
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Authors: | Bruno Buonomo Deborah Lacitignola |
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Institution: | a Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples, Italy b Department of Mathematics, University of Salento, via Provinciale Lecce-Arnesano, I-73100 Lecce, Italy |
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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. |
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Keywords: | Global stability Bendixson criterion Bilinear system Epidemic models |
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