O. Arino, I. Györi, and A. Jawhari, Oscillation criteria in delay equations, Journal of Differential Equations, vol.53, issue.1, pp.115-123, 1984.
DOI : 10.1016/0022-0396(84)90028-7

O. Arino, K. P. Hadeler, and M. L. Hbid, Existence of periodic solutions for delaydifferential equations with state-depending delay, J.Diff.Equat, vol.1442, pp.263-301, 1998.

O. Arino and K. Niri, Oscillations in vector spaces: A comparison result for monotone delay differential systems, Journal of Mathematical Analysis and Applications, vol.160, issue.1, pp.267-283, 1991.
DOI : 10.1016/0022-247X(91)90305-J

O. Arino and K. Niri, Subdominant behavior in positive semigroups. The case of a class of delay differential equations, Differ. Equ. Dyn. Syst, vol.4, issue.1, pp.99-111, 1996.

O. Arino and P. Seguier, Existence of oscillating solutions for certain differential equations with delay, Proc. Lect. Notes Math, vol.17, issue.51, pp.46-64, 1978.
DOI : 10.1007/BF02417109

J. Arino, C. C. Mccluskey, and . Van-den-driessche, Global Results for an Epidemic Model with Vaccination that Exhibits Backward Bifurcation, SIAM Journal on Applied Mathematics, vol.64, issue.1, pp.260-276, 2003.
DOI : 10.1137/S0036139902413829

N. T. Bayley, The mathematical Theory of Infectious diseases, 1975.

Y. Cao, The oscillation and exponential decay rate of solutions of differential delay equations, Proc. Spec. Sess. AMS Contemp. Math, vol.129, pp.43-54, 1991.
DOI : 10.1090/conm/129/1174133

O. Diekman and J. A. Heesterbeek, Mathematical epidemiology of infectious diseases: Model Building Analysis and Interpretation, Wiley series in Mathematical and computational Biology, 2000.

I. Györi, Connections between compartmental systems with pipes and integro-differential equations, Mathematical Modelling, vol.7, issue.9-12, pp.1215-1238, 1986.
DOI : 10.1016/0270-0255(86)90077-1

I. Gy?-ori and G. Ladas, Oscillation theory of delay differential equations. Oxford Mathematical Monographs, 1991.

J. K. Hale and S. M. , Introduction to Functional Differential Equations, 1991.
DOI : 10.1007/978-1-4612-4342-7

H. W. Hethecote, H. W. Stech, and P. Van-den-drieesshe, PERIODICITY AND STABILITY IN EPIDEMIC MODELS: A SURVEY, differential Equations and Applications in Ecology, Epidemic and Population Problems, 1981.
DOI : 10.1016/B978-0-12-148360-9.50011-1

M. W. Hirsch, Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere, SIAM Journal on Mathematical Analysis, vol.16, issue.3, pp.423-439, 1965.
DOI : 10.1137/0516030

B. B. Hunt and J. A. Yorke, When all solutions of x (t) = ? n i=1 x(t ? T i (t)) oscillate, J.Differential Equations, vol.53, pp.138-145, 1984.

G. Ladas, Y. Sficas, and I. P. Stavroulakis, Necessary and Sufficient Conditions for Oscillations, The American Mathematical Monthly, vol.90, issue.9, p.637, 1983.
DOI : 10.2307/2323283

G. Ladas and I. P. Stavroulakis, Oscillations caused by several retarded and advanced arguments, Journal of Differential Equations, vol.44, issue.1, pp.134-152, 1982.
DOI : 10.1016/0022-0396(82)90029-8

J. Mallet-paret, Morse Decompositions for delay-differential equations, Journal of Differential Equations, vol.72, issue.2, pp.270-315, 1988.
DOI : 10.1016/0022-0396(88)90157-X

K. Niri, Oscillations in Differential Equations with State-Dependent Delays, Nonlinear Oscillations, vol.6, issue.2, pp.250-257, 2003.
DOI : 10.1023/B:NONO.0000007825.34718.61

K. Niri, Etudes des propriétés oscillatoires de systèmes diffèrentielsdiffèrentielsà retard de type monotone , thèse de 3` eme Cycle de l, 1988.

H. W. Smith, Monotone semiflows generated by functional differential equations, Journal of Differential Equations, vol.66, issue.3, pp.420-442, 1987.
DOI : 10.1016/0022-0396(87)90027-1

URL : http://doi.org/10.1016/0022-0396(87)90027-1

H. W. Smith, Monotone dynamical systems: An Introduction to the Theory of competitive and cooperative Systems, Mathematical Surveys and Monographs, vol.41, 1995.
DOI : 10.1090/surv/041

H. R. Thieme, Epidemic and demographic interaction in the spread of potentially fatal disease in governing populations, Math.Biosci, issue.111, pp.99-130, 1992.