Periodic solution of a class of epidemic models

Computers and Mathematics with Applications

Volumn 38, Issue 3, 1999, Pages 61-71

  Zhang, Xin An ^a,b   Chen, Lansun ^b  

^a CENTRAL CHINA NORMAL UNIVERSITY   (China)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; DISEASES; EPIDEMIOLOGY; NUMERICAL METHODS; PROBABILITY; STATISTICAL METHODS;

EPIDEMIOLOGICAL MODELS; GLOBAL ASYMPTOTIC STABILITY; NONLINEAR INCIDENCE RATE; PERIODIC SOLUTION;

MATHEMATICAL MODELS;

EID: 0033177720     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(99)00206-0     Document Type: Article

References (13)

1. H.W. Hethcote, A thousand and one epidemic models, In Lecture Notes in Biology, (Edited by S.A. Levin), Vol. 100, pp. 504-515, Springer-Verlag, (1995).
2. N.T.J. Bailey, The Mathematical Theory of Infections Disease, Hafner, (1975).
3. L. Chen and J. Chen, Nonlinear Dynamical Systems in Biology, (in Chinese), Science Press, Beijing, (1993).
4. W. Liu, S.A. Levin and Y. Iwasa, Influence of nonlinear incidence rates upon the behaviour of SIRS epidemiological models, J. Math. Biology 23, 187-204, (1986).
5. W. Liu, H.W. Hethcote and S.A. Levin, Dynamical behaviour of epidemiological models with nonlinear incidence rates, J. Math. Biology 25, 359-380, (1987).
6. Z. Zhang et al., Qualitative theory of differential equations, Translations of Mathematical Monographs 101, Amer. Math. Soc., Providence, RI, (1992).
7. A.A. Andronov, E.A. Leontovich, I.I. Gordon and A.L. Maier, Qualitative Theory of Second Order Dynamical Systems, Wiley, New York, (1973).
8. W.A. Coppel, Quadratic systems with a degenetate critical point, Bull. Austral. Math. Soc. 38, 1-10, (1988).
9. W.A. Coppel, A new class of quadratic system, J. Diff. Eq. 92, 360-372, (1991).
10. Y. Ye et al., Theory of limit cycles, Translations of Mathematical Monographs 66, Providence, RI, (1986).
11. J. Guckenheimer and P. Holmes, Nonlinear Oscillation, Dynamical Systems and Bifurcation of Vector Fields, Springer-Verlag, (1983).
12. W.A. Coppel, Stability of Asymptotic Behaviour of Differential Equations, D.C. Heath, (1965).
13. E.A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, (1955).