Periodic solutions, global attractivity and oscillation of an impulsive delay host-macroparasite model

Mathematical and Computer Modelling

Volumn 45, Issue 5-6, 2007, Pages 531-543

  Saker, S H ^a   Alzabut, J O ^b  

^a Mansoura University   (Egypt)

^b CANKAYA UNIVERSITY   (Turkey)

Author keywords

Delay; Existence; Global attractivity; Impulse; Macroparasite model; Oscillation

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; THEOREM PROVING;

DELAY; EXISTENCE; GLOBAL ATTRACTIVITY; IMPULSE; MACROPARASITE MODEL;

OSCILLATIONS;

EID: 33751398015     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2006.07.001     Document Type: Article

References (22)

1. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
2. Samoilenko A.M., and Perestyuk N.A. Impulsive Differential Equations (1995), World Scientific
3. Gopalsamy K. Stability and Oscillation in Delay Differential Equations of Population Dynamics (1992), Kluwer Academic, Dordrecht
4. Györi I., and Ladas G. Oscillation Theory of Delay Differential Equations with Applications (1991), Clarendon Press, Oxford
5. May R., and Anderson R.M. Infectious Diseases of Humans: Dynamics and Control (1995), Oxford Science Publications
6. Macdonald N. Biological Delay Systems: Linear Stability Theory. Cambridge Studies in Mathematical Biology (1989), Cambridge Univ. Press
7. V.A. Kostitzin, Symbiose, Parasitisme et Evolution, Paris, 1943
8. Hairston N.G. On the mathematical analysis of schistosome population. Bull. World Health Organ. 33 (1965) 45-62
9. Macdonald G. The dynamics of Hilmenth infectious with special references to schistosomes. Trans. R. Soc. Trop. Med. Hyg. 59 (1965) 489-506
10. Tallis G.M., and Leyton M.K. A schistosome approach to the study of parasite populations. J. Theor. Biol. 13 (1966) 160-172
11. Leyton M.K. Stochastic models in population of Hilmenthic parasites in the definitive host. II Sexual mating functions. Math. Biosci. 39 (1968) 413-419
12. Chao J. On the oscillation of linear differential equations with deviating arguments. Math. Practice Theory 1 (1991) 32-40
13. Elabbasy E.M., Saif K., and Saker S.H. Oscillation in host macroparasite model with delay time. Far East J. Appl. Math. 4 (2000) 119-142
14. Erbe L.H., and Zhang B.G. Oscillation for first order linear differential equations with deviating arguments. Differ. Integral Equ. 1 (1988) 305-314
15. Gaines R.E., and Mawhin J.L. Coincidence Degree and Nonlinear Differential Equations (1977), Springer, Berlin
16. Ladde G.S., Lakshmikantham V., and Zhang B.Z. Oscillation Theory of Differential Equations with Deviating Arguments (1987), Marcel Dekker, New York
17. Li B. Oscillation of delay differential equations with variable coefficients. J. Math. Anal. Appl. 192 (1995) 217-234
18. Luo J. Oscillation of nonlinear delay differential equations with impulses. J. Math. Anal. Appl. 250 (2000) 290-298
19. Nicholson A.J. The balance of animal population. J. Animal Ecology 2 (1993) 132-178
20. Shen J., and Tang X. New oscillation criteria for linear delay differential equations. Comput. Math. Appl. 36 (1998) 53-61
21. Yu J.S., and Wang Z.C. Some further results on oscillation of neutral differential equations. Bull. Austral. Math. Soc. 46 (1992) 149-157
22. Yu J.S., Wang Z.C., Zhang B.G., and Qian X.Z. Oscillations of differential equations with deviating arguments. Panamer. Math. J. 2 (1992) 59-72