Dynamic analysis of a pest-epidemic model with impulsive control

Mathematics and Computers in Simulation

Volumn 79, Issue 1, 2008, Pages 72-84

  Pang, Guoping ^a,b   Chen, Lansun ^b  

^a YULIN NORMAL UNIVERSITY   (China)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Chaos; Extinction; Impulsive control; Permanence; Pest epidemic model

Indexed keywords

AGRICULTURAL ENGINEERING; DYNAMIC ANALYSIS; PESTICIDES;

BIOLOGICAL CONTROLS; CHAOS; COMPARISON THEOREMS; CRITICAL VALUES; EPIDEMIC MODELS; EXTINCTION; FLOQUET THEOREM; GLOBALLY ASYMPTOTICALLY STABLE; IMPULSIVE CONTROL; IMPULSIVE CONTROLS; PERIODIC SOLUTIONS; PERMANENCE; PEST MANAGEMENT; PEST-EPIDEMIC MODEL;

PEST CONTROL;

EID: 48549094712     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2007.10.002     Document Type: Article

References (32)

1. D.D. Bainov, P.S. Simeonov, Impulsive differential equations: periodic solutions and applications, in: Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific and Technical, New York, 1993.
2. Barclay H.J. Models for pest control using predator release, habitat management and pesticide release in combination. J. Appl. Ecol. 19 (1982) 337
3. Bjornson S., and Keddie B.A. Disease prevalence and transmission of Microsporidium phytoseiuli infecting the predatory mite, Phytoseiulus persimilis (Acari: Phytoseiidae). J. Invertebr. Pathol. 77 (2001) 114
4. Chellaboina V.S., Bhat S.P., and Haddad W.M. An invariance principle for nonlinear hybrid and impulsive dynamical systems. Nonlinear Anal. TMA 53 (2003) 527
5. Chen S.L. Environment-friendly bio-pesticide-microbial pesticide. J. Biol. 22 (2005) 62 (in Chinese)
6. d'Onofrio A. Stabil1ty properties of pulse vaccination strategy in the SIR epidemic model. Bull. Math. Biol. 60 (2002) 1
7. Grasman J., Van Herwaarden O.A., and Hemerik L. A two-component model of host-parasitoid interactions: determination of the size of inundative releases of parasitoids in biological pest control. Math. Biosci. 169 (2001) 207
8. Hui J., and Chen L.S. Impulsive vaccination of SIR epidemic models with nonlinear incidence rates. Discrete Contin. Dyn. Syst. Ser. B 4 (2004) 595
9. Hyakutake T., Matsumoto T., and Yanase S. Lattice Boltzmann simulation of blood cell behavior at microvascular bifurcations. Math. Comput. Simulat. 72 (2006) 134
10. Kaitala V., Ylikarjula J., and Heino M. Dynamic complexities in host-parasitioid interaction. J. Theor. Biol. 197 (1999) 331
11. Kuang S.Z., Wang X.R., and Zhang H. Effects of pesticides of PrGV and AfNPV against Pieris rapae and Plutella xylostella in the field. J. Zhongkai Univ. Agric. Technol. 18 (2005) 25 (in Chinese)
12. Lakmeche A., and Arino O. Bifurcation of nontrivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment. Dyn. Contin. Discr. Impul. Syst. 7 (2000) 265
13. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
14. Liu L., and Sun J.T. Existence of periodic solution for a harvested system with impulses at variable times. Phys. Lett. A 360 (2006) 105
15. Lomer C.J. Factors in the success and failure of microbial agents for control of migratory pests. Integr. Pest Manage. Rev. 4 (1999) 307
16. X.Z. Meng, L.S. Chen, H.D. Cheng, Two profitless delays for the SEIRS epidemic disease model with nonlinear incidence and pulse vaccination, Appl. Math. Comput. 186 (2007) 516.
17. Naomi M.F., and Patrick J.K. Alpha and beta subunits of pyruvate dehydrogenase E1 from the microsporidian Nosema locustae: mitochondrion-derived carbon metabolism in microsporidia. Mol. Biochem. Parasitol. 117 (2001) 201
18. G.P. Pang, L.S. Chen, A delayed SIRS epidemic model with pulse vaccination, Chaos Solitons Fractals 34 (2007) 1629.
19. G.P. Pang, F.Y. Wang, L.S. Chen, Analysis of a Monod-Haldene type food chain chemostat with periodically varying substrate, Chaos Solitons Fractals 38 (2008) 731.
20. Roberts M.G., and Kao R.R. The dynamics of an infectious disease in a population with birth pulses. Math. Biosci. 149 (1998) 23
21. Shandelle M.H. Leslie matrix models as "stroboscopic snapshots" of McKendrick PDE models. J. Math. Biol. 37 (1998) 309
22. Shulgin B., Stone L., and Agur Z. Pulse vaccination strategy in the SIR epidemic model. Bull. Math. Biol. 60 (1998) 1
23. Slamovits C.H., and Keeling P.J. Class II photolyase in a microsporidian intracellular parasite. J. Mol. Biol. 341 (2004) 713
24. Stern V.M. Economic thresholds. Ann. Rev. Entomol. (1973) 259
25. Sun J.T. Impulsive control of a new chaotic system. Math. Comput. Simulat. 64 (2004) 669
26. Sun J.T., and Zhang Y.P. Impulsive control and synchronization of Chua's oscillators. Math. Comput. Simulat. 66 (2004) 499
27. Trevor A.J. Factors in the success and failure of microbial controlagents for soil dwelling pests. Integr. Pest Manage. Rev. 4 (1999) 281
28. Van Lenteren J.C. Environmental manipulation advantageous to natural enemies of pests. In: Delucchi V. (Ed). Integrated Pest Management (1987), Parasitis, Geneva
29. Van Lenteren J.C. Integrated pest management in protected crops. In: Dent D. (Ed). Integrated pest management (1995), Chapman & Hall, London
30. Van Lenteren J.C. Measures of success in biological control of arthropods by augmentation of natural enemies. In: Wratten S., and Gurr G. (Eds). Measures of Success in Biological Control (2000), Kluwer Academic Publishers, Dordrecht
31. Van Lenteren J.C., and Woets J. Biological and integrated pest control in greenhouses. Ann. Rev. Ent. 33 (1988) 239
32. Wang F.Y., Zhang S.W., and Chen L.S. Permanence and complexity of a three species food chain with impulsive effect on the top predator. Int. J. Nonlinear Sci. Numer. Simul. 6 (2005) 169