AM  Vol.1 No.3 , September 2010
A Pest Management Epidemic Model with Time Delay and Stage-Structure
ABSTRACT
In this paper, an SI epidemic model with stage structure is investigated. In this model, impulsive biological control which release infected pest to the field at a fixed time periodically is considered, and obtained the sufficient conditions for the global attractivity of pest-extinction periodic solution and permanence of the system. We also prove that all solutions of the model are uniformly ultimately bounded. The sensitive analysis on the two thresholds and to the changes of the releasing amounts of infected pest is shown by numerical simulations. Our results provide a reliable tactic basis for the practice of pest management.

Cite this paper
nullY. Ding, S. Gao, Y. Liu and Y. Lan, "A Pest Management Epidemic Model with Time Delay and Stage-Structure," Applied Mathematics, Vol. 1 No. 3, 2010, pp. 215-221. doi: 10.4236/am.2010.13026.
References
[1]   R. Q. Shi and L. S. Chen, “An Impulsive Predator-Prey Model with Disease in the Prey for Integrated Pest Management,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 2, 2010, pp. 421-429.

[2]   J. A. Cui and X. Y. Song, “Permanence of a Predator-Prey System with Stage Structure,” Discrete Continuous Dynamical Systems-Series B, Vol. 4, No. 3, 2004, pp. 547-554.

[3]   Y. N. Xiao and L. S. Chen, “Global Stability of a Predator-Prey System with Stage Structure for the Predator,” Acta Mathematica Sinica, Vol. 20, No. 1, 2004, pp. 63-70.

[4]   H. Zhang, L. S. Chen and J. J. Nieto, “A Delayed Epidemic Model with Stage-Structure and Pulses for Pest Management Strategy,” Nonlinear Analysis: Real World Applications, Vol. 9, No. 4, 2008, pp. 1714-1726.

[5]   X. Wang, Y. D. Tao and X. Y. Song, “Mathematical Model for the Control of a Pest Population with Im- pulsive Perturbations on Diseased Pest,” Applied Math- ematical Modelling, Vol. 33, No. 7, 2009, pp. 3099-3106.

[6]   H. W. Hethcote, “The Mathematics of Infectious Disease,” Siam Review, Vol. 42, No. 4, 2002, pp. 599- 653.

[7]   R. M. Anderson, R. M. May and B. Anderson, “Infec- tious Diseases of Human: Dynamics and Control,” Oxford Science Publications, Oxford, 1991.

[8]   R. M. Anderson and R. M. May, “Population Biological of Infectious Diseases,” Springer Berlin-Heidelberg, New York, 1982.

[9]   W. M. Liu, S. A. Levin and Y, Lwasa, “Infuence of Nonlinear Incidence Rates upon the Behavior of SIRS Epidemiological Models,” Journal of Mathematical Biology, Vol. 23, No. 2, 1986, pp. 187-204.

[10]   T. Lindstrom, “A Generalized Uniqueness Theorem for Limit Cycles in a Predator-Prey System,” Acta Academic Akoensis, Series B, Vol. 49, No. 2, 1989, pp. 1-9.

[11]   J. J. Jiao, X. Z. Meng ang L. S. Chen, “Global Attra- ctivity and Permanence of a Stage-Structured Pest Mana- gement SI Model with Time Delay and Diseased Pest Impulsive Transmission,” Chaos, Solitons and Fractals, Vol. 38, No. 3, 2008, pp. 658-668.

[12]   V. Lakshmikantham, D. D. Bainov and P. Simeonov, “Theory of Impulsive Differential Equations,” World Scientific, Singapor, 1989.

[13]   Y. Kuang, “Delay Differential Equation with Application in Population Dynamics,” Academic Press, New York, 1993.

 
 
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