Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 693472, 16 pages
doi:10.1155/2009/693472
Global dynamics behaviors of viral infection model for pest management
Chunjin Wei1
and Lansun Chen2
1Science College, Jimei University, Xiamen 361021, China
2Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China
Abstract
According to biological strategy for pest control, a mathematical model with periodic releasing virus particles for insect viruses attacking pests is considered. By using Floquet's theorem, small-amplitude perturbation skills and comparison theorem, we prove that all solutions of the system are uniformly ultimately bounded and there exists a globally asymptotically stable pest-eradication periodic solution when the amount of virus particles released is larger than some critical value. When the amount of virus particles released is less than some critical value, the system is shown to be permanent, which implies that the trivial pest-eradication solution loses its stability. Further, the mathematical results are also confirmed by means of numerical simulation.