The dynamics of an epidemic model for pest control with impulsive effect
Tài liệu tham khảo
DeBach, 1964
Huffaker, 1976
Van Lenteren, 1995, Integrated pest, management in protected crops
Van Lenteren, 1988, Biological and Integrated pest control in greenhouse, Annual Review Entomology, 33, 239, 10.1146/annurev.en.33.010188.001323
Zhang, 2003, Grassland rodent damage and management strategy, Bulletin of the Chinese Academy of Sciences, 5, 343
Zhao, 1984
Yang, 2002, Application of bio-control in forestry mouse management, Journal of Northwest Forestry University, 17, 58
Burges, 1981
Glare, 1992
Hochberg, 1989, The potential role of pathogens in biological control, Nature, 337, 262, 10.1038/337262a0
Anderson, 1980, Infectious disease and population cycles of forest insect, Science, 210, 658, 10.1126/science.210.4470.658
Anderson, 1980, The population dynamics of microparasites and their invertebrate hosts, Philosophical Transactions of the Royal Society, Series B (Biological Sciences), 291, 451, 10.1098/rstb.1981.0005
Briggs, 1995, The dynamics of insect-Pathogen interactions in stage-structured populations, American Naturalist, 145, 855, 10.1086/285774
Brown, 1984, Stability in an insect–pathogen mode incorporating age-dependent immunity and seasonal host reproduction, Bulletin of Mathematical Biology, 46, 139, 10.1007/BF02463727
Browers, 1993, Host-pathogen population cycles in forest insect? Lessons from simple models reconsidered, Oikos, 67, 529, 10.2307/3545365
Myers, 1988, Can a general hypothesis explain population cycles of forest Lepidoptera?, Adv Ecol Res, 18, 179, 10.1016/S0065-2504(08)60181-6
Begon, 1992, Disease and community structure: The importance of host self-regulation in a host–host–pathogen model, Am Nat, 139, 1131, 10.1086/285379
Moerbeek, 1997, Insect-pathogen dynamics: Stage-specific susceptibility and insect density dependence, Mathematical Bioscience, 141, 115, 10.1016/S0025-5564(96)00175-7
Samoilenko, 1995
Zavalishchin, 1997
Panetta, 1996, A mathematical model of periodically pulsed chemotherapy: Tumor recurrence and metastasis in a competition environment, Bulletin of Mathematical Biology, 58, 425, 10.1007/BF02460591
Shulgin, 1998, Pulse vaccination strategy in the SIR epidemic model, Bulletin of Mathematical Biology, 60, 1123, 10.1016/S0092-8240(98)90005-2
Abdelkader, 2000, Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment, Dynamics of Continuous, Discrete & Impulsive Systems, 7, 265
Wang, 2007, Permanence and periodic solution of predator-prey system with Holling type functional response and impulses, Discrete Dynamics in Nature and Society, 2007, 10.1155/2007/81756
Goh, 1980
Liu, 1992, Practical stabilization of control systems with impulsive effects, Journal of Mathematical Analysis and Applications, 166, 563, 10.1016/0022-247X(92)90315-5
Liu, 1994, Impulsive stabilizability of autonomous systems, Journal of Mathematical Analysis and Applications, 187, 17, 10.1006/jmaa.1994.1342
Loos, 1980
Liu, 2003, Complex dynamics of Holling II Lotka–Volterra Predator–Prey system with impulsive perturbations on the predator, Chaos, Solitons and Fractals, 16, 311, 10.1016/S0960-0779(02)00408-3
Hui, 2006, Dynamic complexities in a periodically pulsed ratio-dependent predator–prey ecosystem modeled on a chemostat, Chaos, Solitons & Fractals, 29, 407, 10.1016/j.chaos.2005.08.036
Wang, 2007, Impulsive diffusion in single species model, Chaos, Solitons & Fractals, 33, 1213, 10.1016/j.chaos.2006.01.102
Y. Tan, L. Chen, Modelling approach for biological control of insect pest by releasing infected pest. Chaos, Solitons & Fractals (in press)
Gao, 2007, Analysis of an SIR epidemic model with pulse vaccination and distributed time delay, Journal of Biomedicine and Biotechnology, 2007, 10.1155/2007/64870
R. Shi, L. Chen, Stage-structured impulsive SI model for pest management. Discrete Dynamics in Nature and Society, 2007 Article ID 97608, 11 pages
Haddad, 2004, Vector dissipativity theory for large-scale impulsive dynamical systems, Mathematical Problems in Engineering, 2004, 225, 10.1155/S1024123X04310021
Nieto, 2009, Variational approach to impulsive differential equations, Nonlinear Analysis: Real World Applications, 10, 680, 10.1016/j.nonrwa.2007.10.022
Guo, 2009, Time-limited pest control of a Lotka–Volterra model with impulsive harvest, Nonlinear Analysis: Real World Applications, 10, 840, 10.1016/j.nonrwa.2007.11.007
Haddad, 2008, Energy dissipating hybrid control for impulsive dynamical systems, Nonlinear Analysis: Theory, Methods & Applications, 69, 3232, 10.1016/j.na.2005.10.052
Zhang, 2008, A delayed epidemic model with stage-structure and pulses for pest management strategy, Nonlinear Analysis: Real World Problems, 9, 1714, 10.1016/j.nonrwa.2007.05.004
Meng, 2007, a new mathematical model for optimal control strategies of integrated pest management, Journal of Biological Systems, 15, 219, 10.1142/S0218339007002143
Jiao, 2008, An appropriate pest management SI model with biological and chemical control concern, Applied Mathematics and Computation, 196, 285, 10.1016/j.amc.2007.05.072
Meng, 2008, A stage structured SI eco-epidemiological model with time delay and impulsive controlling, Journal of Systems Science and Complexity, 21, 427, 10.1007/s11424-008-9124-8
Xiao, 2003, The dynamics of an eco-epidemic model with biological control, Ecological Modelling, 168, 203, 10.1016/S0304-3800(03)00197-2