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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 252718, 14 pages
Dynamics and Biocontrol: The Indirect Effects of a Predator Population on a Host-Vector Disease Model
1Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
2Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000, China
3School of Finance and Economics, Jiangsu University, Zhenjiang, Jiangsu 212013, China
Received 11 July 2013; Revised 29 November 2013; Accepted 10 December 2013; Published 27 January 2014
Academic Editor: Yanni Xiao
Copyright © 2014 Fengyan Zhou and Hongxing Yao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- N. T. J. Bailey, The Biomathematics of Malaria, Charles Griffin & Company, High Wycombe, UK, 1982.
- J. Hemingway and H. Ranson, “Insecticide resistance in insect vectors of human disease,” Annual Review of Entomology, vol. 45, pp. 371–391, 2000.
- K. F. Haynes, “Sublethal effects of neurotoxic insecticides on insect behavior,” Annual Review of Entomology, vol. 33, pp. 149–168, 1988.
- D. W. Jenkins, “Pathogens, parasites and predators of medically important arthropods. Annotated list and bibliography,” Bulletin of the World Health Organization, vol. 30, pp. 1–150, 1964.
- E. Legner, “Biological control of diptera of medical and veterinary importance,” Journal of Vector Ecology, vol. 20, pp. 59–120, 1995.
- J. R. Stauffer Jr., M. E. Arnegard, M. Cetron et al., “Controlling vectors and hosts of parasitic diseases using fishes,” BioScience, vol. 47, no. 1, pp. 41–49, 1997.
- M. Samish and J. Rehacek, “Pathogens and predators of ticks and their potential in biological control,” Annual Review of Entomology, vol. 44, pp. 159–182, 1999.
- E.-J. Scholte, K. Ng'Habi, J. Kihonda et al., “An entomopathogenic fungus for control of adult African malaria mosquitoes,” Science, vol. 308, no. 5728, pp. 1641–1642, 2005.
- R. Kumar and J.-S. Hwang, “Larvicidal efficiency of aquatic predators: a perspective for mosquito biocontrol,” Zoological Studies, vol. 45, no. 4, pp. 447–466, 2006.
- R. S. Ostfeld, A. Price, V. L. Hornbostel, M. A. Benjamin, and F. Keesing, “Controlling ticks and tick-borne zoonoses with biological and chemical agents,” BioScience, vol. 56, no. 5, pp. 383–394, 2006.
- K. Walker and M. Lynch, “Contributions of Anopheles larval control to malaria suppression in tropical Africa: review of achievements and potential,” Medical and Veterinary Entomology, vol. 21, no. 1, pp. 2–21, 2007.
- B. Kay and V. S. Nam, “New strategy against Aedes aegypti in Vietnam,” The Lancet, vol. 365, no. 9459, pp. 613–617, 2005.
- P. Kittayapong, S. Yoksan, U. Chansang, C. Chansang, and A. Bhumiratana, “Suppression of dengue transmission by application of integrated vector control strategies at sero-positive GIS-based foci,” The American Journal of Tropical Medicine and Hygiene, vol. 78, no. 1, pp. 70–76, 2008.
- S. K. Ghosh, S. N. Tiwari, T. S. Sathyanarayan et al., “Larvivorous fish in wells target the malaria vector sibling species of the Anopheles culicifacies complex in villages in Karnataka, India,” Transactions of the Royal Society of Tropical Medicine & Hygiene, vol. 99, no. 2, pp. 101–105, 2005.
- S. K. Ghosh and A. P. Dash, “Larvivorous fish against malaria vectors: a new outlook,” Transactions of the Royal Society of Tropical Medicine & Hygiene, vol. 101, no. 11, pp. 1063–1064, 2007.
- R. F. Luck, B. M. Shepard, and P. E. Kenmore, “Experimental methods for evaluating arthropod natural enemies,” Annual Review of Entomology, vol. 33, pp. 367–389, 1988.
- G. Zehnder, G. M. Gurr, S. Kühne, M. R. Wade, S. D. Wratten, and E. Wyss, “Arthropod pest management in organic crops,” Annual Review of Entomology, vol. 52, pp. 57–80, 2007.
- R. M. Anderson and R. M. May, “Regulation and stability of host-parasite interactions: I. regulatory processes,” Journal of Animal Ecology, vol. 47, no. 1, pp. 219–247, 1978.
- P. D. N. Srinivasu and B. S. R. V. Prasad, “Role of quantity of additional food to predators as a control in predator-prey systems with relevance to pest management and biological conservation,” Bulletin of Mathematical Biology, vol. 73, no. 10, pp. 2249–2276, 2011.
- H. Zhang, L. Chen, and J. J. Nieto, “A delayed epidemic model with stage-structure and pulses for pest management strategy,” Nonlinear Analysis, vol. 9, no. 4, pp. 1714–1726, 2008.
- S. Bhattacharyya and D. K. Bhattacharya, “Pest control through viral disease: mathematical modeling and analysis,” Journal of Theoretical Biology, vol. 238, no. 1, pp. 177–197, 2006.
- B. J. Cardinale, C. T. Harvey, K. Gross, and A. R. Ives, “Biodiversity and biocontrol: emergent impacts of a multi-enemy assemblage on pest suppression and crop yield in an agroecosystem,” Ecology Letters, vol. 6, no. 9, pp. 857–865, 2003.
- J. M. Tylianakis and C. M. Romo, “Natural enemy diversity and biological control: making sense of the context-dependency,” Basic and Applied Ecology, vol. 11, no. 8, pp. 657–668, 2010.
- W. W. Murdoch, J. Chesson, and P. L. Chesson, “Biological control in theory and practice,” The American Naturalist, vol. 125, no. 3, pp. 344–366, 1985.
- S. M. Moore, E. T. Borer, and P. R. Hosseini, “Predators indirectly control vector-borne disease: linking predator-prey and host-pathogen models,” Journal of the Royal Society Interface, vol. 7, no. 42, pp. 161–176, 2009.
- M. J. Jeger, J. Holt, F. Van Den Bosch, and L. V. Madden, “Epidemiology of insect-transmitted plant viruses: modelling disease dynamics and control interventions,” Physiological Entomology, vol. 29, no. 3, pp. 291–304, 2004.
- P. W. Ewald and G. De Leo, “Alternative transmission modes and the evolution of virulence,” in Adaptive Dynamics of Infectious Diseases, U. Dieckmann, J. A. J. Metz, M. W. Sabelis, and K. Sigmund, Eds., pp. 10–26, Cambridge University Press, New York, NY, USA, 2005.
- W. E. Fitzgibbon, M. E. Parrott, and G. F. Webb, “Diffusion epidemic models with incubation and crisscross dynamics,” Mathematical Biosciences, vol. 128, no. 1-2, pp. 131–155, 1995.
- J. Holt, M. J. Jeger, J. M. Thresh, and G. W. Otim-Nape, “An epidemiological model incorporating vector population dynamics applied to African cassava mosaic virus disease,” Journal of Applied Ecology, vol. 34, no. 3, pp. 793–806, 1997.
- S. A. Gourley, R. Liu, and J. Wu, “Eradicating vector-borne diseases via age-structured culling,” Journal of Mathematical Biology, vol. 54, no. 3, pp. 309–335, 2007.
- H.-M. Wei, X.-Z. Li, and M. Martcheva, “An epidemic model of a vector-borne disease with direct transmission and time delay,” Journal of Mathematical Analysis and Applications, vol. 342, no. 2, pp. 895–908, 2008.
- J. Tumwiine, J. Y. T. Mugisha, and L. S. Luboobi, “A host-vector model for malaria with infective immigrants,” Journal of Mathematical Analysis and Applications, vol. 361, no. 1, pp. 139–149, 2010.
- Z. P. Qiu, Q. K. Kong, X. Z. Li, and M. Martcheva, “The vector-host epidemic model with multiple strains in a patchy environment,” Journal of Mathematical Analysis and Applications, vol. 405, no. 1, pp. 12–36, 2013.
- A. A. Lashari and G. Zaman, “Global dynamics of vector-borne diseases with horizontal transmission in host population,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 745–754, 2011.
- M. J. Jeger, F. Van den Bosch, and L. V. Madden, “Modelling virus-and host-limitation in vectored plant disease epidemics,” Virus Research, vol. 159, no. 2, pp. 215–222, 2011.
- J. G. Schraiber, A. N. Kaczmarczyk, R. Kwok et al., “Constraints on the use of lifespan-shortening Wolbachia to control dengue fever,” Journal of Theoretical Biology, vol. 297, pp. 26–32, 2012.
- H. Hughes and N. F. Britton, “Modelling the use of Wolbachia to control dengue fever transmission,” Bulletin of Mathematical Biology, vol. 75, no. 5, pp. 796–818, 2013.
- K. W. Okamoto and P. Amarasekare, “The biological control of disease vectors,” Journal of Theoretical Biology, vol. 309, pp. 47–57, 2012.
- C. S. Holling, “The functional response of predators to prey density and its role in mimicry and population regulations,” Memoirs of the Entomological Society of Canada, vol. 45, pp. 3–60, 1965.
- O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, “On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations,” Journal of Mathematical Biology, vol. 28, no. 4, pp. 365–382, 1990.
- P. Van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, no. 1-2, pp. 29–48, 2002.
- J. K. Hale, Ordinary Differential Equations, John Wiley & Sons, New York, NY, USA, 1969.
- H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, vol. 41 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1995.
- H. L. Smith, “Cooperative systems of differential equations with concave nonlinearities,” Nonlinear Analysis: Theory, Methods & Applications, vol. 10, no. 10, pp. 1037–1052, 1986.
- C. Castillo-Chavez and H. R. Thieme, “Asymptotically autonomous epidemic models,” in Mathematical Population Dynamics: Analysis of Heterogeneity, O. Arino and M. Kimmel, Eds., vol. 1 of Theory of Epidemics, pp. 33–50, Wuerz, Winnipeg, Canada, 1995.
- J. J. Tewa, V. Y. Djeumen, and S. Bowong, “Predator-prey model with Holling response function of type II and SIS infectious disease,” Applied Mathematical Modelling, vol. 37, no. 7, pp. 4825–4841, 2013.