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Volume 15   Issue 2   Year 2020
Sangeeta Saha, Guruprasad Samanta

Modeling of Insect-Pathogen Dynamics with Biological Control

Mathematical Biology & Bioinformatics. 2020;15(2):268-294.

doi: 10.17537/2020.15.268.

References

  1. Van Lenteren J.C., Woets J. Biological and integrated pest control in greenhouses. Ann. Rev. Entomol. 1988;33:239-250.
  2. Van Lenteren J.C. Integrated pest management in protected crops. In: Integrated pest management. Ed. Dent D. London: Chapman & Hall,. 1995. P. 311-343.
  3. Burges H.D. Microbial Control of Pests and Plant Diseases 1970-1980. London, New York: Academic Press, 1981.
  4. Glare J.R., Jackson T.A. Use of Pathogens in Scarab Pest Management. Andover, Hampshire, UK: Intercept Ltd., 1992.
  5. Hochberg M.E. The potential role of pathogens in biological control. Nature. 1989;337:262-265. doi: 10.1038/337262a0
  6. Anderson R.M., May R.M. Infectious disease and population cycles of forest insect. Science. 1980;210:658-661. doi: 10.1126/science.210.4470.658
  7. Anderson R.M., May R.M. The population dynamics of microparasities and their invertebrate hosts. Philos. Trans. R. Soc. Lond. Ser. B. 1980;291:451-524.
  8. Briggs C.J., Godfray H.C.J. The dynamics of insect-pathogen interactions in stage-structured populations. Am. Nat. 1995;145:855-887.
  9. Brown G.C. Stability in an insect-pathogen mode incorporating age-dependent immunity and seasonal host reproduction. Bull. Math. Biol. 1984;46:139-153. doi: 10.1007/BF02463727
  10. Browers R.G., Begon M., Hodgkinson D.E. Host-pathogen population cycles in forest insect? Lwssons from simple models reconsidered. Oikos. 1993;67:529-538. doi: 10.2307/3545365
  11. Myers J.H. Can a general hypothesis explain population cycles of forest Lepidoptera? Adv. Ecol. Res. 1988;18:179-242. doi: 10.1016/S0065-2504(08)60181-6
  12. Begon M., Bowers R.G., Kadianakis N., Hodgkinson D.E. Disease and community structure: the importance of host self-regulation in a host-pathogen model. Am. Nat. 1992;139:1131-1150.
  13. Moerbeek, M., Van Den Bosch, F. Insect-pathogen dynamics: stage-specific susceptibility and insect density dependence. Math. Biosci. 1997;141:115-148.
  14. Holt R.D., Pickering J. Infectious disease and species coexistence: a model in Lotka-Volterra form. Am. Nat. 1985;126:196-211.
  15. Dwyer G. Density dependence and spatial structure in the dynamics of insect pathogens. Am. Nat. 1994;143:533-562.
  16. Browers R.G., Begon M. A host-pathogen model with free living infective stages, applicable to microbial pest control. J. Theor. Biol. 1991;148:305-329.
  17. Begon M., Bowers R.G. Host-pathogen models and microbial pest control: the effect of host self-regulation. J. Theor. Biol. 1995;169:275-287.
  18. Sharma S., Samanta G.P. A ratio-dependent predator-prey model with Allee effect and disease in prey. Journal of Applied Mathematics and Computing. 2014;47(1-2):345-364. doi: 10.1007/s12190-014-0779-0
  19. Hadeler K.P., Freedman H.I. Predator-prey population with parasitic infection. J. Math. Biol. 1989;27:609-631.
  20. Freedman H.I. A model of predator-prey dynamics as modified by the action of parasite. Math. Biosci. 1990;99:143-155. doi: 10.1016/0025-5564(90)90001-F
  21. Beltrami E., Carroll T.D. Modelling the role of viral disease in recurrent phytoplankton blooms. J. Math. Biol. 1994;32:857-863.
  22. Venturino E. The effects of disease on competing species. Math. Biosci. 2001;174:111-131. doi: 10.1016/S0025-5564(01)00081-5
  23. Venturino E. The influence of disease on Lotka-Volterra systems. Rockymount. J. Math. 1994;24:389-402. doi: 10.1216/rmjm/1181072471
  24. Xiao Y., Chen L. Modelling and analysis of a predator-prey model with disease in the prey. Math. Biosci. 2001;171:59-82.
  25. Xiao, Y., Chen, L. Analysis of a three species eco-epidemiological model. J. Math. Anal. Appl. 2001;171:59-82.
  26. Mondal A., Pal A.K., Samanta G.P. On the dynamics of evolutionary Leslie-Gower predator-prey eco-epidemiological model with disease in predator. Ecological Genetics and Genomics. 2019;10:100034. doi: 10.1016/j.egg.2018.11.002
  27. Hale J.K. Theory of functional Differential Equations. Heidelberg: Springer-Verlag, 1977. doi: 10.1007/978-1-4612-9892-2
  28. Saha S., Samanta G.P. Local dynamics of a predator–prey community in a moderate period of time. Energy, Ecology and Environment. 2020;5(1):47-60. doi: 10.1007/s40974-019-00146-1
  29. Freedman H.I., Ruan S. Uniform persistence in functional differential equations. J Differ Equ. 1995;115:173-192. doi: 10.1006/jdeq.1995.1011
  30. Perko L. Differential equations and dynamical systems. Berlin: Springer, 2013.
  31. Murray J.D. Mathematical biology. New York: Springer-Verlag, 1993. doi: 10.1007/978-3-662-08542-4
  32. Saha S., Samanta G.P. Analysis of a predator–prey model with herd behaviour and disease in prey incorporating prey refuge. International Journal of Biomathematics. 2019;12(1):1950007. doi: 10.1142/S1793524519500074
  33. Saha S., Maiti A., Samanta G.P. A Michaelis–Menten Predator–Prey Model with Strong Allee Effect and Disease in Prey Incorporating Prey Refuge. International Journal of Bifurcation and Chaos. 2018;28(6). Article No. 1850073. doi: 10.1142/S0218127418500736
  34. LaSalle J. The stability of dynamical systems. Regional conference series in applied mathematics. SIAM, Philadelphia, 1976.
  35. Cushing J.M., Dennis B., Desharnais R.A., Costantino R.F. Moving toward an unstable equilibrium: saddle nodes in population systems. J. Anim. Ecol. 1998;67:298-306.
  36. Hastings A. Transient dynamics and persistence of ecological systems. Ecol. Lett. 2001;4:215-220.
  37. Hastings A. Transients: the key to long-term ecological understanding? Trends in Ecology and Evolution. 2004;19:39-45. doi: 10.1016/j.tree.2003.09.007
  38. Lai Y.C., Winslow R.L. Geometric-properties of the chaotic saddle responsible for supertransients in spatiotemporal chaotic systems. Phys. Rev. Lett. 1995;74:5208-5211. doi: 10.1103/PhysRevLett.74.5208
Table of Contents
Original Article
Math. Biol. Bioinf.
2020;15(2):268-294
doi: 10.17537/2020.15.268
published in English

Abstract (eng.)
Abstract (rus.)
Full text (eng., pdf)
References

 
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