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Research Article

An ecogenetic disease-affected predator–prey model

, & ORCID Icon | (Reviewing Editor)
Article: 1195716 | Received 20 Oct 2015, Accepted 20 May 2016, Published online: 22 Jun 2016

References

  • Angulo, O., & López-Marcos, J. C. (1999). Numerical schemes for size-structured population equations. Mathematical Biosciences, 157, 169–188.
  • Auger, P., Mchich, R., Chowdhury, T., Sallet, G., Tchuente, M., & Chattopadhyay, J. (2009). Effects of a disease affecting a predator on the dynamics of a predator--prey system. Journal of Theoretical Biology, 258, 344–351.
  • Bairagi, N., Roy, P. K., & Chattopadhyay, J. (2007). Role of infection on the stability of a predator--prey system with several response functions---A comparative study. Journal of Theoretical Biology, 248, 10–25.
  • Bairagi, N., Sarkar, R. R., & Chattopadhyay, J. (2008). Impacts of incubation delay on the dynamics of an eco-epidemiological system---A theoretical study. Bulletin of Mathematical Biology, 70, 2017–2038. doi:10.1007/s11538-008-9337-y
  • Bairagi, N., Chaudhuri, S., & Chattopadhyay, J. (2009). Harvesting as a disease control measure in an eco-epidemiological system -- A theoretical study. Mathematical Biosciences, 217, 134–144.
  • Bate, A. M., & Hilker, F. M. (2013). Complex dynamics in an eco-epidemiological model. Bulletin of Mathematical Biology, 75, 2059–2078. doi:10.1007/s11538-013-9880-z
  • Beltrami, E., & Carroll, T. O. (1994). Modelling the role of viral disease in recurrent phytoplankton blooms. Journal of Mathematical Biology, 32, 857–863.
  • Beretta, E., & Kuang, Y. (1998). Modeling and analysis of a marine bacteriophage infection. Mathematical Biosciences, 149, 57–76.
  • Bhattacharyya, S., & Bhattacharya, D. K. (2006). Pest control through viral disease: Mathematical modeling and analysis. Journal of Theoretical Biology, 238, 177–196.
  • Chattopadhyay, J., & Arino, O. (1999). A predator--prey model with disease in the prey. Nonlinear Analysis, 36, 747–766.
  • Clarke, Bryan (2003). Heredity -- The art of innuendo. Heredity, 90(4), 279–280. doi:10.1038/sj.hdy.6800229
  • Cushing, J. M. (1998). An introduction to structured population dynamics. Philadelphia: SIAM. doi:10.1038/sj.hdy.6800229
  • Cuthbertson, A. G. S., Blackburn, L. F., & Audsley, N. (2014). Efficacy of commercially available invertebrate predators against Drosophila suzukii. Insects, 5, 952–960. doi:10.3390/insects5040952
  • Delgado, M., Molina-Becerra, M., & Suarez, A. (2005). Relating disease and predation: equilibria of an epidemic model. Mathematical Methods in the Applied Sciences, 28, 349–362.
  • Grant, B. S. (1999). Fine tuning the peppered moth paradigm. Evolution, 53(3), 980–984.
  • Gurtin, M. E., & Levine, D. S. (1979). On predator-prey interactions with predation dependent on age of prey. Mathematical Biosciences, 47, 207–219.
  • Gurtin, M. E., & McCamy, R. C. (1974). Nonlinearly age-dependent population dynamics. Archive for Rational Mechanics and Analysis, 54, 281–300.
  • Gurtin, M. E., & McCamy, R. C. (1979). Some simple models for nonlinear age-dependent population dynamics. Mathematical Biosciences, 43, 199–211.
  • Hadeler, K. P., & Freedman, H. I. (1989). Predator--prey population with parasitic infection. Journal of Mathematical Biology, 27, 609–631.
  • Hooper, J. (2002). Of moths and men: An evolutionary tale. New York, NY: W.W. Norton & Company.
  • Hotopp, I. S., Malchow, H., & Venturino, E. (2010). Switching feeding among sound and infected prey in ecoepidemic systems. Journal of Biological Systems, 18, 727–747. doi:10.1142/S0218339010003718
  • Jaenike, J. (1993). Rapid evolution of host specificity in a parasitic nematode. Evolutionary Ecology, 7, 103–108.
  • Jana, S., & Kar, T. K. (2013). Modeling and analysis of a prey--predator system with disease in the prey. Chaos, Solitons & Fractals, 47, 42–53.
  • Kar, T. K., & Jana, S. (2013). A theoretical study on mathematical modelling of an infectious disease with application of optimal control. Biosystems, 111, 37–50.
  • Kermack, W. O., & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London, 115, 700–721.
  • Khan, Q. J. A., Balakrishnan, E., & Wake, G. C. (2004). Analysis of a predator--prey system with predator switching. Bulletin of Mathematical Biology, 66, 109–123.
  • Kooi, B.W., van Voorn, G.A.K. & Das, Kp (2011). Stabilization and complex dynamics in a predator–prey model with predator suffering from an infectious disease. Ecological Complexity, 8, 113–122.
  • Lively, C.M., & Apanius, V. (1995). Genetic diversity in host-parasite interactions. In: Grenfell, B.T. & Dobson, A.P. (Eds), Ecology of infectious diseases (pp. 419–449). Cambridge: Cambridge University Press.
  • Lively, C. M., Craddock, C., & Vrijenhoek, R. C. (1990). Red Queen hypothesis supported by parasitism in sexual and clonal fish. Nature, 344, 864–866.
  • Malchow, H., Petrovskii, S., & Venturino, E. (2008). Spatiotemporal patterns in ecology and epidemiology. Boca Raton, FL: CRC.
  • Read, A. F. (1991). Passerine polygyny: A role for parasites? American Naturalist, 138, 434–459.
  • Saenz, R. A., & Hethcote, H. W. (2006). Competing species models with an infectious disease. Mathematical Biosciences and Engineering, 3, 219–235.
  • Scudo, F. M., & Ziegler, J. R. (1976). Vladimir Aleksandrovich Kostitzin and theoretical ecology. Theoretical Population Biology, 10, 395–412.
  • Sieber, M., & Hilker, F. M. (2011). Prey, predators, parasites: Intraguild predation or simpler community modules in disguise? Journal of Animal Ecology, 80, 414–421. doi:10.1111/j.1365-2656.2010.01788.x
  • Singh, B. K., Chattopadhyay, J., & Sinha, S. (2004). The role of virus infection in a simple phytoplankton zooplankton system. Journal of Theoretical Biology, 231, 153–166.
  • Smith, G.D. (1985). Numerical solution of partial differential equations: Finite difference methods. Oxford: Oxford University Press.
  • Venturino, E. (1984). Age-structured predator--prey models. Mathematical Modelling, 5, 117–128.
  • Venturino, E. (1985). A generalization of the classical epidemiology model. IMACS Transactions on Scientific Computation ’85. Modelling of Biomedical Systems (Vol. 5, pp. 243–248). North-Holland: Amsterdam.
  • Venturino E. (1987). Non-linearly interacting age-dependent populations. Computers and Mathematics with Applications, 13, 901–911.
  • Venturino, E. (1994). The influence of diseases on Lotka--Volterra systems. Rocky Mountain Journal of Mathematics, 24, 381–402.
  • Venturino, E. (1995). Epidemics in predator-prey models: disease in the prey. In: Arino, O., Axelrod, D., Kimmel, M., & Langlais, M. (Eds), Mathematical population dynamics, analysis of heterogeneity (Vol. 1, pp. 381–393). Winnipeg: Wuerz Publishing.
  • Venturino, E. (2002). Epidemics in predator--prey models: Disease in the predators. IMA Journal of Mathematics Applied Medicine and Biology, 19, 185–205.
  • Venturino, E. (2012). An ecogenetic model. Applied Mathematics Letters, 25, 1230–1233.
  • Venturino, E. (2016). Ecoepidemiology: A more comprehensive view of population interactions. Mathematical Modelling of Natural Phenomena, 11, 49–90.
  • Viberti, C. & Venturino, E. (2014). An ecosystem with Holling type II response and predators’ genetic variability. Mathematical Modelling and Analysis, 19, 371–394.
  • Vrijenhoek, R. C. (1993). The origin and evolution of clones versus the maintenance of sex in Poeciliopsis. Journal of Heredity, 84, 388–395.
  • Webb, G. (1985). Theory of nonlinear age-dependent population dynamics, Monographs and textbooks in pure & applied mathematics series Vol. 89. New York, NY: Dekker.
  • Zhen, J. & Haque, M. (2006). Global stability analysis of an eco-epidemiological model of the Salton sea. Journal of Biological Systems, 14, 373–385.