123
Views
3
CrossRef citations to date
0
Altmetric
Articles

Discretization of an eco-epidemiological model and its dynamic consistency

&
Pages 860-877 | Received 15 Nov 2016, Accepted 04 Mar 2017, Published online: 27 Mar 2017

References

  • D. Adak, and N. Bairagi, Complexity in a predator-prey-parasite model with nonlinear incidence rate and incubation delay, Chaos, Soli. Fract. 81 (2015), pp. 271–289.
  • R.M. Anderson, and R.M. May, The invasion, persistence, and spread of infectious diseases within animal and plant communities, Philos. Trans. R. Soc. Lond. B 314 (1986), pp. 533–570.
  • N. Bairagi, and D. Adak, Switching from simple to complex dynamics in a predator-prey-parasite model: an interplay between infection rate and incubation delay, Math. Bios. 277 (2016), pp. 1–14.
  • N. Bairagi, and M. Biswas, A predator-prey model with Beddington-DeAngelis functional response: a non-standard finite-difference method, J. Differ. Equ. Appl. 22 (2016), pp. 581–593.
  • N. Bairagi, P.K. Roy, and J. Chattopadhyay, Role of infection on the stability of a predator-prey system with several response functions - A comparative study, J. Theor. Biol. 248 (2007), pp. 10–25.
  • N. Bairagi, R. Sarkar, and J. Chattopadhyay, Impacts of incubation delay on the dynamics of an eco-epidemiological system - a theoretical study, Bull. Math. Biol. 70 (2008), pp. 2017–2038.
  • D.T. Dimitrov, H.V. Kojouh arov, Positive and elementary stable nonstandard numerical methods with applications to predator-prey models, J. Comput. Appl. Math. 189 (2006), pp. 98–108.
  • D.T. Dimitrov, and H.V. Kojouharov, Nonstandard numerical methods for a class of predator-prey models with predator inference, Electron. J. Differ. Equ. Confer. 15 (2007), pp. 67–75.
  • Y. Enatsua, Y. Nakatab, Y. Muroyac, G. Izzod, and A. Vecchio, Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates, J. Differ. Equ. Appl. 18 (2012), pp. 1163–1181.
  • A. Fenton, and S.A. Rands, The impact of parasite manipulation and predator foraging behavior on predator-prey communities, Ecology 87 (2006), pp. 2832–2841.
  • G. Gabbriellini, Nonstandard finite difference scheme for mutualistic interaction description, Int. J. Differ. Equ. 9 (2014), pp. 147–161.
  • A.B. Gumel, K.C. Patidar, and R.J. Spiteri, Asymptotically consistent nonstandard finite difference methods for solving mathematical models arising in population biology, in Advances in the Applications of Nonstandard Finite Difference Schemes, R.E. Mickens, ed., World Scientific, Singapore, 2005, pp. 513–560.
  • H.W. Hethcote, W. Wang, L. Han, and Z. Ma, A predator-prey model with infected prey, Theor. Popul. Biol. 66 (2004), pp. 259–268.
  • J.D. Lambert, Numerical methods for ordinarry differential systems: The initial value problem, Wiley, Chichester, 1991.
  • Y. Li, Bifurcation analysis of a non-standard finite difference scheme for a time-delayed model of asset prices, J. Differ. Equ. Appl. 19 (2013), pp. 507–519.
  • R.E. Mickens, Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: Implications for numerical analysis, Numer. Method Partial Differ. Equ. 5 (1989), pp. 313–325.
  • R.E. Mickens, Numerical Study of a non-standard finiteÂdifference scheme for the Van Der Pol equation, J. Sound Vibr. 250 (2002), pp. 955–963.
  • R.E. Mickens, A SIR-model with square-root dynamics: An NSFD scheme, J. Differ. Equ. Appl. 16 (2010), pp. 209–216.
  • S.M. Moghadas, M.E. Alexander, B.D. Corbett, and A.B. Gumel, A Positivity-preserving Mickens-type discretization of an epidemic model, J. Differ. Equ. Appl. 9 (2003), pp. 1037–1051.
  • M.Y. Ongun, and I. Turhan, A numerical comparison for a discrete HIV infction of CD4+ T-cell model derived from non-standard numerical scheme, J. Appl. Math. 2013 (2013), pages. 9. Article ID 375094. doi:10.1155/2013/375094.
  • L.-I.W. Roeger, and G. Lahodny, Dynamically consistent discrete Lokta-Volterra competition systems, J. Differ. Equ. Appl. 19 (2013), pp. 191–200.
  • M. Roy, and R.D. Holt, Effects of predation on host-pathogen dynamics in SIR models, Theor. Popul. Biol. 73 (2008), pp. 319–331.
  • A. Serfaty de Markus, and R.E. Mickens, Suppression of numerically induced chaos with non-standard finite difference schemes, J. Comput. Appl. Math. 106 (1999), pp. 317–324.
  • R.J. Spiteri, and C. Mary, MacLachlan, An efficient non-standard finite difference scheme for an ionic model of cardiac action potentials, J. Differ. Equ. Appl. 9 (2003), pp. 1069–1081.
  • E. Venturino, Epidemics in predator-prey models:diseaseinthepredators, IMA J. Math. Appl. Med. Biol. 19 (2002), pp. 185–205.
  • Y. Xiao, and F. Van Den Bosch, The dynamics of an eco-epidemic model with biological control, Ecol. Modell. 168 (2003), pp. 203–214.
  • Y. Zhou, Z. Ma, and F. Brauer, A discrete epidemic model for SARS transmission and control in China, Math. Comput. Model. 40 (2004), pp. 1491–1506.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.