IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v75y2015icp1-19.html
   My bibliography  Save this article

Effects of allochthonous inputs in the control of infectious disease of prey

Author

Listed:
  • Sahoo, Banshidhar
  • Poria, Swarup

Abstract

Allochthonous inputs are important sources of productivity in many food webs and their influences on food chain model demand further investigations. In this paper, assuming the existence of allochthonous inputs for intermediate predator, a food chain model is formulated with disease in the prey. The stability and persistence conditions of the equilibrium points are determined. Extinction criterion for infected prey population is obtained. It is shown that suitable amount of allochthonous inputs to intermediate predator can control infectious disease of prey population, provided initial intermediate predator population is above a critical value. This critical intermediate population size increases monotonically with the increase of infection rate. It is also shown that control of infectious disease of prey is possible in some cases of seasonally varying contact rate. Dynamical behaviours of the model are investigated numerically through one and two parameter bifurcation analysis using MATCONT 2.5.1 package. The occurrence of Hopf and its continuation curves are noted with the variation of infection rate and allochthonous food availability. The continuation curves of limit point cycle and Neimark Sacker bifurcation are drawn by varying the rate of infection and allochthonous inputs. This study introduces a novel natural non-toxic method for controlling infectious disease of prey in a food chain model.

Suggested Citation

  • Sahoo, Banshidhar & Poria, Swarup, 2015. "Effects of allochthonous inputs in the control of infectious disease of prey," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 1-19.
    • Handle: RePEc:eee:chsofr:v:75:y:2015:i:c:p:1-19
    DOI: 10.1016/j.chaos.2015.02.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791500034X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2015.02.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lewi Stone & Ronen Olinky & Amit Huppert, 2007. "Seasonal dynamics of recurrent epidemics," Nature, Nature, vol. 446(7135), pages 533-536, March.
    2. Mainul Haque & Joydev Chattopadhyay, 2007. "Role of transmissible disease in an infected prey-dependent predator -- prey system," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 13(2), pages 163-178, April.
    3. Sahoo, Banshidhar & Poria, Swarup, 2014. "The chaos and control of a food chain model supplying additional food to top-predator," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 52-64.
    4. Hu, Guang-Ping & Li, Xiao-Ling, 2012. "Stability and Hopf bifurcation for a delayed predator–prey model with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 229-237.
    5. Jana, Soovoojeet & Kar, T.K., 2013. "Modeling and analysis of a prey–predator system with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 42-53.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ghorai, Santu & Poria, Swarup, 2016. "Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 57-67.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wei Yang, 2021. "Modeling COVID-19 Pandemic with Hierarchical Quarantine and Time Delay," Dynamic Games and Applications, Springer, vol. 11(4), pages 892-914, December.
    2. Juneja, Nishant & Agnihotri, Kulbhushan, 2018. "Conservation of a predator species in SIS prey-predator system using optimal taxation policy," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 86-94.
    3. Hossain, Mainul & Pati, N.C. & Pal, Saheb & Rana, Sourav & Pal, Nikhil & Layek, G.C., 2021. "Bifurcations and multistability in a food chain model with nanoparticles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 808-825.
    4. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    5. Pedro, S.A. & Rwezaura, H. & Mandipezar, A. & Tchuenche, J.M., 2021. "Qualitative Analysis of an influenza model with biomedical interventions," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Baba, Isa Abdullahi & Hincal, Evren, 2018. "A model for influenza with vaccination and awareness," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 49-55.
    7. Thirthar, Ashraf Adnan & Majeed, Salam J. & Alqudah, Manar A. & Panja, Prabir & Abdeljawad, Thabet, 2022. "Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    8. José M Ponciano & Marcos A Capistrán, 2011. "First Principles Modeling of Nonlinear Incidence Rates in Seasonal Epidemics," PLOS Computational Biology, Public Library of Science, vol. 7(2), pages 1-14, February.
    9. Christensen, Claire & Albert, István & Grenfell, Bryan & Albert, Réka, 2010. "Disease dynamics in a dynamic social network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2663-2674.
    10. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.
    11. Kaniadakis, G., 2024. "Novel class of susceptible–infectious–recovered models involving power-law interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    12. Timothy R. Julian & Robert A. Canales & James O. Leckie & Alexandria B. Boehm, 2009. "A Model of Exposure to Rotavirus from Nondietary Ingestion Iterated by Simulated Intermittent Contacts," Risk Analysis, John Wiley & Sons, vol. 29(5), pages 617-632, May.
    13. Ma, Zhan-Ping & Yue, Jia-Long, 2023. "Cross diffusion induced spatially inhomogeneous Hopf bifurcation for a three species Lotka–Volterra food web model with cycle," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    14. Steindorf, Vanessa & Srivastav, Akhil Kumar & Stollenwerk, Nico & Kooi, Bob W. & Aguiar, Maíra, 2022. "Modeling secondary infections with temporary immunity and disease enhancement factor: Mechanisms for complex dynamics in simple epidemiological models," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    15. Mukhopadhyay, B. & Bhattacharyya, R., 2009. "Role of predator switching in an eco-epidemiological model with disease in the prey," Ecological Modelling, Elsevier, vol. 220(7), pages 931-939.
    16. Hu, Zengyun & Teng, Zhidong & Zhang, Tailei & Zhou, Qiming & Chen, Xi, 2017. "Globally asymptotically stable analysis in a discrete time eco-epidemiological system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 20-31.
    17. Zhang, Jia-Fang & Chen, Heshan, 2014. "Global asymptotic behavior in a Lotka–Volterra competition system with spatio-temporal delays," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 69-75.
    18. Ross Sparks & Tim Keighley & David Muscatello, 2010. "Early warning CUSUM plans for surveillance of negative binomial daily disease counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1911-1929.
    19. Sahoo, Banshidhar, 2015. "Role of additional food in eco-epidemiological system with disease in the prey," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 61-79.
    20. Joseph Pateras & Ashwin Vaidya & Preetam Ghosh, 2022. "Network Thermodynamics-Based Scalable Compartmental Model for Multi-Strain Epidemics," Mathematics, MDPI, vol. 10(19), pages 1-19, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:75:y:2015:i:c:p:1-19. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.