IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v144y2021ics0960077921000552.html
   My bibliography  Save this article

Dynamic study of SIAISQVR−B fractional-order cholera model with control strategies in Cameroon Far North Region

Author

Listed:
  • Nguiwa, Tchule
  • Kolaye, Gabriel Guilsou
  • Justin, Mibaile
  • Moussa, Djaouda
  • Betchewe, Gambo
  • Mohamadou, Alidou

Abstract

In this work, mathematical SIAISQVR−B fractional-order cholera model is investigated. We provide a theoretical study of the model. We derive the basic reproduction number R0 which determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever R0≤1, while when R0>1, the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is locally asymptotically stable on a positively invariant region of the positive orthant. Using the sensitivity analysis, we find that the parameters related to the vaccination and therapeutic treatment are more influencing the model. Theoretical results are supported by numerical simulations by means of fde12 solver, which further suggest using of vaccination in endemic area. We observe from Fig. 4 that, extinction of disease can occur with vaccination of susceptible individuals for ϕ>0.6. In case of lack of necessary funding to fight again cholera, Fig. 3 revealed that efforts should focus to keep contamination rates σ<0.09 and β<0.09 in other to die out with success the disease.

Suggested Citation

  • Nguiwa, Tchule & Kolaye, Gabriel Guilsou & Justin, Mibaile & Moussa, Djaouda & Betchewe, Gambo & Mohamadou, Alidou, 2021. "Dynamic study of SIAISQVR−B fractional-order cholera model with control strategies in Cameroon Far North Region," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
  • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000552
    DOI: 10.1016/j.chaos.2021.110702
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921000552
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2021.110702?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. Uçar, Sümeyra & Uçar, Esmehan & Özdemir, Necati & Hammouch, Zakia, 2019. "Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 300-306.
    2. Liu, Qun & Jiang, Daqing, 2020. "Stationary distribution of a stochastic cholera model with imperfect vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    3. Atangana, Abdon, 2020. "Fractional discretization: The African’s tortoise walk," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution of a stochastic cholera model between communities linked by migration," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    5. Hassouna, M. & Ouhadan, A. & El Kinani, E.H., 2018. "On the solution of fractional order SIS epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 168-174.
    6. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Wang, Huazheng & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution of stochastic NP ecological model under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    8. Danane, Jaouad & Allali, Karam & Hammouch, Zakia, 2020. "Mathematical analysis of a fractional differential model of HBV infection with antibody immune response," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    9. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    10. Ndolane Sene & Ameth Ndiaye & Chokkalingam Ravichandran, 2020. "On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative," Journal of Mathematics, Hindawi, vol. 2020, pages 1-15, November.
    11. Ndolane Sene, 2020. "Analysis of a Four-Dimensional Hyperchaotic System Described by the Caputo–Liouville Fractional Derivative," Complexity, Hindawi, vol. 2020, pages 1-20, November.
    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. Ain, Qura tul & Khan, Aziz & Ullah, Muhammad Irfan & Alqudah, Manar A. & Abdeljawad, Thabet, 2022. "On fractional impulsive system for methanol detoxification in human body," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

    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. Rahman, Mati ur & Arfan, Muhammad & Shah, Kamal & Gómez-Aguilar, J.F., 2020. "Investigating a nonlinear dynamical model of COVID-19 disease under fuzzy caputo, random and ABC fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D.G. & Gao, Wei & Yel, Gulnur, 2020. "Regarding new numerical solution of fractional Schistosomiasis disease arising in biological phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    4. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Abboubakar, Hamadjam & Kombou, Lausaire Kemayou & Koko, Adamou Dang & Fouda, Henri Paul Ekobena & Kumar, Anoop, 2021. "Projections and fractional dynamics of the typhoid fever: A case study of Mbandjock in the Centre Region of Cameroon," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Goyal, Manish & Baskonus, Haci Mehmet & Prakash, Amit, 2020. "Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Zafar, Zain Ul Abadin & Zaib, Sumera & Hussain, Muhammad Tanveer & Tunç, Cemil & Javeed, Shumaila, 2022. "Analysis and numerical simulation of tuberculosis model using different fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    8. Gao, Wei & Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D. G. & Kumar, Pushpendra, 2020. "A new study of unreported cases of 2019-nCOV epidemic outbreaks," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    9. Gao, Wei & Veeresha, P. & Prakasha, D.G. & Baskonus, Haci Mehmet & Yel, Gulnur, 2020. "New approach for the model describing the deathly disease in pregnant women using Mittag-Leffler function," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    10. Zafar, Zain Ul Abadin & Younas, Samina & Hussain, Muhammad Tanveer & Tunç, Cemil, 2021. "Fractional aspects of coupled mass-spring system," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    11. Rashid, Saima & Sultana, Sobia & Jarad, Fahd & Jafari, Hossein & Hamed, Y.S., 2021. "More efficient estimates via ℏ-discrete fractional calculus theory and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    12. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    13. Mohamed M. Mousa & Fahad Alsharari, 2021. "A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases," Mathematics, MDPI, vol. 9(22), pages 1-12, November.
    14. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    15. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    16. Aliyu, Aliyu Isa & Inc, Mustafa & Yusuf, Abdullahi & Baleanu, Dumitru, 2018. "A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 268-277.
    17. Bonyah, Ebenezer & Gómez-Aguilar, J.F. & Adu, Augustina, 2018. "Stability analysis and optimal control of a fractional human African trypanosomiasis model," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 150-160.
    18. Djilali, Salih & Ghanbari, Behzad & Bentout, Soufiane & Mezouaghi, Abdelheq, 2020. "Turing-Hopf bifurcation in a diffusive mussel-algae model with time-fractional-order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    19. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.
    20. Amiri, Pari & Afshari, Hojjat, 2022. "Common fixed point results for multi-valued mappings in complex-valued double controlled metric spaces and their applications to the existence of solution of fractional integral inclusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

    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:144:y:2021:i:c:s0960077921000552. 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.