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Numerical solution of hybrid mathematical model of dengue transmission with relapse and memory via Adam–Bashforth–Moulton predictor-corrector scheme

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  • Agarwal, Praveen
  • Singh, Ram
  • Rehman, Attiq ul

Abstract

In this paper, a novel hybrid compartmental model of the dengue transmission process is proposed and studied with memory and relapse between host-to-vector and vice versa. The memory and correlated learning system in the dengue models by using the fractional differential operators such as Riemann–Liouville and Caputo has been a fascinating area of research. A threshold parameter which is called basic reproduction number R0 is investigated and calculated by next-generation technique. It’s also shows that if basic reproduction number R0<1, the disease-free equilibrium(DFE) is locally asymptotically stable(LAS) and if R0>1 then, the DFE is unstable. It’s also found that the fractional-order α also depends upon R0. Therefore, if fractional-order α=1 and R0>1, then dengue fever model doesn’t show Hopf-type bifurcation. Further, it’s also worth mentioning that although R0<1, the DFE E0 may not be always stable but it’s necessary and the model shows a Hopf-type bifurcation. We employed the scheme of Adams–Bashforth–Moulton predictor-corrector to find an approximate the solution of the dengue model. The numerical simulation is carried out to validate the analytic solution.

Suggested Citation

  • Agarwal, Praveen & Singh, Ram & Rehman, Attiq ul, 2021. "Numerical solution of hybrid mathematical model of dengue transmission with relapse and memory via Adam–Bashforth–Moulton predictor-corrector scheme," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309553
    DOI: 10.1016/j.chaos.2020.110564
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    References listed on IDEAS

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    1. Fengrong Zhang & Changpin Li & YangQuan Chen, 2011. "Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-12, August.
    2. Agarwal, Praveen & Singh, Ram, 2020. "Modelling of transmission dynamics of Nipah virus (Niv): A fractional order Approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    3. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
    4. Abdon Atangana & Aydin Secer, 2013. "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    5. Jan, Rashid & Khan, Muhammad Altaf & Kumam, Poom & Thounthong, Phatiphat, 2019. "Modeling the transmission of dengue infection through fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 189-216.
    6. Qureshi, Sania & Yusuf, Abdullahi & Shaikh, Asif Ali & Inc, Mustafa, 2019. "Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
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    Cited by:

    1. Rehman, Attiq ul & Singh, Ram & Singh, Jagdev, 2022. "Mathematical analysis of multi-compartmental malaria transmission model with reinfection," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Rehman, Attiq ul & Singh, Ram & Agarwal, Praveen, 2021. "Modeling, analysis and prediction of new variants of covid-19 and dengue co-infection on complex network," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Baleanu, Dumitru & Shekari, Parisa & Torkzadeh, Leila & Ranjbar, Hassan & Jajarmi, Amin & Nouri, Kazem, 2023. "Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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