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Modeling the transmission of dengue infection through fractional derivatives

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  • Jan, Rashid
  • Khan, Muhammad Altaf
  • Kumam, Poom
  • Thounthong, Phatiphat

Abstract

It is prominent that memory has a prodigious influence on the development of every process associated with human societies. More specifically, the growth of an epidemic process is directly associated with the individuals’ experiences. In fact, the real epidemic process is obviously sustained by non-Markovian dynamics: heredity properties and memory effects perform a critical role in the subsequent spread of infection. These additional properties increase the accuracy and reliability of fractional order systems than the other ordinary systems. In this current study, a dengue infection model with asymptomatic carriers through Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) fractional derivatives is introduced. Analytic skills are used to obtain the basic reproduction number for the proposed dengue model, denoted by R0. We use partial rank correlation coefficient (PRCC) method to detect the effect of input parameters on the outcomes of R0. In addition, we have proven sufficient condition for the existence and uniqueness of solution for the suggested fractional dynamics of dengue infection. To explore the intricate dynamics of dengue infection with the effect of asymptomatic carriers, we perform numerical simulations of the suggested dengue model by varying the fractional order ℓ. Fractional order model offers realistic information about the dynamics of the suggested dengue model and sharply decrease infected individuals by decreasing the fractional order parameter ℓ for the case of Caputo–Fabrizio model while a rapid decrease in the case of Atangana–Baleanu model. We show that the Atangana–Baleanu model gives good decrease for the infected compartments in case of decreasing the fractional order parameter than that of the Caputo–Fabrizio model. It is shown that the asymptomatic fraction can be greatly decreased by decreasing the parameter ℓ. Furthermore, the influence of the biting rate of mosquitoes on infected humans is investigated numerically, and it is suggested to the control policymakers that controlling the biting rate can significantly reduce the level of dengue infection.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:189-216
    DOI: 10.1016/j.chaos.2019.07.002
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    References listed on IDEAS

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    1. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
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    5. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 111-119.
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    3. 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).
    4. Shah Hussain & Elissa Nadia Madi & Naveed Iqbal & Thongchai Botmart & Yeliz Karaca & Wael W. Mohammed, 2021. "Fractional Dynamics of Vector-Borne Infection with Sexual Transmission Rate and Vaccination," Mathematics, MDPI, vol. 9(23), pages 1-22, December.
    5. Malik, Hafiz Abid Mahmood & Abid, Faiza & Wahiddin, Mohamed Ridza & Waqas, Ahmad, 2021. "Modeling of internal and external factors affecting a complex dengue network," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Kumar, Sunil & Chauhan, R.P. & Momani, Shaher & Hadid, Samir, 2021. "A study of fractional TB model due to mycobacterium tuberculosis bacteria," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).

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