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Real life application of Caputo fractional derivative for measles epidemiological autonomous dynamical system

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  • Qureshi, Sania

Abstract

Various infectious diseases primarily contain the characteristics of memory and non-locality. Keeping this in view; we have, in the present paper, proposed a new epidemiological system for the measles epidemic via Caputo fractional order operator which is not only a non-local operator but also contains all characteristics concerned with memory of the epidemic. The proposed system is autonomous in nature which has been made physically meaningful by dimensional homogeneity among the fractional order Caputo derivative and the biological parameters used in the system. Caputo fractional order parameter “τ” and the disease transmission rate “β” are fitted with nonlinear least-squares curve fitting technique while using real confirmed measles incidence cases for May-December, 2018 in Pakistan as reported by World Health Organization (WHO). Coming to mathematical analysis, the system is found to have unique solution under fixed point theory with biologically feasible region which is shown as positively invariant. Steady-states are determined to be locally asymptotically stable under different conditions on the basic reproduction number whereas the least and the most influential parameters for the system are computed via forward sensitivity index analysis. Finally, the Caputo system is simulated using Adams technique devised for finding approximate solutions of fractional Caputo ordinary differential equations. Comparative analysis is carried out and effects of different biological parameters on dynamics and transmission of the measles epidemic have been thoroughly investigated.

Suggested Citation

  • Qureshi, Sania, 2020. "Real life application of Caputo fractional derivative for measles epidemiological autonomous dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301466
    DOI: 10.1016/j.chaos.2020.109744
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    References listed on IDEAS

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    1. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    2. 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).
    3. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 32-40.
    4. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    5. Qureshi, Sania & Bonyah, Ebenezer & Shaikh, Asif Ali, 2019. "Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
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    4. Arshad, Sadia & Siddique, Imran & Nawaz, Fariha & Shaheen, Aqila & Khurshid, Hina, 2023. "Dynamics of a fractional order mathematical model for COVID-19 epidemic transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    5. Mohamed Jleli & Bessem Samet & Calogero Vetro, 2021. "Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative," Mathematics, MDPI, vol. 9(16), pages 1-11, August.
    6. Zhang, Tao & Lu, Zhong-rong & Liu, Ji-ke & Chen, Yan-mao & Liu, Guang, 2023. "Parameter estimation of linear fractional-order system from laplace domain data," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    7. Dalal Yahya Alzahrani & Fuaada Mohd Siam & Farah A. Abdullah, 2023. "Elucidating the Effects of Ionizing Radiation on Immune Cell Populations: A Mathematical Modeling Approach with Special Emphasis on Fractional Derivatives," Mathematics, MDPI, vol. 11(7), pages 1-21, April.
    8. Kaviya, R. & Priyanka, M. & Muthukumar, P., 2022. "Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    9. Manuel De la Sen & Asier Ibeas & Santiago Alonso-Quesada, 2022. "On the Supervision of a Saturated SIR Epidemic Model with Four Joint Control Actions for a Drastic Reduction in the Infection and the Susceptibility through Time," IJERPH, MDPI, vol. 19(3), pages 1-26, January.
    10. Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

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