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Periodic dynamics of rubella epidemic under standard and fractional Caputo operator with real data from Pakistan

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  • Qureshi, Sania

Abstract

Memory effects of epidemics play a vital role in mathematical models of infectious diseases. In this research study, an epidemiological SEIR (Susceptible, Exposed, Infectious, Removed) type model for the rubella epidemic has been proposed via classical and fractional order Caputo differential operators while assuming the periodic transmission rate β(t). The Caputo model has been investigated for the existence and uniqueness of its solutions via fixed point theory while the unique non-negative solution remains bounded within the biologically feasible region. Later, the non-fixed biological parameters of the classical and the Caputo model are obtained via nonlinear least squares fitting technique taking the real monthly cases for the rubella epidemic in Pakistan for the period 2010–2012. The performance rate of the Caputo model is 35% higher than that of the model with integer order derivative. The numerical simulations are obtained under different cases and it is highly suggested that the infectious rate σ must be controlled as much as possible to eradicate the rubella epidemic.

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  • Qureshi, Sania, 2020. "Periodic dynamics of rubella epidemic under standard and fractional Caputo operator with real data from Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 151-165.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:151-165
    DOI: 10.1016/j.matcom.2020.06.002
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    1. Ullah, Saif & Khan, Muhammad Altaf & Farooq, Muhammad & Gul, Taza, 2019. "Modeling and analysis of Tuberculosis (TB) in Khyber Pakhtunkhwa, Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 181-199.
    2. Rahman, Ghaus ur & Shah, Kamal & Haq, Fazal & Ahmad, Naveed, 2018. "Host vector dynamics of pine wilt disease model with convex incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 31-39.
    3. Qureshi, Sania & Memon, Zaib-un-Nisa, 2020. "Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. 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.
    5. 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).
    6. Muhammad Altaf Khan & S. F. Saddiq & Saeed Islam & Ilyas Khan & Dennis Ling Chuan Ching, 2014. "Epidemic Model of Leptospirosis Containing Fractional Order," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, December.
    7. 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).
    8. Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Saad, Khaled M. & Khan, Muhammad Altaf & Agarwal, P., 2019. "Analytic solution for oxygen diffusion from capillary to tissues involving external force effects: A fractional calculus approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 48-65.
    9. Ullah, Saif & Altaf Khan, Muhammad & Farooq, Muhammad, 2018. "A fractional model for the dynamics of TB virus," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 63-71.
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    Cited by:

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    2. Yusuf, Abdullahi & Tasiu Mustapha, Umar & Abdulkadir Sulaiman, Tukur & Hincal, Evren & Bayram, Mustafa, 2021. "Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. 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).
    4. Trikha, Pushali & Mahmoud, Emad E. & Jahanzaib, Lone Seth & Matoog, R.T. & Abdel-Aty, Mahmoud, 2021. "Fractional order biological snap oscillator: Analysis and control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Hussain, Takasar & Aslam, Adnan & Ozair, Muhammad & Tasneem, Fatima & Gómez-Aguilar, J.F., 2021. "Dynamical aspects of pine wilt disease and control measures," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

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