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Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data

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  • Qureshi, Sania
  • Atangana, Abdon

Abstract

In connection with issues pertinent with humans’ health, it is highly significant to comprehend the complex dynamics of the related infectious disease since the non-Markovian effects play a vital role in its spread. This research analysis investigates an epidemiological model related with diarrhea transmission dynamics that occurred in Ghana during 2008–2018. The real data of 11 years have been obtained from Ministry of Health-Ghana and used to validate the proposed model. The epidemiological model is designed for the very first time with newly devised fractal fractional Caputo type operator having the fractional order α and the fractal dimension τ. The working parameters of the model are estimated and fitted with the real data using nonlinear least-squares fitting method and the basic reproduction number is found to be R0≈2.09665. Existence and uniqueness of the special solution of the proposed model are investigated. The disease free and the endemic equilibria are also computed. Finally, numerical simulations of the model are carried out via proposed numerical method and results in the graphical illustrations based upon effects of the estimated and fitted parameters show that the disease can either be substantially controlled or eradicated if the transmission rate of the epidemic is reduced and the rate of treatment is increased.

Suggested Citation

  • Qureshi, Sania & Atangana, Abdon, 2020. "Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302058
    DOI: 10.1016/j.chaos.2020.109812
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    References listed on IDEAS

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