On rotavirus infectious disease model using piecewise modified $ ABC $ fractional order derivative

Eiman; Kamal Shah; Muhammad Sarwar; Thabet Abdeljawad; Eiman; Kamal Shah; Muhammad Sarwar; Thabet Abdeljawad

doi:10.3934/nhm.2024010

Networks and Heterogeneous Media

2024, Volume 19, Issue 1: 214-234. doi: 10.3934/nhm.2024010

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On rotavirus infectious disease model using piecewise modified $ ABC $ fractional order derivative

1.
Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematics and Applied Mathematics School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Received: 22 November 2023 Revised: 05 February 2024 Accepted: 18 February 2024 Published: 23 February 2024

The goal of this manuscript is to use a mathematical model with four compartments to examine the positive effects of rotavirus vaccinations. Susceptible, vaccinated, infected, and recovered (SVIR) classes are included in the suggested model. Some qualitative conclusions are established for the complicated pediatric disease epidemic model of rotavirus, which travels through a population at an inconsistent rate. The model has been fitted with piecewise equations of non-singular kernel-type derivatives in the modified Atangana-Balaneu-Caputo $ (mABC) $ sense. Using the Laplace transform and the notion of non-singular-type derivatives, we prove several basic conclusions regarding the solution's feasibility and positivity. We have used the matrix approach to compute the reproductive number further. Also, the sensitivity of the model has been computed. Additionally, we have used an efficient numerical approach to simulate the model by using some numerical values for the nomenclature of the model. Additionally, using the numerical approach, various graphical illustrations are given.
- SVIR model,
- piecewise derivative,
- $ mABC $,
- sensitivity analysis,
- mumerical technique
Citation: Eiman, Kamal Shah, Muhammad Sarwar, Thabet Abdeljawad. On rotavirus infectious disease model using piecewise modified $ ABC $ fractional order derivative[J]. Networks and Heterogeneous Media, 2024, 19(1): 214-234. doi: 10.3934/nhm.2024010

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Abstract

The goal of this manuscript is to use a mathematical model with four compartments to examine the positive effects of rotavirus vaccinations. Susceptible, vaccinated, infected, and recovered (SVIR) classes are included in the suggested model. Some qualitative conclusions are established for the complicated pediatric disease epidemic model of rotavirus, which travels through a population at an inconsistent rate. The model has been fitted with piecewise equations of non-singular kernel-type derivatives in the modified Atangana-Balaneu-Caputo $ (mABC) $ sense. Using the Laplace transform and the notion of non-singular-type derivatives, we prove several basic conclusions regarding the solution's feasibility and positivity. We have used the matrix approach to compute the reproductive number further. Also, the sensitivity of the model has been computed. Additionally, we have used an efficient numerical approach to simulate the model by using some numerical values for the nomenclature of the model. Additionally, using the numerical approach, various graphical illustrations are given.

References

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