Modelling and analysis tuberculosis (TB) model with hybrid fractional operator
In this work, we aim to propose a hybrid fractional-order model for investigation and observation of the tuberculosis (TB) disease involving constant-proportional Caputo (CPC) operator. We treat the proposed model’s positivity, boundedness, well-posedness, and biological viability with a reproductiv...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-06-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016823002922 |
| _version_ | 1797842477329154048 |
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| author | Muhammad Farman Cicik Alfiniyah Aamir Shehzad |
| author_facet | Muhammad Farman Cicik Alfiniyah Aamir Shehzad |
| author_sort | Muhammad Farman |
| collection | DOAJ |
| description | In this work, we aim to propose a hybrid fractional-order model for investigation and observation of the tuberculosis (TB) disease involving constant-proportional Caputo (CPC) operator. We treat the proposed model’s positivity, boundedness, well-posedness, and biological viability with a reproductive number. We prove the existence and uniqueness of the solutions to the proposed model using the fixed-point theorem. For the proposed model, Ulam Hyres’ stability is also presented. To evaluate the fractional integral operator, we use different techniques to invert the proportional-caputo (PC) and constant-proportional caputo (CPC) operators. We also use our suggested model’s fractional differential equations to derive the eigenfunctions of the CPC operator. There is a detailed discussion of additional analysis of the CPC and Hilfer generalized proportional operators. To solve the suggested model, we employ the Laplace Adomian Decomposition (LADM) technique. Fractional order enhances the dynamics of the epidemic model and has a significant impact on the persistence and extinction of the infection. We see that the CPC operator yields excellent results when applied to the TB version’s mathematical modelling. The suggested strategy is a straightforward, useful, and practical plan for resolving and comprehending a range of non-linear physical models. This study serves as an illustration of the application of fractional derivatives in epidemiology. |
| first_indexed | 2024-04-09T16:48:33Z |
| format | Article |
| id | doaj.art-f35589ef2f044997a8e6aaee20476436 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-09T16:48:33Z |
| publishDate | 2023-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-f35589ef2f044997a8e6aaee204764362023-04-22T06:20:38ZengElsevierAlexandria Engineering Journal1110-01682023-06-0172463478Modelling and analysis tuberculosis (TB) model with hybrid fractional operatorMuhammad Farman0Cicik Alfiniyah1Aamir Shehzad2Institute of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan; Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, IndonesiaDepartment of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia; Corresponding author.Institute of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, PakistanIn this work, we aim to propose a hybrid fractional-order model for investigation and observation of the tuberculosis (TB) disease involving constant-proportional Caputo (CPC) operator. We treat the proposed model’s positivity, boundedness, well-posedness, and biological viability with a reproductive number. We prove the existence and uniqueness of the solutions to the proposed model using the fixed-point theorem. For the proposed model, Ulam Hyres’ stability is also presented. To evaluate the fractional integral operator, we use different techniques to invert the proportional-caputo (PC) and constant-proportional caputo (CPC) operators. We also use our suggested model’s fractional differential equations to derive the eigenfunctions of the CPC operator. There is a detailed discussion of additional analysis of the CPC and Hilfer generalized proportional operators. To solve the suggested model, we employ the Laplace Adomian Decomposition (LADM) technique. Fractional order enhances the dynamics of the epidemic model and has a significant impact on the persistence and extinction of the infection. We see that the CPC operator yields excellent results when applied to the TB version’s mathematical modelling. The suggested strategy is a straightforward, useful, and practical plan for resolving and comprehending a range of non-linear physical models. This study serves as an illustration of the application of fractional derivatives in epidemiology.http://www.sciencedirect.com/science/article/pii/S111001682300292237C7593B0565L07 |
| spellingShingle | Muhammad Farman Cicik Alfiniyah Aamir Shehzad Modelling and analysis tuberculosis (TB) model with hybrid fractional operator Alexandria Engineering Journal 37C75 93B05 65L07 |
| title | Modelling and analysis tuberculosis (TB) model with hybrid fractional operator |
| title_full | Modelling and analysis tuberculosis (TB) model with hybrid fractional operator |
| title_fullStr | Modelling and analysis tuberculosis (TB) model with hybrid fractional operator |
| title_full_unstemmed | Modelling and analysis tuberculosis (TB) model with hybrid fractional operator |
| title_short | Modelling and analysis tuberculosis (TB) model with hybrid fractional operator |
| title_sort | modelling and analysis tuberculosis tb model with hybrid fractional operator |
| topic | 37C75 93B05 65L07 |
| url | http://www.sciencedirect.com/science/article/pii/S1110016823002922 |
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