TY - JOUR
T1 - Modelling and analysis tuberculosis (TB) model with hybrid fractional operator
AU - Farman, Muhammad
AU - Alfiniyah, Cicik
AU - Shehzad, Aamir
N1 - Publisher Copyright:
© 2023 Faculty of Engineering, Alexandria University
PY - 2023/6/1
Y1 - 2023/6/1
N2 - 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.
AB - 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.
KW - Biological feasibility
KW - Constant Proportional(CP) operator
KW - Eigenfunctions
KW - Existence
KW - Hilfer Generalized Proportional
KW - Reproductive Number
KW - Stability Analysis
KW - Tuberculosis (TB) Model
UR - http://www.scopus.com/inward/record.url?scp=85152933096&partnerID=8YFLogxK
U2 - 10.1016/j.aej.2023.04.017
DO - 10.1016/j.aej.2023.04.017
M3 - Article
AN - SCOPUS:85152933096
SN - 1110-0168
VL - 72
SP - 463
EP - 478
JO - AEJ - Alexandria Engineering Journal
JF - AEJ - Alexandria Engineering Journal
ER -