Modelling and analysis tuberculosis (TB) model with hybrid fractional operator

Muhammad Farman, Cicik Alfiniyah, Aamir Shehzad

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)463-478
Number of pages16
JournalAEJ - Alexandria Engineering Journal
Publication statusPublished - 1 Jun 2023


  • Biological feasibility
  • Constant Proportional(CP) operator
  • Eigenfunctions
  • Existence
  • Hilfer Generalized Proportional
  • Reproductive Number
  • Stability Analysis
  • Tuberculosis (TB) Model


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