An analysis of tuberculosis model with exponential decay law operator

Ebenezer Bonyah; null Fatmawati

doi:10.3934/dcdss.2021057

Article Contents

2021, Volume 14, Issue 7: 2101-2117. Doi: 10.3934/dcdss.2021057

This issue Previous Article Parallelization of a finite volumes discretization for anisotropic diffusion problems using an improved Schur complement technique Next Article More new results on integral inequalities for generalized

$ \mathcal{K} $

-fractional conformable Integral operators

An analysis of tuberculosis model with exponential decay law operator

Ebenezer Bonyah^1, and
null Fatmawati^2, ,

1.
Department of Mathematics Education, Akenten Appiah Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana
2.
Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia

^* Corresponding author: fatmawati@fst.unair.ac.id
^* Corresponding author: fatmawati@fst.unair.ac.id

Received: March 2020

Revised: May 2020

Early access: May 2021

Published: July 2021

This research is supported by Universitas Airlangga with Riset Kolaborasi Mitra LN 2020

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Abstract

In this paper, we explore the dynamics of tuberculosis (TB) epidemic model that includes the recruitment rate in both susceptible and infected population. Stability and sensitivity analysis of the classical TB model is carried out. Caputo-Fabrizio (CF) operator is then used to explain the dynamics of the TB model. The concept of fixed point theory is employed to obtain the existence and uniqueness of the solution of the TB model in the light of CF operator. Numerical simulations based on Homotopy Analysis Transform Method (HATM) and padé approximations are performed to obtain qualitative information on the model. Numerical solutions depict that the order of the fractional derivative has great dynamics of the TB model.

Keywords:

Mathematics Subject Classification: Primary: 26A33, 47H10.

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Figure 1. Flow diagram of model for TB transmission

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Figure 2. Numerical simulation for TB model (16) with CF fractional using HATM at $ \sigma = 1, 0.95, 0.90, 0.85 $

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Figure 3. Numerical simulation for TB model (16) with CF fractional using padé approximations at $ \sigma = 1, 0.95, 0.90, 0.85 $

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