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July  2021, 14(7): 2101-2117. doi: 10.3934/dcdss.2021057

## An analysis of tuberculosis model with exponential decay law operator

 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

Received  March 2020 Revised  May 2020 Published  July 2021 Early access  May 2021

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

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.

Citation: Ebenezer Bonyah, Fatmawati. An analysis of tuberculosis model with exponential decay law operator. Discrete & Continuous Dynamical Systems - S, 2021, 14 (7) : 2101-2117. doi: 10.3934/dcdss.2021057
##### References:

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##### References:
Flow diagram of model for TB transmission
Numerical simulation for TB model (16) with CF fractional using HATM at $\sigma = 1, 0.95, 0.90, 0.85$
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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