Article Contents
Article Contents

# An analysis of tuberculosis model with exponential decay law operator

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

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.

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

 Citation:

• Figure 1.  Flow diagram of model for TB transmission

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

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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