An analysis of tuberculosis model with exponential decay law operator

Ebenezer Bonyah

doi:10.3934/DCDSS.2021057

An analysis of tuberculosis model with exponential decay law operator

Ebenezer Bonyah, Fatmawati

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2101-2117
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	14
Issue number	7
DOIs	https://doi.org/10.3934/DCDSS.2021057
Publication status	Published - Jul 2021

Keywords

Caputo-Fabizio
Existence and uniqueness
Kernel
Padé approximation
Tuberculosis

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This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.3934/DCDSS.2021057

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title = "An analysis of tuberculosis model with exponential decay law operator",

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 pad{\'e} 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 = "Caputo-Fabizio, Existence and uniqueness, Kernel, Pad{\'e} approximation, Tuberculosis",

author = "Ebenezer Bonyah and Fatmawati",

note = "Funding Information: 2020 Mathematics Subject Classification. Primary: 26A33, 47H10. Key words and phrases. Tuberculosis, Caputo-Fabizio, pad{\'e}approximation, existence and uniqueness, kernel. This research is supported by Universitas Airlangga with Riset Kolaborasi Mitra LN 2020. ∗ Corresponding author: [email protected]. Publisher Copyright: {\textcopyright} 2021 American Institute of Mathematical Sciences. All rights reserved.",

year = "2021",

month = jul,

doi = "10.3934/DCDSS.2021057",

language = "English",

volume = "14",

pages = "2101--2117",

journal = "Discrete and Continuous Dynamical Systems - Series S",

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AU - Fatmawati,

N1 - Funding Information: 2020 Mathematics Subject Classification. Primary: 26A33, 47H10. Key words and phrases. Tuberculosis, Caputo-Fabizio, padéapproximation, existence and uniqueness, kernel. This research is supported by Universitas Airlangga with Riset Kolaborasi Mitra LN 2020. ∗ Corresponding author: [email protected]. Publisher Copyright: © 2021 American Institute of Mathematical Sciences. All rights reserved.

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - Caputo-Fabizio

KW - Existence and uniqueness

KW - Kernel

KW - Padé approximation

KW - Tuberculosis

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An analysis of tuberculosis model with exponential decay law operator

Abstract

Keywords

UN SDGs

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