A mathematical model of tuberculosis (TB) transmission with children and adults groups: A fractional model

Fatmawati; Muhammad Altaf Khan; Ebenezer Bonyah; Zakia Hammouch; Endrik Mifta Shaiful; Fatmawati; Muhammad Altaf Khan; Ebenezer Bonyah; Zakia Hammouch; Endrik Mifta Shaiful

doi:10.3934/math.2020181

AIMS Mathematics

2020, Volume 5, Issue 4: 2813-2842. doi: 10.3934/math.2020181

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A mathematical model of tuberculosis (TB) transmission with children and adults groups: A fractional model

1.
Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga Surabaya 60115, Indonesia
2.
Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa
3.
Department of Mathematics Education, University of Education Winneba, Kumasi Campus, Kumasi, Ghana
4.
Departement de Mathématiques, Faculté des Sciences et Techniques Errachidia, Université Moulay Ismail, Morocco

Received: 01 December 2019 Accepted: 19 February 2020 Published: 17 March 2020
MSC : 34A34

We consider a novel fractional model to investigates the (tuberculosis) TB model dynamics with two age groups of human, that is, the children and the adults. First, we formulate the model and present the basic results associated to the model. Then, using the fractional operators, Caputo and the Atangana-Baleanu and obtain a generalized model. Further, we give a novel numerical approach for the solution of the fractional model and obtain their approximate solution. We show graphical results with various values of the fractional order. A comparison of the two operators are shown graphically. The results obtained through Atangana-Baleanu operator is flexible than that of Caputo derivative. The infection in tuberculosis (TB) infected people decreases fast when decreasing the fractional order.
- tuberculosis,
- two-age-class transmission,
- fractional differential equations,
- Caputo
Citation: Fatmawati, Muhammad Altaf Khan, Ebenezer Bonyah, Zakia Hammouch, Endrik Mifta Shaiful. A mathematical model of tuberculosis (TB) transmission with children and adults groups: A fractional model[J]. AIMS Mathematics, 2020, 5(4): 2813-2842. doi: 10.3934/math.2020181

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Abstract

We consider a novel fractional model to investigates the (tuberculosis) TB model dynamics with two age groups of human, that is, the children and the adults. First, we formulate the model and present the basic results associated to the model. Then, using the fractional operators, Caputo and the Atangana-Baleanu and obtain a generalized model. Further, we give a novel numerical approach for the solution of the fractional model and obtain their approximate solution. We show graphical results with various values of the fractional order. A comparison of the two operators are shown graphically. The results obtained through Atangana-Baleanu operator is flexible than that of Caputo derivative. The infection in tuberculosis (TB) infected people decreases fast when decreasing the fractional order.

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