A new mathematical model for tuberculosis epidemic under the consciousness effect

Mehmet Yavuz; Fatma Özköse; Müzeyyen Akman; Zehra Tuğba Taştan; Mehmet Yavuz; Fatma Özköse; Müzeyyen Akman; Zehra Tuğba Taştan

doi:10.3934/mmc.2023009

Mathematical Modelling and Control

2023, Volume 3, Issue 2: 88-103. doi: 10.3934/mmc.2023009

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Research article

A new mathematical model for tuberculosis epidemic under the consciousness effect

1.
Department of Mathematics and Computer Sciences, Necmettin Erbakan University, 42090 Konya, Türkiye
2.
Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, TR10 9FE, United Kingdom
3.
Department of Mathematics, Faculty of Science, Erciyes University, Kayseri 38039, Türkiye

Received: 01 November 2022 Revised: 08 January 2023 Accepted: 01 March 2023 Published: 02 June 2023

Compared to many infectious diseases, tuberculosis has a high mortality rate. Because of this, a great deal of illustrative research has been done on the modeling and study of tuberculosis using mathematics. In this work, a mathematical model is created by taking into account the underlying presumptions of this disease. One of the main novelties of the paper is to consider two different treatment strategies namely protective treatment for the latent populations from the disease and the main treatment applied to the infected populations. This situation can be regarded as the other novelty of the paper. The susceptible, latent, infected, and recovered populations, as well as the two mentioned treatment classes, are all included in the proposed six-dimensional model's compartmental framework. Additionally, a region that is biologically possible is presented, as well as the solution's positivity, existence, and uniqueness. The suggested model's solutions are carried out as numerical simulations using assumed and literature-based parameter values and analyzing its graphics. To get the results, a fourth-order Runge-Kutta numerical approach is used.
- TB model,
- consciousness effect,
- stability analysis,
- Runge-Kutta numerical scheme,
- reproduction number
Citation: Mehmet Yavuz, Fatma Özköse, Müzeyyen Akman, Zehra Tuğba Taştan. A new mathematical model for tuberculosis epidemic under the consciousness effect[J]. Mathematical Modelling and Control, 2023, 3(2): 88-103. doi: 10.3934/mmc.2023009

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Abstract

Compared to many infectious diseases, tuberculosis has a high mortality rate. Because of this, a great deal of illustrative research has been done on the modeling and study of tuberculosis using mathematics. In this work, a mathematical model is created by taking into account the underlying presumptions of this disease. One of the main novelties of the paper is to consider two different treatment strategies namely protective treatment for the latent populations from the disease and the main treatment applied to the infected populations. This situation can be regarded as the other novelty of the paper. The susceptible, latent, infected, and recovered populations, as well as the two mentioned treatment classes, are all included in the proposed six-dimensional model's compartmental framework. Additionally, a region that is biologically possible is presented, as well as the solution's positivity, existence, and uniqueness. The suggested model's solutions are carried out as numerical simulations using assumed and literature-based parameter values and analyzing its graphics. To get the results, a fourth-order Runge-Kutta numerical approach is used.

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