Dynamics of tuberculosis with fast and slow progression and media coverage

Ya-Dong Zhang; Hai-Feng Huo; Hong Xiang; Ya-Dong Zhang; Hai-Feng Huo; Hong Xiang

doi:10.3934/mbe.2019055

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 3: 1150-1170. doi: 10.3934/mbe.2019055

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Research article Special Issues

Dynamics of tuberculosis with fast and slow progression and media coverage

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People’s Republic of China

Received: 15 November 2018 Accepted: 09 January 2018 Published: 15 February 2019

A new tuberculosis model with fast and slow progression and media coverage is formulated and analyzed. The basic reproductive number R₀ is derived, and the existence and stability of all the equilibria are discussed. The occurrences of forward and backward bifurcation are obtained by using center manifold theory. Numerical simulations are also given to support our theoretical results. Sensitivity analysis on a few parameters is also carried out. Our results show that media coverage can encourage people to take measures to avoid potential infections and control the spread of tuberculosis.
- tuberculosis,
- media coverage,
- fast and slow progression,
- basic reproductive number,
- bifurcation
Citation: Ya-Dong Zhang, Hai-Feng Huo, Hong Xiang. Dynamics of tuberculosis with fast and slow progression and media coverage[J]. Mathematical Biosciences and Engineering, 2019, 16(3): 1150-1170. doi: 10.3934/mbe.2019055

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Abstract

A new tuberculosis model with fast and slow progression and media coverage is formulated and analyzed. The basic reproductive number R₀ is derived, and the existence and stability of all the equilibria are discussed. The occurrences of forward and backward bifurcation are obtained by using center manifold theory. Numerical simulations are also given to support our theoretical results. Sensitivity analysis on a few parameters is also carried out. Our results show that media coverage can encourage people to take measures to avoid potential infections and control the spread of tuberculosis.

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