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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

Special Issues: Transmission dynamics in infectious diseases

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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References

1. World Health Organization, Global tuberculosis report 2017, Available from: https://www. who.int/tb/publications/global_report/en.

2. D.P. Gao and N.J. Huang, Optimal control analysis of a tuberculosis model, Appl. Math. Model., 58 (2018), 47–64.

3. S. Kim, A.A. Reyes and E. Jung, Mathematical model and intervention strategies for mitigating tuberculosis in the Philippines, J. Theor. Biol., 443 (2018), 100–112.

4. C.J. Silva, H. Maurer and D.F. Torres, Optimal control of a tuberculosis model with state and control delays, Math. Biosci. Eng., 14 (2016), 321–337.

5. H.F. Huo, S.J. Dang and Y.N. Li, Stability of a two-strain tuberculosis model with general contact rate, Abstr. Appl. Anal., 2010 (2010), 1–31.

6. H.F. Huo and M.X. Zou, Modelling effects of treatment at home on tuberculosis transmission dynamics, Appl. Math. Model., 40 (2016), 9474–9484.

7. H.F. Huo and L.X. Feng, Global stability for an HIV/AIDS epidemic model with different latent stages and treatment, Appl. Math. Model., 37 (2013), 1480–1489.

8. C.C. Mccluskey, Lyapunov functions for tuberculosis models with fast and slow progression, Math. Biosci. Eng., 3 (2006), 603–614.

9. T. Bergeb, S. Bowonga and J.M. Lubuma, Global stability of a two-patch cholera model with fast and slow transmissions, Math. Comput. Simulat., 133 (2017), 124–164.

10. B. Song, C. Castillo-Chavez and J.P. Aparicio, Tuberculosis models with fast and slow dynamics: the role of close and casual contacts, Math. Biosci., 180 (2002), 187–205.

11. J. Li, Y.L. Zhao and S.M. Li, Fast and slow dynamics of malaria model with relapse, Math. Biosci., 246 (2013), 94–104.

12. J.A. Cui, X. Tao and H.P. Zhu, An SIS infection model incorporating media coverage, Rocky Mt. J. Math., 38 (2008), 1323–1334.

13. H.F. Huo and X.M. Zhang, Complex dynamics in an alcoholism model with the impact of twitter, Math. Biosci., 281 (2016), 24–35.

14. H.F. Huo, P. Yang and H. Xiang, Stability and bifurcation for an SEIS epidemic model with the impact of media, Physica A, 490 (2018), 702–720.

15. J.G. Cui, Y.H. Sun and H.P. Zhu, The impact of media on the control of infectious diseases, J. Differ. Equations, 20 (2008), 31–53.

16. H. Xiang, Y.Y. Wang and H.F. Huo, Analysis of the binge drinking models with demographics and nonlinear infectivity on networks, J. Appl. Anal. Comput., 8 (2018), 1535–1554.

17. H.F. Huo, F.F. Cui and H. Xiang, Dynamics of an SAITS alcoholism model on unweighted and weighted networks, Physica A, 496 (2018), 249–262.

18. Y.L. Cai, J.J. Jiao, Z.J. Gui, Y.T. Liu and W.M. Wang, Environmental variability in a stochastic epidemic model, Appl. Math. Comput., 329 (2018), 210–226.

19. Z. Du and Z. Feng, Existence and asymptotic behaviors of traveling waves of a modified vectordisease model, Commun. Pur. Appl. Anal., 17 (2018), 1899–1920.

20. X.B. Zhang, Q.H. Shi, S.H. Ma, H.F. Huo and D.G. Li, Dynamic behavior of a stochastic SIQS epidemic model with levy jumps, Nonlinear Dynam., 93 (2018), 1481–1493.

21. W.M. Wang, Y.L. Cai, Z.Q. Ding and Z.J. Gui, A stochastic differential equation SIS epidemic model incorporating Ornstein-Uhlenbeck process, Physica A, 509 (2018), 921–936.

22. P.V. Driessche and J.Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.

23. J.P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathmatics, Society for Industrial and Applied Mathematics, Berlin, New Jersey, 1976.

24. J.D. Murray, Mathematical Biology, Springer-Verlag, Berlin, 1998.

25. C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361–401.

26. K.A. Pawelek, A. Oeldorfhirsch and L. Rong, Modeling the impact of twitter on influenza epidemics, Math. Biosci. Eng., 11 (2014), 1337–1356.

27. K. Styblo, J. Meijer and I. Sutherland, The transmission of Tubercle Bacilli: its trend in a human population, Bull. World Health Organ., 41 (1969), 137–178.

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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