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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Mathematical Model of HBV/HCV Co-Infection

Discontinuity, Nonlinearity, and Complexity 10(3) (2021) 409--424 | DOI:10.5890/DNC.2021.09.005

Nita H Shah, Nisha Sheoran, Ekta Jayswal

Department of Mathematics, Gujarat University, Ahmedabad-380009, Gujarat, India

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Abstract

The co-infection of hepatitis B (HBV) and hepatitis C (HCV) virus is a complex clinical entity that has an estimated worldwide prevalence of 1--15%. In this paper HBV/HCV co-infection is modelled mathematically through the set of deterministic non-linear differential equations. This dynamical system has four equilibrium points i.e. disease-free, co-infection free, HCV free and endemic point. Reproduction number is computed for endemic equilibria. Local stability for all the equilibrium point is proved using Routh-Hurwitz criterion. Global stability is also studied for all the equilibria. The sensitivity analysis of relevant parameters in reproduction number is analyzed to see the effect of each parameter in disease spread.

Acknowledgments

The authors thank DST-FIST file {\#} MSI-097 for technical support to the department. The paper is prepared under the guidance of Prof. (Dr.) Nita H. shah.

References

  1. [1]  {https://www.hepb.org/what-is-hepatitis-b/hepatitis-c-co-infection/}/
  2. [2]  {https://www.ccohs.ca/oshanswers/diseases/hepatitis{\_}b.html}/
  3. [3]  {https://www.who.int/news-room/fact-sheets/detail/hepatitis-c}/
  4. [4]  Sagnelli, E., Sagnelli, C., Macera, M., Pisaturo, M., and Coppola, N. (2017), An update on the treatment options for HBV/HCV coinfection, Expert opinion on pharmacotherapy, 18(16), 1691-1702.
  5. [5]  Papadopoulos, N., Papavdi, M., Pavlidou, A., Konstantinou, D., Kranidioti, H., Kontos, G., ... and Deutsch, M. (2018), Hepatitis B and C coinfection in a real-life setting: viral interactions and treatment issues, Annals of gastroenterology, 31(3), 365.
  6. [6]  Potthoff, A., Manns, M.P., and Wedemeyer, H. (2010), Treatment of HBV/HCV coinfection, Expert opinion on pharmacotherapy, 11(6), 919-928.
  7. [7]  Pol, S., Haour, G., Fontaine, H., Dorival, C., Petrov-Sanchez, V., Bourliere, M., ... and Marcellin, P. (2017), The negative impact of HBV/HCV coinfection on cirrhosis and its consequences, Alimentary pharmacology {$\&$ therapeutics}, 46(11-12), 1054-1060.
  8. [8]  Butt, A.A., Yan, P., Aslam, S., Sherman, K.E., Siraj, D., Safdar, N., and Hameed, B. (2020), Hepatitis C virologic response in hepatitis B and C coinfected persons treated with directly acting antiviral agents: Results from ERCHIVES, International Journal of Infectious Diseases, 92, 184-188.
  9. [9]  Gaeta, G.B., Stornaiuolo, G., Precone, D.F., Lobello, S., Chiaramonte, M., Stroffolini, T., ... and Rizzetto, M. (2003), Epidemiological and clinical burden of chronic hepatitis B virus/hepatitis C virus infection. A multicenter Italian study, Journal of hepatology, 39(6), 1036-1041.
  10. [10]  Calvaruso, V., Ferraro, D., Licata, A., Bavetta, M.G., Petta, S., Bronte, F., ... and Di Marco, V. (2018), HBV reactivation in patients with HCV/HBV cirrhosis on treatment with direct-acting antivirals, Journal of viral hepatitis, 25(1), 72-79.
  11. [11]  Mavilia, M.G. and Wu, G.Y. (2018), HBV-HCV coinfection: viral interactions, management, and viral reactivation, Journal of clinical and translational hepatology, 6(3), 296.
  12. [12]  Zacharakis, G. (2018), Hepatitis B and C Coinfection. In~Hepatitis C in Developing Countries, (pp. 157-175). Academic Press.
  13. [13]  Pitcher, A.B., Borquez, A., Skaathun, B., and Martin, N.K. (2019), Mathematical modeling of hepatitis c virus (HCV) prevention among people who inject drugs: A review of the literature and insights for elimination strategies, Journal of theoretical biology, 481, 194-201.
  14. [14]  Nampala, H., Luboobi, L.S., Mugisha, J.Y., Obua, C., and Jablonska-Sabuka, M. (2018), Modelling hepatotoxicity and antiretroviral therapeutic effect in HIV/HBV coinfection, Mathematical biosciences, 302, 67-79.
  15. [15]  Carvalho, A.R. and Pinto, C.M. (2014), A coinfection model for HIV and HCV, Biosystems, 124, 46-60.
  16. [16]  Mushayabasa, S., Bhunu, C.P., and Stewart, A.G. (2012), A mathematical model for assessing the impact of intravenous drug misuse on the dynamics of HIV and HCV within correctional institutions, ISRN Biomathematics, $2012$.
  17. [17]  Bowong, S. and Kurths, J. (2010), Modelling tuberculosis and hepatitis b co-infections, Mathematical Modelling of Natural Phenomena, 5(6), 196-242.
  18. [18]  Aggarwala, B.D. (2016), ``On a Mathematical Model for HBV and HCV Co-infection", Proceedings of the World Congress on Engineering and Computer Science 2016 Vol II WCECS 2016, October 19-21, 2016, San Francisco, USA.
  19. [19]  Diekmann, O., Heesterbeek, J.A.P., and Metz, J.A. (1990), On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 28(4), 365-382.
  20. [20]  Routh, E.J. (1877), A treatise on the stability of a given state of motion: particularly steady motion. Macmillan and Company.
  21. [21]  Castillo-Chavez, C., Blower, S., van den Driessche, P., Kirschner, D., and Yakubu, A.A. (Eds.). (2002), Mathematical approaches for emerging and reemerging infectious diseases: an introduction, (Vol. 1), Springer Science & Business Media.
  22. [22]  LaSalle, J.P. (1976), The Stability of Dynamical Systems, Society for Industrial and Applied Mathematics, Philadelphia, Pa.
  23. [23]  Chitnis, N., Hyman J., and Cushing. J., (2008), Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of Mathematical Biology, 70, 1272-1296.