Mathematical Biosciences and Engineering, 2013, 10(4): 1045-1065. doi: 10.3934/mbe.2013.10.1045.

Primary: 34D20, 92D30; Secondary: 65L20, 93C15.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Model for hepatitis C virus transmissions

1. Merck Research Laboratories, UG1C-60, PO Box 1000, North Wales, PA 19454-1099

Hepatitis C virus (HCV) is a leading cause of chronic liver disease. Thispaper presents a deterministic model for HCV infection transmission and usesthe model to assess the potential impact of antiviral therapy. The model isbased on the susceptible-infective-removed-susceptible (SIRS) compartmentalstructure with chronic primary infection and possibility of reinfection.Important epidemiologic thresholds such as the basic and controlreproduction numbers and a measure of treatment impact are derived. We findthat if the control reproduction number is greater than unity, there is alocally unstable infection-free equilibrium and a unique, globallyasymptotically stable endemic equilibrium. If the control reproductionnumber is less than unity, the infection-free equilibrium is globallyasymptotically stable, and HCV will be eliminated. Numerical simulationssuggest that, besides the parameters that determine the basic reproductionnumber, reinfection plays an important role in HCV transmissions andmagnitude of the public health impact of antiviral therapy. Further,treatment regimens with better efficacy holds great promise for lowering thepublic health burden of HCV disease.
  Figure/Table
  Supplementary
  Article Metrics

Keywords reproduction number.; global stability; endemic equilibrium; HCV; mathematical model; treatment; reinfection

Citation: Elamin H. Elbasha. Model for hepatitis C virus transmissions. Mathematical Biosciences and Engineering, 2013, 10(4): 1045-1065. doi: 10.3934/mbe.2013.10.1045

References

  • 1. N. Engl. J. Med., 327 (1992), 1899-1905.
  • 2. Clin. Infect. Dis., 46 (2008), 1852-1858.
  • 3. J. Gastroenterol. Hepatol., 15 (2000), E105-E110.
  • 4. Oxford University Press, Oxford, 1991.
  • 5. Ann. Intern. Med., 144 (2006), 705-714.
  • 6. Arch. Intern. Med., 167 (2007), 166-173.
  • 7. J. Gastroenterol. Hepatol., 25 (2010), 1276-1280.
  • 8. Ann. Intern. Med., 127 (1997), 55-65.
  • 9. Int. Stat. Rev., 62 (1994), 229-243.
  • 10. in "Quantitative Evaluation of HIV Prevention Programs" (Eds. Brookmeyer Kaplan ), (2002), 260-289. Yale University Press, New Haven.
  • 11. Gut, 56 (2007), 385-389.
  • 12. MMWR Recomm Rep., 47 (1998), 1-39.
  • 13. 2010. (accessed October 5, 2012), http://www.cdc.gov/hepatitis/HCV/HCVfaq.htm\#section1.
  • 14. Recommendations and Reports, 61 (2012), 1-18.
  • 15. Hepatology, 39 (2004), 74-80.
  • 16. Hepatology, 31 (2000), 1014-1018.
  • 17. J. Biol. Sys., 13 (2005), 331-339.
  • 18. J. Math. Biol., 28 (1990), 365-382 .
  • 19. J. R. Soc. Interface, 7 (2010), 873-885.
  • 20. Nat. Biotechnology, 27 (2009), 305-306.
  • 21. J. Infect. Dis., 198 (2008), 1651-1655.
  • 22. Bull. Math. Biol., 70 (2008), 894-909.
  • 23. Antivir Ther., 16 (2011), 1187-1201.
  • 24. Hepatology, 49 (2009), 1335-1374.
  • 25. Hepatology, 44 (2006), 1139-1145.
  • 26. SIAM Rev., 42 (2000), 599-653.
  • 27. Am. J. Gastroenterol, 103 (2008), 1283-1297.
  • 28. 3rd edn. Prentice Hall, New York, 2002.
  • 29. BMJ, 341 (2010), c3374.
  • 30. Proc. Roy. Soc. Lond. A., 115 (1927), 700-721.
  • 31. Transfusion, 49 (2009), 2454-2489.
  • 32. in "Hepatitis C and Injecting Drug Use: Impact, Costs and Policy Options" (eds. J. C. Jager, W. Limburg, M. Kretzschmar, M. J. Postma and L. Wiessing), Lisbon: European Monitoring Centre For Drugs And Drug Addiction, (2004).
  • 33. J. Virol., 76 (2002), 6586-6595.
  • 34. J. Theor. Biol., 254 (2008), 178-196.
  • 35. Math. Biosci., 182 (2003), 1-25.
  • 36. J. Viral. Hepat., 15 (2008), 399-408.
  • 37. J. Community Health, 33 (2008), 126-133.
  • 38. Proc. Roy. Soc. Lond. B., 253 (1993), 9-13.
  • 39. Lancet., 359 (2002), 1478-1483.
  • 40. Science, 282 (1998), 103-107.
  • 41. N. Engl. J. Med., 330 (1994), 744-750.
  • 42. Gastroenterology, 138 (2010), 315-324.
  • 43. Infec. Gene. Evol., 5 (2005), 131-139.
  • 44. Crit. Rev. Immunol., 30 (2010), 131-148.
  • 45. Math Biosci. Eng., 1 (2004), 81-93.
  • 46. Nat. Med., 6 (2000), 578-582.
  • 47. Math. Biosci., 180 (2002), 29-48.
  • 48. Hepatology, 50 (2009), 1750-1755.
  • 49. Transfusion, 42 (2002), 537-548.
  • 50. http://www.who.int/mediacentre/factsheets/fs164/en/index.html (accessed October 29, 2012).
  • 51. Drug Alcohol. Depend., 110 (2010), 228-233.

 

This article has been cited by

  • 1. F. Nazari, A.B. Gumel, E.H. Elbasha, Differential characteristics of primary infection and re-infection can cause backward bifurcation in HCV transmission dynamics, Mathematical Biosciences, 2015, 263, 51, 10.1016/j.mbs.2015.02.002
  • 2. Wei Wang, Wanbiao Ma, Hepatitis C virus infection is blocked by HMGB1: A new nonlocal and time-delayed reaction–diffusion model, Applied Mathematics and Computation, 2018, 320, 633, 10.1016/j.amc.2017.09.046
  • 3. A. Cousien, V. C. Tran, S. Deuffic-Burban, M. Jauffret-Roustide, J.-S. Dhersin, Y. Yazdanpanah, Dynamic modelling of hepatitis C virus transmission among people who inject drugs: a methodological review, Journal of Viral Hepatitis, 2015, 22, 3, 213, 10.1111/jvh.12337
  • 4. David P. Durham, Laura A. Skrip, Robert Douglas Bruce, Silvia Vilarinho, Elamin H. Elbasha, Alison P. Galvani, Jeffrey P. Townsend, The Impact of Enhanced Screening and Treatment on Hepatitis C in the United States, Clinical Infectious Diseases, 2016, 62, 3, 298, 10.1093/cid/civ894
  • 5. Emily D. Bethea, Qiushi Chen, Chin Hur, Raymond T. Chung, Jagpreet Chhatwal, Should we treat acute hepatitis C? A decision and cost-effectiveness analysis, Hepatology, 2018, 67, 3, 837, 10.1002/hep.29611
  • 6. Lauren E. Cipriano, Jeremy D. Goldhaber-Fiebert, Population Health and Cost-Effectiveness Implications of a “Treat All” Recommendation for HCV: A Review of the Model-Based Evidence, MDM Policy & Practice, 2018, 3, 1, 238146831877663, 10.1177/2381468318776634
  • 7. Wei Wang, Wanbiao Ma, Block effect on HCV infection by HMGB1 released from virus-infected cells: An insight from mathematical modeling, Communications in Nonlinear Science and Numerical Simulation, 2018, 59, 488, 10.1016/j.cnsns.2017.11.024
  • 8. Ignacio Rozada, Daniel Coombs, Viviane D. Lima, Conditions for eradicating hepatitis C in people who inject drugs: A fibrosis aware model of hepatitis C virus transmission, Journal of Theoretical Biology, 2016, 395, 31, 10.1016/j.jtbi.2016.01.030
  • 9. Karen Van Nuys, Ronald Brookmeyer, Jacquelyn W. Chou, David Dreyfus, Douglas Dieterich, Dana P. Goldman, Broad Hepatitis C Treatment Scenarios Return Substantial Health Gains, But Capacity Is A Concern, Health Affairs, 2015, 34, 10, 1666, 10.1377/hlthaff.2014.1193
  • 10. Ruiqing Shi, Yunting Cui, Global analysis of a mathematical model for Hepatitis C virus transmissions, Virus Research, 2016, 217, 8, 10.1016/j.virusres.2016.02.006
  • 11. Mingwang Shen, Yanni Xiao, Weike Zhou, Zhen Li, Global Dynamics and Applications of an Epidemiological Model for Hepatitis C Virus Transmission in China, Discrete Dynamics in Nature and Society, 2015, 2015, 1, 10.1155/2015/543029
  • 12. A. Nwankwo, D. Okuonghae, Mathematical Analysis of the Transmission Dynamics of HIV Syphilis Co-infection in the Presence of Treatment for Syphilis, Bulletin of Mathematical Biology, 2018, 80, 3, 437, 10.1007/s11538-017-0384-0
  • 13. M. E. Woode, M. Abu-Zaineh, J. Perriëns, F. Renaud, S. Wiktor, J.-P. Moatti, Potential market size and impact of hepatitis C treatment in low- and middle-income countries, Journal of Viral Hepatitis, 2016, 23, 7, 522, 10.1111/jvh.12516
  • 14. Ashley B Pitcher, Annick Borquez, Britt Skaathun, Natasha K Martin, 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, 2018, 10.1016/j.jtbi.2018.11.013

Reader Comments

your name: *   your email: *  

Copyright Info: 2013, , 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)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved