Model for hepatitis C virus transmissions

  • Received: 01 October 2012 Accepted: 29 June 2018 Published: 01 June 2013
  • MSC : Primary: 34D20, 92D30; Secondary: 65L20, 93C15.

  • 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.

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

    Related Papers:

    [1] Amar Nath Chatterjee, Fahad Al Basir, Yasuhiro Takeuchi . Effect of DAA therapy in hepatitis C treatment — an impulsive control approach. Mathematical Biosciences and Engineering, 2021, 18(2): 1450-1464. doi: 10.3934/mbe.2021075
    [2] Tailei Zhang, Hui Li, Na Xie, Wenhui Fu, Kai Wang, Xiongjie Ding . Mathematical analysis and simulation of a Hepatitis B model with time delay: A case study for Xinjiang, China. Mathematical Biosciences and Engineering, 2020, 17(2): 1757-1775. doi: 10.3934/mbe.2020092
    [3] Suxia Zhang, Hongbin Guo, Robert Smith? . Dynamical analysis for a hepatitis B transmission model with immigration and infection age. Mathematical Biosciences and Engineering, 2018, 15(6): 1291-1313. doi: 10.3934/mbe.2018060
    [4] Yuhua Long, Yining Chen . Global stability of a pseudorabies virus model with vertical transmission. Mathematical Biosciences and Engineering, 2020, 17(5): 5234-5249. doi: 10.3934/mbe.2020283
    [5] Xiaowen Xiong, Yanqiu Li, Bingliang Li . Global stability of age-of-infection multiscale HCV model with therapy. Mathematical Biosciences and Engineering, 2021, 18(3): 2182-2205. doi: 10.3934/mbe.2021110
    [6] Martin Luther Mann Manyombe, Joseph Mbang, Jean Lubuma, Berge Tsanou . Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers. Mathematical Biosciences and Engineering, 2016, 13(4): 813-840. doi: 10.3934/mbe.2016019
    [7] Dwi Lestari, Noorma Yulia Megawati, Nanang Susyanto, Fajar Adi-Kusumo . Qualitative behaviour of a stochastic hepatitis C epidemic model in cellular level. Mathematical Biosciences and Engineering, 2022, 19(2): 1515-1535. doi: 10.3934/mbe.2022070
    [8] Tingting Xue, Long Zhang, Xiaolin Fan . Dynamic modeling and analysis of Hepatitis B epidemic with general incidence. Mathematical Biosciences and Engineering, 2023, 20(6): 10883-10908. doi: 10.3934/mbe.2023483
    [9] Junli Liu . Threshold dynamics of a time-delayed hantavirus infection model in periodic environments. Mathematical Biosciences and Engineering, 2019, 16(5): 4758-4776. doi: 10.3934/mbe.2019239
    [10] Yicang Zhou, Zhien Ma . Global stability of a class of discrete age-structured SIS models with immigration. Mathematical Biosciences and Engineering, 2009, 6(2): 409-425. doi: 10.3934/mbe.2009.6.409
  • 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.


    [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, 2015, 263, 00255564, 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, 2018, 320, 00963003, 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, 2015, 22, 13520504, 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, 2016, 62, 1058-4838, 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, 2018, 67, 02709139, 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, 2018, 3, 2381-4683, 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, 2018, 59, 10075704, 488, 10.1016/j.cnsns.2017.11.024
    8. Cheng Ding, Xiaoxiao Liu, Shigui Yang, The value of infectious disease modeling and trend assessment: a public health perspective, 2021, 1478-7210, 1, 10.1080/14787210.2021.1882850
    9. 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, 2016, 395, 00225193, 31, 10.1016/j.jtbi.2016.01.030
    10. 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, 2015, 34, 0278-2715, 1666, 10.1377/hlthaff.2014.1193
    11. 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, 2019, 481, 00225193, 194, 10.1016/j.jtbi.2018.11.013
    12. Ruiqing Shi, Yunting Cui, Global analysis of a mathematical model for Hepatitis C virus transmissions, 2016, 217, 01681702, 8, 10.1016/j.virusres.2016.02.006
    13. Mingwang Shen, Yanni Xiao, Weike Zhou, Zhen Li, Global Dynamics and Applications of an Epidemiological Model for Hepatitis C Virus Transmission in China, 2015, 2015, 1026-0226, 1, 10.1155/2015/543029
    14. A. Nwankwo, D. Okuonghae, Mathematical Analysis of the Transmission Dynamics of HIV Syphilis Co-infection in the Presence of Treatment for Syphilis, 2018, 80, 0092-8240, 437, 10.1007/s11538-017-0384-0
    15. Yao Wang, Zeyu Zhao, Mingzhai Wang, Mikah Ngwanguong Hannah, Qingqing Hu, Jia Rui, Xingchun Liu, Yuanzhao Zhu, Jingwen Xu, Meng Yang, Jing-An Cui, Yanhua Su, Benhua Zhao, Tianmu Chen, The transmissibility of hepatitis C virus: a modelling study in Xiamen City, China, 2020, 148, 0950-2688, 10.1017/S0950268820002885
    16. 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, 2016, 23, 1352-0504, 522, 10.1111/jvh.12516
    17. Oluwasegun M. Ibrahim, Daniel Okuonghae, Monday N.O. Ikhile, Mathematical Modeling of the Population Dynamics of Age-Structured Criminal Gangs with Correctional Intervention Measures, 2022, 107, 0307904X, 39, 10.1016/j.apm.2022.02.005
    18. S. P. Rajasekar, M. Pitchaimani, Quanxin Zhu, Probing a Stochastic Epidemic Hepatitis C Virus Model with a Chronically Infected Treated Population, 2022, 42, 0252-9602, 2087, 10.1007/s10473-022-0521-1
    19. Louiza Tabharit, Maghnia Hamou Maamar, 2021, Mathematical Modeling of Chronic Hepatitis C Treatment’s Effect on the Evolution of its Complications, 978-1-6654-4171-1, 1, 10.1109/ICRAMI52622.2021.9585963
    20. Oluwakemi E. Abiodun, Olukayode Adebimpe, James A. Ndako, Olajumoke Oludoun, Benedicta Aladeitan, Michael Adeniyi, Mathematical modeling of HIV-HCV co-infection model: Impact of parameters on reproduction number, 2022, 11, 2046-1402, 1153, 10.12688/f1000research.124555.1
    21. Baolin Li, Fengqin Zhang, Xia Wang, A delayed diffusive HBV model with nonlinear incidence and CTL immune response, 2022, 45, 0170-4214, 11930, 10.1002/mma.8547
    22. Yuqiong Lan, Yanqiu Li, Dongmei Zheng, Global dynamics of an age-dependent multiscale hepatitis C virus model, 2022, 85, 0303-6812, 10.1007/s00285-022-01773-9
    23. Dwi Lestari, Noorma Yulia Megawati, Nanang Susyanto, Fajar Adi-Kusumo, Qualitative behaviour of a stochastic hepatitis C epidemic model in cellular level, 2021, 19, 1551-0018, 1515, 10.3934/mbe.2022070
    24. R. Rakkiyappan, V. Preethi Latha, F. A. Rihan, Global Dynamics of a Fractional-order Ebola Model with Delayed Immune Response on Complex Networks, 2021, 91, 0369-8203, 681, 10.1007/s40010-021-00756-7
    25. Ke Qi, Zhijun Liu, Lianwen Wang, Qinglong Wang, A nonlinear HCV model in deterministic and randomly fluctuating environments, 2023, 46, 0170-4214, 4644, 10.1002/mma.8792
    26. Nauman Ahmed, Ali Raza, Ali Akgül, Zafar Iqbal, Muhammad Rafiq, Muhammad Ozair Ahmad, Fahd Jarad, New applications related to hepatitis C model, 2022, 7, 2473-6988, 11362, 10.3934/math.2022634
    27. Oluwakemi E. Abiodun, Olukayode Adebimpe, James A. Ndako, Olajumoke Oludoun, Benedicta Aladeitan, Michael Adeniyi, Mathematical modeling of HIV-HCV co-infection model: Impact of parameters on reproduction number, 2022, 11, 2046-1402, 1153, 10.12688/f1000research.124555.2
    28. Vuk Vujović, Influence of environmental fluctuations on Hepatitis C transmission, 2022, 191, 03784754, 203, 10.1016/j.matcom.2021.08.008
    29. Robert B Hood, Alison H Norris, Abigail Shoben, William C Miller, Randall E Harris, Laura W Pomeroy, Forecasting Hepatitis C Virus Status for Children in the United States: A Modeling Study, 2024, 1058-4838, 10.1093/cid/ciae157
    30. Parvaiz Ahmad Naik, Mehmet Yavuz, Sania Qureshi, Mehraj-ud-din Naik, Kolade M. Owolabi, Amanullah Soomro, Abdul Hamid Ganie, Memory impacts in hepatitis C: A global analysis of a fractional-order model with an effective treatment, 2024, 01692607, 108306, 10.1016/j.cmpb.2024.108306
    31. Shewafera Wondimagegnhu Teklu, Tsegaye Simon Lachamo, Tibebu Tulu Guya, Analyses of a stage structure hepatitis c virus compartmental model with optimal control theory, 2025, 11, 2363-6203, 10.1007/s40808-025-02288-0
  • Reader Comments
  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3114) PDF downloads(789) Cited by(31)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog