An SEICR hepatitis C model with relapse and latent infection

KANG Yujiao; ZHANG Tailei; MA Yiting; LIU Junli

doi:10.13471/j.cnki.acta.snus.2022A008

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An SEICR hepatitis C model with relapse and latent infection

Research articles | 更新时间：2023-11-01

- An SEICR hepatitis C model with relapse and latent infection
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 62, Issue 3, Pages: 149-160(2023)
- 作者机构：
  
  1.长安大学理学院，陕西西安 710064
  2.西安工程大学理学院，陕西西安 710048
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2022A008
  CLC： O175.1
- Published：25 May 2023，
  
  Published Online：19 March 2023，
  
  Received：16 January 2022，
  
  Accepted：21 September 2022
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康玉娇,张太雷,马怡婷等.一类具有复发和潜伏期传染的SEICR丙肝模型[J].中山大学学报(自然科学版),2023,62(03):149-160.

KANG Yujiao,ZHANG Tailei,MA Yiting,et al.An SEICR hepatitis C model with relapse and latent infection[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(03):149-160.
康玉娇,张太雷,马怡婷等.一类具有复发和潜伏期传染的SEICR丙肝模型[J].中山大学学报(自然科学版),2023,62(03):149-160. DOI： 10.13471/j.cnki.acta.snus.2022A008.

KANG Yujiao,ZHANG Tailei,MA Yiting,et al.An SEICR hepatitis C model with relapse and latent infection[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(03):149-160. DOI： 10.13471/j.cnki.acta.snus.2022A008.

摘要

依据丙肝的传播机理，我们建立了一类潜伏期具有传染性并且考虑复发效应的SEICR丙肝模型，给出了模型的基本再生数。证明了当

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9.22866726

3.30200005

时，无病平衡点全局渐近稳定；当

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9.22866726

3.30200005

时，无病平衡点不稳定且地方病平衡点全局渐近稳定。选取陕西省丙肝患者病例数据，利用模型数值模拟未来几年丙肝的流行趋势。最后进行参数的敏感性分析，结果表明近几年丙肝患者还将持续增加。提高公众对丙肝的检测意识、加强免疫力可以提升丙肝患者的恢复率同时减少疾病复发的可能性，这样可以控制丙肝的进一步蔓延。

Abstract

According to the transmission mechanism of hepatitis C， we establish an SEICR hepatitis C model with infectious latency and relapse effect， and give the basic reproductive number of the model. It is proved that the disease-free equilibrium is globally asymptotically stable when

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10.66800022

3.80999994

；the disease-free equilibrium is unstable and the endemic equilibrium is globally asymptotically stable when

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10.66800022

3.80999994

. Choosing the case data of hepatitis C patients of Shaanxi Province， we use the model to simulate the epidemic trend of hepatitis C in the next a few years. Finally， the sensitivity analysis of parameters shows that the number of hepatitis C cases will continue to increase in recent years. Improving public awareness of hepatitis C detection and strengthening immunity can improve the recovery rate of hepatitis C patients and reduce the proportion of disease relapse， so as to control the further spread of hepatitis C.

关键词

SEICR模型丙型肝炎稳定性数值模拟

Keywords

SEICR modelhepatitis Cstabilitynumerical simulation

references

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贾璐，张国洪， 2021.考虑DAAs治疗的丙肝病毒RNA模型的全局稳定性分析［J］.西南大学学报（自然科学版）， 43（5）： 83-87.

马知恩，周义仓， 2001.常微分方程定性与稳定性方法［M］.北京：北京科学出版社.

王嫒，贾建文， 2021.具有Lévy噪声的丙肝流行病随机模型［J］.应用数学， 34（4）： 855-862.

张太雷，刘俊利，王凯， 2016.常微分方程教程［M］.西安：西北工业大学出版社.

CHEN S L， MORGAN T R， 2006. The natural history of hepatitis C virus （HCV） infection［J］. Int J Med Sci， 3（2）： 47-52.

CUI J A， ZHAO S， GUO S， et al， 2020. Global dynamics of an epidemiological model with acute and chronic HCV infections［J］. Appl Math Lett， 103： 106203.

ELBASHA E H， 2013. Model for hepatitis C virus transmissions［J］. Math Biosci Eng， 10（4）： 1045-1065.

KITAGAWA K， KUNIYA T， NAKAOKA S， et al， 2019. Mathematical analysis of a transformed ODE from a PDE multiscale model of hepatitis C virus infection［J］. Bull Math Biol， 81（5）： 1427-1441.

LASALLE J P， 1976. The stability of dynamical systems［M］. Philadelphia： SIAM.

MURAKAMI C， HINO K， KORENAGA M， et al， 1999. Factors predicting progression to cirrhosis and hepatocellular carcinoma in patients with transfusion-associated hepatitis C virus infection［J］. J Clin Gastroenterol， 28（2）： 148-152.

RAO H Y， DUAN Z P， WANG G Q， et al， 2020. Highlights of the guidelines of prevention and treatment for hepatitis C （2019 version）［J］. Zhonghua Gan Zang Bing Za Zhi， 28（2）： 129-132.

STOCKS T， MARTIN L J， KÜHLMANN-BERENZON S， et al， 2020. Dynamic modeling of hepatitis C transmission among people who inject drugs［J］. Epidemics， 30： 100378.

van den DRIESSCHE P， WATMOUGH J， 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission［J］. Math Biosci， 180（1/2）： 29-48.

YUAN J， YANG Z， 2008. Global dynamics of an SEI model with acute and chronic stages［J］. J Comput Appl Math， 213（2）： 465-476.

ZEILER I， LANGLANDS T， MURRAY J M， et al， 2010. Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone maintenance programs［J］. Drug Alcohol Dependence， 110（3）： 228-233.

ZHANG S， ZHOU Y， 2012. Dynamics and application of an epidemiological model for hepatitis C［J］. Math Comput Modelling， 56（1/2）： 36-42.

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