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A model of bi-mode transmission dynamics of hepatitis C with optimal control

Mudassar Imran1, Hassan Rafique, Adnan Khan

  • 1Lahore University of Management Sciences, Sector U DHA, Lahore, Pakistan, mudassar.imran@lums.edu.pk.

Theory in Biosciences = Theorie in Den Biowissenschaften
|December 31, 2013
PubMed

Insights

This study models hepatitis C virus (HCV) transmission, finding disease eradication depends on the basic reproduction number. An optimal quarantine strategy is developed to minimize persistent HCV infections.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health

Background:

  • Hepatitis C virus (HCV) poses a significant public health challenge.
  • Dominant transmission routes include unsafe blood transfusions and intravenous drug use.
  • Mathematical modeling is crucial for understanding disease dynamics and control.

Purpose of the Study:

  • To develop and analyze a deterministic mathematical model for HCV transmission.
  • To identify key factors determining HCV eradication or persistence.
  • To design and evaluate an optimal quarantine strategy for minimizing chronic infections.

Main Methods:

  • Deterministic modeling of HCV transmission dynamics.
  • Analysis of disease-free and endemic equilibria based on the basic reproduction number (R(c)).
  • Uncertainty and sensitivity analyses of model parameters.
  • Application of Pontryagin's Maximum Principle for optimal quarantine control.

Main Results:

  • HCV eradication is achieved when the basic reproduction number (R(c)) is less than 1.
  • Disease persistence is observed when R(c) is greater than 1.
  • An optimal time-dependent quarantine strategy effectively minimizes persistent HCV infections.

Conclusions:

  • The basic reproduction number (R(c)) is a critical determinant of HCV's epidemiological fate.
  • Mathematical modeling provides valuable insights into HCV transmission and control.
  • Optimal quarantine strategies can significantly reduce the burden of chronic hepatitis C infections.

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