Mathematically modelling the spread of hepatitis C in injecting drug users

S Corson, D Greenhalgh, S Hutchinson

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


Mathematical modelling can provide valuable insights into the biological and epidemiological properties of infectious diseases as well as the potential impact of intervention strategies employed by health organizations worldwide. In this paper, we develop a deterministic, compartmental mathematical model to approximate the spread of the hepatitis C virus (HCV) in an injecting drug user (IDU) population. Using analytical techniques, we find that the model behaviour is determined by the basic reproductive number R(0), where R(0) = 1 is a critical threshold separating two different outcomes. If R(0) ≤ 1 and HCV is initially present in the population, we find that the system will reach a disease-free equilibrium where HCV has been eliminated in all IDUs and needles. If R(0) > 1, then there is a unique positive endemic equilibrium which we show is locally stable. We then use simulations to verify our analytical results and examine the effect of different parameter values and intervention measures on HCV prevalence estimates.
Original languageEnglish
Pages (from-to)205-230
Number of pages26
JournalMathematical Medicine and Biology
Issue number3
Early online date6 Sept 2011
Publication statusPublished - Sept 2012


  • hepatitis C
  • injecting drug user
  • IDUs
  • HCV elimination
  • mathematical modelling


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