Professor John Murray

School of Mathematics and Statistics

University of New South Wales

hepatitis C virus modelling

Hepatitis C virus (HCV) is a major public health burden with 170 million people infected worldwide. The majority of HCV-infected individuals will develop a persistent infection that can lead to severe liver complications and death. Liver cirrhosis occurs in 10–20% of chronically HCV-infected individuals and up to 5% of these cases progress towards hepatocellular carcinoma (HCC). In 2005 in Australia there were an estimated 5300 people living with HCV-related cirrhosis and 105 cases of HCC, with a median time to death of approximately 1 year after HCC diagnosis.

In most countries, transmission occurs primarily through intravenous drug use and sharing of equipment. In Australia, by the end of 2005 over 225,000 HCV diagnoses had been recorded. The current HCV treatment combining pegylated interferon-alfa (PEG-IFN-α) and ribavirin is effective in only 50% of patients infected with genotype 1, the most common genotype in Europe, North America and Australia. Studies to develop a prophylactic HCV vaccine have largely been limited to mouse and chimpanzees, with only Phase I human trials in healthy volunteers. The development of a HCV vaccine is a difficult task.

Bioinformatics of HCV sequences

Mathematical modelling related to HCV covers a number of areas. Collaborations with groups in France investigates differences in the envelope sequences of virus in genotype 1 chronically infected individuals commencing antiviral therapy, and uses bioinformatics and optimization methods to determine what is different in these sequences between those who clear the virus and those who do not.

Optimal distribution of antiviral therapy to those enrolled/not enrolled in methadone maintenance programs

Although some cases of HCV are obtained through sexual transmission, the vast majority of infections in Australia and most other developed countries are limited to sharing of injecting drug equipment. Approximately 60% of individuals attending Australian Needle and Syringe Programs in 2006 were infected with HCV, while prevalence among blood donors in the general community was 0.01%. In collaboration with colleagues at the Drug Policy Modelling Program at UNSW we determined that best allocation of antiviral therapy required this to be preferentially directed to individuals still actively injecting. A combination of ordinary differential equation modelling plus optimization techniques were used in this analysis.

Stochastic process modelling of progression from HCV infection to hepatocellular carcinoma

One of the main health risks associated with HCV infection is its progression to liver complications such as cirrhosis and hepatocellular carcinoma (HCC). Work with Dr Chakrabarty at the Indian Institute of Technology, Guwahati, was the first attempt at mathematically modelling the full course of HCV infection and the impact that viral and immune processes have on the progression to hepatocellular carcinoma (HCC). The model was based on the premise that these long term conditions are ultimately random and likely driven by the cell-mediated immune response. The risk of cancer arising is modelled through a stochastic model that incorporates the dynamics of HCV over the course of infection.