A quasi-markov model for transmission and disease elimination: Hepatitis C among people who inject drugs

Abstract

Background: The use of mathematic modeling to better understand the spread of Hepatitis C and the impact of interventions can be invaluable for localities, states and countries with a large burden of injection drug use. New York State (NYS) is estimated to be home to a large number of people who inject drugs (PWID), however the burden of hepatitis C among this population and the impact of interventions are not known and/or fully understood. Since accurate modeling can be complex and require costly data analysis software to implement, the purpose of this paper was to derive a methodology to accurately model the prevalence of hepatitis C at the state level that is tractable and easily implemented with free software. Methods: A non-stationary quasi-Markov model, is proposed that is implemented using free software R © . The methodology aims to estimate hepatitis C prevalence and evaluate impacts of interventions on disease burden among PWID in NYS. The approach is "quasi-Markov" because transition probabilities among states change in time and depend on past information. Interventions evaluated aimed to: reduce sharing needles and/or other drug use paraphernalia; increase needle disinfection rates; and increase availability of clean needles and other drug use paraphernalia. Results:The quasi-Markov model estimated hepatitis C prevalence among PWID reached an equilibrium value of 63.6 percent after 50 years. In order to eliminate disease, all proposed interventions were needed, resulting in an estimated prevalence less than 1.0 percent, 56 years after implementation. Using parameters defined for an alternate study modeling hepatitis C prevalence found similar results, serving to reinforce the validity of the proposed methods. Conclusion:The results of this analysis demonstrate the feasibility of using a non-stationary quasiMarkov methodology to model the spread of hepatitis C among PWID using free programming software. Coding provided can be used by other researchers to use and modify for their own purposes and could further impact this field of research as well as inform and promote additional education prevention and interventions for PWID.