Mathematical models of the spread of Hepatitis C among injecting drug users, the effects of heterogeneity

The world faces an immense burden of hepatitis C virus (HCV) infection related morbidity and mortality. Transmission of HCV is ongoing, and the incidence of HCV infection has been increasing in recent years. Approximately 130 - 150 million people are estimated to be chronically infected with HCV and each year an estimated three to four million individuals are newly infected (WHO, 2013; Mohd Hanafiah et al., 2013). In developed countries, injecting drug users are considered as being at the highest risk of prevalence of HCV. Thus, this thesis describes the spread of HCV amongst injecting drug users. We use a mathematical model to study the effect of heterogeneity on the progress of the disease by dividing the population of addicts into p groups where they are sharing injecting needles in q shooting galleries and investigate the epidemic behavior of the virus. Moreover, we estimate the basic reproductive number R₀ and show analytically that HCV is controlled by this number R₀, if R₀ ≤ 1 then the disease dies out and if R₀ > 1 the disease takes off in both addicts and needles and there is a unique endemic equilibrium. We look at analytical results on the effect of heterogeneity on the spread of HCV and optimal control of the epidemic by needle exchange and needle cleaning. Simulations with realistic parameter values estimated from data and the literature confirm the theoretical results and we numerically investigate the effect of heterogeneity on the spread of HCV. Then we extend the basic model to more realistic assumptions where addicts move in and out of groups, and investigate the HCV dynamic behaviour. We obtain similar analytical results again validated by simulations with realistic parameter values estimated from data and the literature.The world faces an immense burden of hepatitis C virus (HCV) infection related morbidity and mortality. Transmission of HCV is ongoing, and the incidence of HCV infection has been increasing in recent years. Approximately 130 - 150 million people are estimated to be chronically infected with HCV and each year an estimated three to four million individuals are newly infected (WHO, 2013; Mohd Hanafiah et al., 2013). In developed countries, injecting drug users are considered as being at the highest risk of prevalence of HCV. Thus, this thesis describes the spread of HCV amongst injecting drug users. We use a mathematical model to study the effect of heterogeneity on the progress of the disease by dividing the population of addicts into p groups where they are sharing injecting needles in q shooting galleries and investigate the epidemic behavior of the virus. Moreover, we estimate the basic reproductive number R₀ and show analytically that HCV is controlled by this number R₀, if R₀ ≤ 1 then the disease dies out and if R₀ > 1 the disease takes off in both addicts and needles and there is a unique endemic equilibrium. We look at analytical results on the effect of heterogeneity on the spread of HCV and optimal control of the epidemic by needle exchange and needle cleaning. Simulations with realistic parameter values estimated from data and the literature confirm the theoretical results and we numerically investigate the effect of heterogeneity on the spread of HCV. Then we extend the basic model to more realistic assumptions where addicts move in and out of groups, and investigate the HCV dynamic behaviour. We obtain similar analytical results again validated by simulations with realistic parameter values estimated from data and the literature