W Alfwzan, D Greenhalgh
Department of Mathematics and Statistics, University of Strathclyde.
Objective: We develop the model of Corson et al. [1] to study the effects of heterogeneity in spread HCV among drug users. We derive the system equations, describing the spread of HCV in addicts and needles. We determine a formula for the basic reproduction number R0, key parameter. Mathematical results are shown and followed by a numerical simulation results.
Methods: Exploring the effects of heterogeneity and disease behaviour by dividing population into groups. We allow for variability in the sharing rate, their choice of shooting gallery. Six models are studied each model has different number of groups and sharing rates. This was displayed where R0 <1 or >1. Data of survey Glasgow drug users in 1990-93 [2] to calculate sharing rate.
Results: If R0 <1 model has unique equilibrium solution where the disease has died out. Disease will die out whatever the initial conditions if R0 <1. If R0 >1 the DFE is unstable, and there is a non-zero endemic equilibrium solution. Simulation results are compatible with these mathematical results. When R0 >1(1990) the disease takes off over time and has endemic equilibrium prevalence. Homogeneous model has highest proportions of infected addicts whilst heterogeneity model has lowest. This indicates that increasing of heterogeneity in may reduce spread of HCV. When R0<1(1993) in homogenous model, disease may die out. It is observed that highest proportion of prevalence of HCV is in two group model whilst lowest proportion is in homogenous. Thus as number of groups increases, initial speed of increase of the epidemic (related to R0) increases.
Conclusion: We have studied the effects of heterogeneity on the spread of HCV. We divide the population into groups, along with different shooting galleries. The results fit into a familiar pattern followed by most simple epidemic models. R0, determines the behaviour of the disease. The simulation results emphasize the importance of R0 and the importance of heterogeneity on the spread of HCV.
References:
[1] S Corson, D Greenhalgh, S Hutchinson (2011). Mathematically modelling the spread of hepatitis C in injecting drug users. Math Med Biol , 29: 205-230.
[2] S Hutchinson, A. Taylor, et al (2000). Factors associated with injecting risk behaviour among serial community-wide samples of injecting drug users in Glasgow 1990 to 1994: Implications for control and prevention of blood-borne viruses. Addiction 95, 931-940.
Reference: PAGE 22 () Abstr 2672 [www.page-meeting.org/?abstract=2672]
Poster: Other Drug/Disease Modelling