Modeling the indirect transmission of hepatitis C virus via contaminated injecting equipment and environmental reservoirs with treatment intervention

Abstract

This study creates and evaluates a deterministic mathematical model for the indirect spread of Hepatitis C virus (HCV) among PWID. The model incorporates behavioural variation by categorising PWID into two separate groups, high-risk and low-risk, with explicit dynamics of contaminated injecting equipment serving as an environmental reservoir. Reinfection, therapy, mobility between behavioural risk categories, and equipment sterilisation are all completely included in the model framework. Analytical results are presented that use the next-generation matrix approach to determine the feasible zone, disease-free equilibrium, endemic equilibrium, and the basic reproduction number \(\mathcal{R}_0\). The disease-free equilibrium is globally asymptotically stable for \(\mathcal{R}_0 < 1\). Bifurcation analyses reveal that the contamination-related transmission rate among high-risk PWID (\(\alpha_{wh}\)) and the behavioural transition rate (\(\kappa\)) strongly influence the emergence and stability of endemic states, while the reinfection rate (\(\psi\)) influences endemic levels without affecting the threshold quantity \(\mathcal{R}_0\). Furthermore, sensitivity analysis utilising Partial Rank Correlation Coefficients (PRCC) revealed that recruitment into high-risk behaviour, contamination rates, and sterilisation of contaminated equipment are important predictors of transmission. The numerical simulations looks into the effectiveness of therapy, sterilization, and the availability of clean equipment in reversing infection dynamics. The findings highlight the critical role that environmental contamination and high-risk behaviours play in disease transmission, emphasising the need for integrated harm-reduction strategies that include increased treatment, increased access to sterile equipment, and reduced behavioural risks among PWID. Our findings also show that relapse into high-risk injecting conduct is a critical driver of persistent HCV transmission, emphasizing the relevance of behavioural-risk reduction strategies.