This study introduces a deterministic compartmental model of hepatitis C virus (HCV) transmission with behavioral awareness, diagnosis tests, and treatment interventions as control strategies. The study evaluates the autonomous fixed-control system to determine its basic reproduction number ($ \mathcal{R}_0 $), which enables the description of its equilibrium points and an analysis of its stability and bifurcation patterns. The study considers the local asymptotic stability of the disease-free equilibrium when $ \mathcal{R}_0 < 1 $, and finds at least one endemic equilibrium when $ \mathcal{R}_0 > 1 $. The local stability of the endemic equilibrium is assessed using the Routh-Hurwitz conditions, whereas global asymptotic stability is established under additional assumptions, including no disease-induced mortality and the uniqueness of the endemic state. Using the theory of the center manifold, it was subsequently proven that the model goes through a forward transcritical bifurcation when \(\mathcal{R}_0 = 1\). Sensitivity analysis performed at the local level and also with Latin hypercube sampling–partial rank correlation coefficient analysis showed that both diagnostic testing and behavior awareness are the most effective interventions to reduce transmission, while treatment primarily reduces disease prevalence and its burden. The analytical results are verified through numerical simulations, which strongly emphasize the importance of integrating intervention strategies to improve HCV control.
Citation: Debnarayan Khatua, Bapin Mondal, Md Sadikur Rahman, Sadiah M. Aljeddani. Mathematical analysis of hepatitis C virus transmission with awareness, testing, and treatment interventions[J]. AIMS Mathematics, 2026, 11(4): 11776-11809. doi: 10.3934/math.2026485
This study introduces a deterministic compartmental model of hepatitis C virus (HCV) transmission with behavioral awareness, diagnosis tests, and treatment interventions as control strategies. The study evaluates the autonomous fixed-control system to determine its basic reproduction number ($ \mathcal{R}_0 $), which enables the description of its equilibrium points and an analysis of its stability and bifurcation patterns. The study considers the local asymptotic stability of the disease-free equilibrium when $ \mathcal{R}_0 < 1 $, and finds at least one endemic equilibrium when $ \mathcal{R}_0 > 1 $. The local stability of the endemic equilibrium is assessed using the Routh-Hurwitz conditions, whereas global asymptotic stability is established under additional assumptions, including no disease-induced mortality and the uniqueness of the endemic state. Using the theory of the center manifold, it was subsequently proven that the model goes through a forward transcritical bifurcation when \(\mathcal{R}_0 = 1\). Sensitivity analysis performed at the local level and also with Latin hypercube sampling–partial rank correlation coefficient analysis showed that both diagnostic testing and behavior awareness are the most effective interventions to reduce transmission, while treatment primarily reduces disease prevalence and its burden. The analytical results are verified through numerical simulations, which strongly emphasize the importance of integrating intervention strategies to improve HCV control.
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Debnarayan Khatua, Bapin Mondal, Md Sadikur Rahman, Sadiah M. Aljeddani. Mathematical analysis of hepatitis C virus transmission with awareness, testing, and treatment interventions[J]. AIMS Mathematics, 2026, 11(4): 11776-11809. doi: 10.3934/math.2026485
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