## On stability analysis study and strategies for optimal control of a mathematical model of hepatitis HCV with the latent state

In this work, we analyze a viral hepatitis C model. This epidemic remains a major problem for global public health, in all communities, despite the efforts made. The model is analyzed using the stability theory of systems of nonlinear differential equations. Based on the results of the analysis, the proposed model has two equilibrium points: a disease-free equilibrium point $E_0$ and an endemic equilibrium point $E^{*}$. We investigate the existence of equilibrium point of the model. Furthermore, based on the indirect Lyapunov method, we study the local stability o