Mathematical modeling and optimal control of Hepatitis B virus dynamics

Document Type : Review Article

Authors

Loubna El houari ¹

Mariem Elkaf ²

Jaouad Danane ³

¹ LaMAO Laboratory, Faculty of Sciences, Mohammed First University, Oujda, Morocco.

² Royal Naval School, Casablanca, Morocco.

³ National School of Applied Sciences, Hassan First University, Berrechid, Morocco.

10.22067/ijnao.2026.97045.1806

Abstract

In this study, we examine the dynamics of Hepatitis B Virus, formulated through a system of four differential equations that describe the interactions between healthy hepatocytes, infected hepatocytes, capsids, and the HBV virus. To establish the well-posedness of the proposed model, we prove the positivity and the boundedness of solutions, under two control strategies. Then, we give some numerical results confirming that control strategies play a crucial role in reducing viral load, leading to improved disease management and prevention of complications such as liver damage. The overall findings emphasize the importance of intervention in maintaining biological balance and enhancing health outcomes.

Keywords

HBV

Dynamical systems

Ordinary Differential Equations

Stability

Optimal control

Optimization

Numerical simulation

Subjects

• Modeling and Simulation

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