The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg" display="inline" id="d1e268"><mml:mi>Θ</mml:mi></mml:math>-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission

This study examines the mathematical model of Hepatitis B Virus (HBV) dynamics, focusing on its various stages of infection, including acute and chronic phases, and transmission pathways. By utilizing mathematical modeling and fractional calculus techniques with the Θ -Hilfer operator, we analyze the epidemic’s behavior. The research proposes control strategies, such as treatment and vaccination, aimed at reducing both acute and chronic infections. To achieve optimal control, we employ Pontryagin’s Maximum Principle. Through simulations, we demonstrate the effectiveness of our approach using the Non-Standard Two-Step Lagrange Interpolation Method (NS2LIM), supported by numerical findings and graphical representations. Additionally, we identify two control variables to minimize the populations of acute and chronic infections while enhancing recovery rates.