Fractional optimal control strategies for hepatitis B virus infection with cost-effectiveness analysis

Abstract

Abstract Hepatitis B disease is a communicable disease that is caused by the hepatitis B virus and has become a significant health problem in the world. It is a contagious disease that is transmittable from person to person either horizontally or vertically. This current study is aimed at sensitivity analysis and optimal control strategies for a fractional hepatitis B epidemic model with a saturated incidence rate in the sense of the Caputo order fractional derivative approach. Fundamental properties of the proposed fractional order model are obtained and discussed. A detailed analysis of disease-free equilibrium and endemic equilibrium points is given by applying fractional calculus theory, which is a generalized version of classical calculus. Sensitivity indexes are calculated for the classical order model. Illustrative graphics that show the dependence of the sensitivity index on fractional order derivative for $$\alpha \in (0,1)$$ α ∈ ( 0 , 1 ) are provided. Based on the results of the sensitivity analysis and using Pontryagin’s Maximum Principle, optimal control strategies for preventing hepatitis B infection with vaccination and treatment are considered. Fractional Euler’s method is used to carry out the numerical simulation for the proposed fractional optimal control system and the obtained results are analyzed. The results of the analysis reveal that hepatitis B disease can be prevented if necessary precautionary is taken or effective vaccination and treatment control measures are applied. The analysis of cost-effectiveness is also conducted and discussed.