Control strategy design for the anti-HBV mathematical model

Currently, the anti-viral therapy has been extensively utilised to reduce the viral burden and switch off certain infectious sources for hepatitis B virus (HBV) infected patients in clinical treatment. Several pieces of existing evidence have demonstrated that large-scale coverage with anti-viral therapy has obtained a certain great contribution in hygiene and disease control. In this study, an anti-HBV mathematical model is considered and its control strategy of the drug treatment is designed. Based on the Lyapunov theory, this study derives three main theorems to propose three different control strategies, respectively, for drug treatments $m\lpar t\rpar $m(t) and $n\lpar t\rpar $n(t), such that all states of the anti-HBV model can finally converge to the infection-free equilibrium point $E-1$E1 asymptotically. Especially, the designed drug treatment $m\lpar t\rpar $m(t) or $n\lpar t\rpar $n(t) is not a fixed value, but it is time-varying and dependent on states. In Theorem 1, the single drug treatment $m\lpar t\rpar $m(t) without $n\lpar t\rpar $n(t) is synthesised. Theorem 2 considers the single drug treatment $n\lpar t\rpar $n(t) without $m\lpar t\rpar $m(t). In Theorem 3, the combination therapy of $m\lpar t\rpar $m(t) and $n\lpar t\rpar $n(t) is designed. Finally, there are several simulations to show that the proposed combination therapy is much more effective to cure HBV infected patients than the drug treatment with solely single $m\lpar t\rpar $m(t) or single $n\lpar t\rpar $n(t).