Optimal control strategies of cell infections in a covid-19 model with inflammatory response

In this work, we investigate the optimal strategies to limit cell infections and virus production at low cost in a mathematical virus model for Covid-19 with inflammatory response. We consider treatment and introduce two intervention control parameters: u1 for the drug therapy efficacy in preventing new infections, and u2 for the drug therapy efficacy in inhibiting viral production (with 0⩽u1,u2⩽1). We fully analyse the optimal control problem and establish the existence and uniqueness of the optimal solution. Moreover, we show that the optimal control is not only measurable, but is also continuous. Our numerical illustrations show how therapy can overturn a lethal infection state into a survivable stage, and vice versa.