A nonlinear mathematical model for exploring the optimal cost-effective therapeutic strategies and within-host viral infections spread dynamics

This study presents a nonlinear mathematical model to capture the constant rates of three different target cells class-specific drug therapeutic measures (namely, drug therapy for blocking new infections, drug therapy for actively infected cells, and drug therapy inhibiting viral production) for the dynamics of within-host viral infections with multiple classes of target cells. The threshold quantity of the control reproduction number of the model is calculated. The global asymptotic behaviours of the model around the steady states are investigated in terms of the control reproduction number. Moreover, the model is extended to an optimal control problem by considering the three constant parameters for drug therapeutic measures as time-dependent control variables. Qualitative analysis of the proposed model is conducted using optimal control theory. Numerical solutions of the derived optimality system are sought to illustrate the efficacies of different combination strategies consisting of using at least any of the three target cells’ class-specific optimal controls in reducing the burden of within-host virus transmission and spread at a minimum cost. Cost-effectiveness analysis is further carried out to determine the least costly and most effective intervention strategy. The cost analysis reveals that the use of only target cells class-specific drug therapy control for blocking new infections is the most cost-effective control strategy.