Modeling viral mutant-variant dynamics: From continuous optimal control to discrete dosing protocols

The emergence of viral mutant-variants poses a significant public health challenge, as existing treatments often exhibit reduced efficacy against new lineages compared to the original strains. This paper presents a mathematical framework to model the competitive dynamics between these lineages within a host using a Lotka–Volterra competition scheme. To mitigate the impact of more contagious or resistant microorganisms, we apply optimal control theory to investigate strategies for mutant suppression. We conduct a comparative study between continuous control, representing ideal treatment scenarios, and discrete-time control, which reflects the clinical reality of periodic dosing protocols. We introduce a discrete-time optimal control formulation to connect the theoretical continuous-control framework with periodic dosing protocols. The analytical study identifies the stability conditions for viral extinction under constant and impulsive interventions, while numerical simulations validate the expected behaviors. Our results show that the effectiveness of discrete treatment depends strongly on the dosing interval and treatment intensity, with a transition from effective mutant suppression to loss of control as the dosing interval increases. Specifically, our quantitative results demonstrate that periodic interventions can achieve complete mutant suppression while effectively halving the total cumulative dose compared to continuous protocols. These findings provide quantitative insights into the design of antiviral dosing strategies.