Time Optimal Control Studies on COVID-19 Incorporating Adverse Events of the Antiviral Drugs

TL;DR

This paper develops a delayed SIV model for COVID-19, analyzes stability, and formulates time-optimal control strategies using antiviral drugs, highlighting the effectiveness of combined reduced-dose first-line drugs and second-line drugs in minimizing infection duration.

Contribution

It introduces a delayed SIV model with stability analysis and proposes a novel time-optimal control framework for COVID-19 treatment strategies.

Findings

Optimal control is bang-bang with switches between control extremes.

Reduced first-line drug dosage combined with second-line drugs effectively reduces infection.

Higher control values lead to faster achievement of infection-free state.

Abstract

In this study, we first develop SIV model by incorporating the intercellular time delay and analyze the stability of the equilibrium points. The model dynamics admits disease-free equilibrium and the infected equilibrium with their stability, based on the value of basic reproduction number $R_0$. We then frame an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the infected cell count and the viral load. The comparative study done in the optimal control problem suggests that when the first line antiviral drugs shows adverse events, considering these drugs in reduced quantity along with the second line drug would be highly effective in reducing the infected cell and viral load in a COVID infected patients. Later, we formulate a time-optimal control problem with the objective to drive the system from any given initial state to the desired infection-free equilibrium state in minimal time. Using Pontryagin's Minimum Principle the optimal control strategy is shown to be of bang-bang type with possibility of switches between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in less time when the higher values of both the optimal controls are chosen.