New COVID 19 Mathematical Modeling Studies Explores Adverse Events of the Antiviral Drugs

Identifying the Issue

• While there are many vector-host models developed to study the spread of COVID-19 at population level, there are very few works done to understand the interplay of the immune response and the virus particles in the body. Also there is no mathematical modelling studies that talks about the time optimal control studies on COVID-19
• In this work, firstly, a mathematical model is developed incorporating inter-cellular time delay and the stability analysis of the equilibrium points admitted by the model is performed. Secondly, an optimal control problem is studied with antiviral agents and second-line drugs as control measures incorporating the adverse events caused by antiviral drugs. Lastly, a time-optimal control problem is formulated with the objective to drive the system from any given initial state to the desired infection-free equilibrium state in minimal time

Objective of the Research

• We propose to study the role and efficacies of the first line and second line drugs in reducing COVID-19 burden by framing an optimal control problem
• We propose to perform the stability analysis of the equilibrium points and find the condition for the global stability of the infection-free state
• We propose to frame and study the time-optimal control problem to drive the system from any given initial state to the desired infection-free equilibrium state in minimal time

Who should read this?

Academics, Mathematics, Bio-Mathematics, Mathematical Modelling, Doctors-Physicians, Research

Solution

In this study, we first develop SIV model at within-host level by incorporating the intercellular time delay and analyzing the stability of equilibrium points. The model dynamics admits a disease-free equilibrium and an infected equilibrium with their stability based on the value of the basic reproduction number $R_0$. We then formulate an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the number of infected cells and viral load. The comparative study conducted in the optimal control problem suggests that if the first-line antiviral drugs show adverse effects, considering these drugs in reduced amounts along with the second-line drugs would be very effective in reducing the number of infected cells and viral load in a COVID-19 infected patient. Later, we formulate a time-optimal control problem with the goal of driving the system from any initial state to the desired infection-free equilibrium state in finite minimal time. Using Pontryagin’s Minimum Principle, it is shown that the optimal control strategy is of the bang-bang type, with the possibility of switching between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in a shorter time when the higher values of the optimal controls. The results of this study may be very helpful to researchers, epidemiologists, clinicians and physicians working in this field.
 

Key Features and Benefits

• When the first line antiviral drugs starts showing adverse events, considering first line antiviral drugs in reduced quantity along with the second line drug is found to be highly effective in reducing the infected cells and viral load in a COVID infected patients and this alternative also proved to be cost effective
• It is found that with higher values of first line and second line drugs the time to reach the desired infection free state decreases. This would imply that the infected cells and viral load in the body of a COVID infected individual becomes zero in short period of time with the higher values of the first line and second line drugs

Impact

• The work presented in this paper could enhance our understanding of complex interplay of immune response and virus particles in the body
• It can help physicians with decision making in the treatment of life-threatening COVID-19 pneumonia

Team

Bishal Chhetri, Vijay M. Bhagat, Swapna Muthusamy, Ananth V S, D. K. K. Vamsi, Carani B Sanjeevi

Paper Published in: RSC Advances (Royal Society of Chemistry)

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

Read Paper Here: Computational and Mathematical Biophysics, 2021, 9:214 – 241