Within Host Between Host and Multiscale Mathematical Modeling Studies with reference to COVID19 Pandemic

Abstract

Mathematical models have been used to predict the behavior of physical and newlinebiological systems and to define strategies aimed at minimizing the impact on newlinedifferent types of diseases. Mathematical modeling of infectious diseases has contributed to a better understanding of the dynamic behavior of diseases and their newlineeffects. These models are used to compare, plan, implement, evaluate, and optimize different detection, prevention, treatment, and control strategies. The emergence of coronavirus disease (COVID-19) caused by the SARS-CoV-2 virus has newlineposed a major challenge to health authorities around the world. In this context, newlinemathematical modeling studies of COVID-19 can be extremely useful to gain a newlinebetter understanding of the dynamics and behavior of the spread of the disease newlineand to determine the optimal control strategies. As part of the doctoral thesis, newlinewe have done mathematical modeling studies on COVID-19 at three different levels: within-host, between-host, and multiscale. At the within-host level, we have newlinedeveloped models based on the pathogenesis and course of COVID-19 infection newlineand have first studied the natural history of the disease. In the second part of newlinethe study, at the within-host level, we formulated the optimal control problems newlineand studied the roles and efficacies of antiviral drugs, immunomodulators, and newlineBCG vaccine booster doses in treating the COVID-19 infected individual. Filippov s existence theorem and Pontryagin s maximum principle are used to show newlinethe existence and characterization of optimal controls. In order to overcome the newlineasymptotic nature of the infection-free equilibrium point and to account for the newlineside effects or adverse events caused by the administration of antiviral drugs, in newlinethe third part of our study at the within-host level, a time-optimal control problem was formulated and studied with antiviral drugs and second-line drugs as the newlinecontrol measures. newline