Dynamical study of SARS-CoV-2 mathematical models under antiviral treatments

Abstract

Several target-cell models have been developed to describe and understand the spread of SARS-CoV-2 in thehost and the effectiveness of antiviral treatments. Although a proper dynamical characterization of such modelsplays a crucial role to classify every potential behavior of the controlled system, little attention has been paidto it. Concepts as the critical fraction of susceptible/non-infected cells (under which the infection can no longerincrease) can be fully understood and used in more general control objectives if put in terms of the equilibriumsets and their stability. In this work, a full characterization of the dynamical behavior of the target-cell modelsunder control actions is made. Based on the concept of virus spreadability, antiviral effectiveness thresholds aredetermined to establish whether or not a given treatment will be able to clear the infection without secondaryeffects. Also, it is shown how to simultaneously minimize the total fraction of infected cells while maintainingthe virus load under a given level, by means of an optimal control strategy. Several simulation results illustrate thepotential benefits of the proposal.