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

D' JORGE, AGUSTINA; SANCHEZ, IGNACIO; GONZÁLEZ, ALEJANDRO H.

Mathematical Modeling, Simulations, and AI for Emergent Pandemic Diseases. Lessons Learned From COVID-19

Elsevier Wordmark

Año: 2023; p. 261 - 286

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