RESUMO
Mathematical models are critical to understand the spread of pathogens in a population and evaluate the effectiveness of non-pharmaceutical interventions (NPIs). A plethora of optimal strategies has been recently developed to minimize either the infected peak prevalence ( I P P ) or the epidemic final size ( E F S ). While most of them optimize a simple cost function along a fixed finite-time horizon, no consensus has been reached about how to simultaneously handle the I P P and the E F S , while minimizing the intervention's side effects. In this work, based on a new characterization of the dynamical behaviour of SIR-type models under control actions (including the stability of equilibrium sets in terms of herd immunity), we study how to minimize the E F S while keeping the I P P controlled at any time. A procedure is proposed to tailor NPIs by separating transient from stationary control objectives: the potential benefits of the strategy are illustrated by a detailed analysis and simulation results related to the COVID-19 pandemic.
RESUMO
Mathematical models describing SARS-CoV-2 dynamics and the corresponding immune responses in patients with COVID-19 can be critical to evaluate possible clinical outcomes of antiviral treatments. In this work, based on the concept of virus spreadability in the host, antiviral effectiveness thresholds are determined to establish whether or not a treatment will be able to clear the infection. In addition, the virus dynamic in the host - including the time-to-peak and the final monotonically decreasing behavior - is characterized as a function of the time to treatment initiation. Simulation results, based on nine patient data, show the potential clinical benefits of a treatment classification according to patient critical parameters. This study is aimed at paving the way for the different antivirals being developed to tackle SARS-CoV-2.
RESUMO
While many epidemiological models were proposed to understand and handle COVID-19 pandemic, too little has been invested to understand human viral replication and the potential use of novel antivirals to tackle the infection. In this work, using a control theoretical approach, validated mathematical models of SARS-CoV-2 in humans are characterized. A complete analysis of the main dynamic characteristic is developed based on the reproduction number. The equilibrium regions of the system are fully characterized, and the stability of such regions is formally established. Mathematical analysis highlights critical conditions to decrease monotonically SARS-CoV-2 in the host, as such conditions are relevant to tailor future antiviral treatments. Simulation results show the aforementioned system characterization.