Predicting Viral Evolution from a Single Early Measurement Using the Target Cell Limited Model

RESUMO

Recent advances in diagnostic techniques have enabled the accurate quantification of early-stage viral loads. A key problem of interest is translating these measurements into predictive clinical insights, such as forecasting a patient's onset of infectiousness and peak infection severity. In this work, we address this problem using the Target Cell Limited (TCL) model. Because the host's internal biological states are practically unobservable, predicting the viral trajectory from a single noisy viral load measurement is highly nontrivial. To overcome this, we introduce a novel coordinate transformation that converts the nonlinear viral dynamics into a monotone system. By leveraging monotone systems theory and taking into account invariant subspaces of the transformed system, we derive explicit analytical formulae that establish a strict upper bound on the peak viral load and a guaranteed lower bound on the time to infectiousness using a single early viral observation.