Predictability of viral load dynamics in the early phases of SARS-CoV-2 through a model-based approach

TL;DR

The paper addresses the challenge of predicting early SARS-CoV-2 VL dynamics and transmission by integrating in-host VL trajectories with population-level spread through a multiscale $SIR$-type model that includes age of infection and uncertainty. It derives VL-based infectiousness shapes from two Italian cohorts using a Gamma-like VL fit and links them to epidemic dynamics via a two-step calibration, followed by uncertainty quantification to obtain an expected infectiousness function $\mathbb{E}_z[\beta(\tau,\mathbf{z})]$. Across three waves (2020–2021), the approach reveals a shrinking infection peak but longer tails, with the Alpha variant associated with greater spread, and demonstrates that a time-varying contact rate $\bar{\beta}(t)$ improves long-range fit. The work provides a data- and model-driven framework for assessing viral infectiousness evolution and informs public health decisions for quarantine and containment, with potential extension to other respiratory pathogens.

Abstract

A pipeline to evaluate the evolution of viral dynamics based on a new model-driven approach has been developed in the present study. The proposed methods exploit real data and the multiscale structure of the infection dynamics to provide robust predictions of the epidemic dynamics. We focus on viral load kinetics whose dynamical features are typically available in the symptomatic stage of the infection. Hence, the epidemiological evolution is obtained by relying on a compartmental approach characterized by a varying infection rate to estimate early-stage viral load dynamics, of which few data are available. We test the proposed approach with real data of SARS-CoV-2 viral load kinetics collected from patients living in an Italian province. The considered database refers to early-phase infections, whose viral load kinetics have not been affected by the mass vaccination policies in Italy.

Figures (7)

• Figure 1: Evolution of individuals' viral load kinetics over time with an ordering based on the first negative test taken by the infective patients, where a patient is considered negative if $\textrm{Ct} \ge 40$ is detected, based on the conversion formula \ref{['eq:conversion']}. We use a simple linear interpolation to connect values that are relative to the same subject. We distinguish between the two observation periods of November--December 2020, accounting for 71 patients (left), and January--May 2021, accounting for 162 patients (right).
• Figure 2: Best fit of the patients' viral loads depending on the time of the infection, for the two monitoring periods of November--December 2020 (left) and January--May 2021 (right). The black crosses denote all the individuals' infection cycles ordered based on their first negativization. The blue dots represent the averages of the daily viral loads. The red curves are the best fit for these averages, weighted by the number of patients counted on each day. The shaded region gives the $80 \%$ and $95 \%$ prediction bounds for the whole dataset.
• Figure 3: Data- and model-driven inference of the optimal shape of the infection rate in the province of Pavia (Italy) over two different epidemic waves: the one occurred at the beginning of the pandemic in 2020, with a focus on the two weeks (February 24--March 9) preceding the first lockdown (top), and the other occurred in the fall of the same year, with a focus on the two weeks (October 7--22) preceding the imposition of a national curfew (bottom). The figures on the left provide the optimal shapes $\mathbb{E}_z(\beta(\tau,\mathbf{z}))$ of the infectiousness function (red curves) determined for these two periods, starting from the data collected by Fondazione IRCCS Policlinico San Matteo to infer an initial guess of the infection rate through the function \ref{['eq:VL_shape']} rescaled by the factor $\alpha_0 = 10^7$. The shaded areas show how the infectiousness function is altered when a uniform noise $\mathcal{U}([-2,2])$ modifies the day of first contact. The figures on the right present the evolution of infected individuals from SARS-CoV-2 in the province of Pavia over the considered windows of time. We compare computed (in red) and reported (in black) number of cases.
• Figure 4: Investigations on the SARS-CoV-2 pandemic in Italy during three distinct epidemic waves, starting from the data collected by Fondazione IRCCS Policlinico San Matteo to infer an initial guess of the infection rate through the function \ref{['eq:VL_shape']}. Top row: analysis of the epidemic wave that started in February--March 2020. Optimal shape $\mathbb{E}_z(\beta(\tau,\mathbf{z}))$ of the infectiousness function (left) and model approximation (right) for the cases of infection registered during the period February 24--March 9 2020. Middle row: analysis of the new epidemic outburst that took place in October 2020. Optimal shape of the infection rate (left) and model approximation (right) for the cases of infection registered during the period October 7--22 2020. Bottom row: analysis of the epidemic wave occurred from March 2021.
• Figure 5: Left: comparison between infection rates from the first (in orange, March 2020) and the second (in blue, October 2020) epidemic waves in the province of Pavia. In order for the model \ref{['SIR-AOI']} to best fit the data on confirmed cases, the peak of the infection should be reached about 6 to 8 days after the first contact with an infected subject. Right: evolution of infected individuals from SARS-CoV-2 in Pavia from February 24 2020 to January 18 2021. Comparison between computed (in red) and reported (in black) number of cases.