Clarisse Schumer [1], Paskal Lukas [2], Frederik Graw [2], Jérémie Guedj [1]
[1] Université Paris Cité, IAME, INSERM F-75018 Paris, France [2] Department of Medicine 5, Friedrich-Alexander-University Erlangen-Nu ̈ rnberg, Erlangen, Germany
Introduction: Several mathematical models have been used to characterize viral kinetics of SARS-CoV-2 since 2020. While models may commence with a simplistic form, such as the well-established target cell limited (TCL) model, they can evolve into more intricate frameworks by integrating immune response, innate and adaptive ([1]-[4].)
This project seeks to construct a model incorporating innate and adaptive immunity by comparing a spectrum of mathematical models used during the pandemic, and to compare the metrics predicted by the different models.
Methods: As the complexity of sophisticated models is exacerbated by the fact that many studies rely on data from a limited number of infected individuals, often at a later stage of infection [5], we used the National Basketball Association’s (NBA) testing program data. This initiative systematically tested NBA players, staff and other affiliated individuals at regular intervals, thereby providing on of the most exhaustive data set of viral kinetics [6].
The publicly available dataset comprised 607 documented infections with at least four positive viral load measurements, occurring between June 2020 and January 2022, spanning alpha, delta and early omicron VOC waves. We first aimed to compare different models for the innate immune response and interferon (IFN) response. IFN has been suggested to either induce refractory cells and/or to modulate different parameters of viral kinetics such as viral production or transmission, viral clearance and loss rate of infected cells. To tease out these mechanisms, we proposed a forward procedure to build our IFN model. Once the best model IFN effects was built, we added an adaptive immune response mediated by either antibodies or cytotoxic responses. Model selection relied on Bayesian Information Criteria (BIC) and Visual Predictive Check (VPC.)
Next, we used metrics of viral loads such as time to viral peak, time to viral clearance, area under viral curve (AUC), proportion of cells that are not dead or been infected at viral peak, and number of infected cells at end of infection. We also explored several types of treatment effect, including their impact on the viral production rate, viral transmission rate and the proportion of infectious virus.
Results: We found that considering a refractory compartment (FR) systematically yielded superior BIC score compared to models solely featuring the action of IFN on viral parameters. Furthermore, the inclusion of both a refractory compartment and an IFN action on viral production rate (Fp) resulted in a more favourable score (BIC: 19283.26.) Between the two types of adaptive immunity added to the refractory model, the cytotoxic response (FRCtx) mediated by a changing cell death rate gives a better BIC (19168.32) compared to antibodies response (BIC: 19260.56.) Finally, integrating all components, namely refractory compartment, IFN action on viral production rate, and cytotoxic response yielded the most optimal model (FRCtxp) with a BIC of 18790.52.
Through the simulation, we investigating whether excluding the IFN effect, refractory cells, or adaptive immune response from the best model would yield different results in the metrics. Metrics including time to viral clearance (median of 15 days), time to viral peak (5 days) and AUC (80 log10 copies. days/mL) remained unchanged when these effects were removed. However, in the best model, the proportion of cells that have not been infected until viral peak was 70%, whereas when all components were removed, it dropped to 20%.
Regarding treatment efficacy, treatments reducing viral production rate (eg, protease inhibitors) resulted in the most significant changes across all metrics compared to other treatment effects. Specifically, reductions in time to viral clearance and AUC were particularly pronounced. Indeed, in the best model, we observed that the treatment resulted in a reduction of the time to viral clearance to 5 days.
Conclusion: A model incorporating innate (refractory cells and IFN action on viral production rate) and adaptive immunity provided the best fit to the data, and suggests a pivotal role of IFN in modulating the kinetics of viral load. Ignoring this effect as done, in the target cell limited model, could also have implications in estimating treatment antiviral efficacy.
References:
[1] A. Marc et al., ‘Quantifying the relationship between SARS-CoV-2 viral load and infectiousness’, eLife, vol. 10, p. e69302, Sep. 2021, doi: 10.7554/eLife.69302.
[2] N. Néant et al., ‘Modeling SARS-CoV-2 viral kinetics and association with mortality in hospitalized patients from the French COVID cohort’, Proc Natl Acad Sci U S A, vol. 118, no. 8, p. e2017962118, Feb. 2021, doi: 10.1073/pnas.2017962118.
[3] R. Ke, C. Zitzmann, R. M. Ribeiro, and A. S. Perelson, ‘Kinetics of SARS-CoV-2 infection in the human upper and lower respiratory tracts and their relationship with infectiousness’. medRxiv, p. 2020.09.25.20201772, Sep. 27, 2020. doi: 10.1101/2020.09.25.20201772.
[4] K. Owens, S. Esmaeili-Wellman, and J. T. Schiffer, ‘Heterogeneous SARS-CoV-2 kinetics due to variable timing and intensity of immune responses’. medRxiv, p. 2023.08.20.23294350, Aug. 21, 2023. doi: 10.1101/2023.08.20.23294350.
[5] C. Zitzmann, R. Ke, R. M. Ribeiro, and A. S. Perelson, ‘How reliable are estimates of key parameters in viral dynamic models?’ bioRxiv, p. 2023.08.17.553792, Aug. 18, 2023. doi: 10.1101/2023.08.17.553792.
[6] S. M. Kissler et al., ‘Viral dynamics of acute SARS-CoV-2 infection and applications to diagnostic and public health strategies’, PLOS Biology, vol. 19, no. 7, p. e3001333, Jul. 2021, doi: 10.1371/journal.pbio.3001333.
[7] C. Zitzmann and L. Kaderali, ‘Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling’, Frontiers in Microbiology, vol. 9, 2018, Accessed: Sep. 05, 2023. [Online]. Available: https://www.frontiersin.org/articles/10.3389/fmicb.2018.01546
Reference: PAGE 32 (2024) Abstr 11207 [www.page-meeting.org/?abstract=11207]
Poster: Drug/Disease Modelling - Infection