A recent modeling study published in the Proceedings of the National Academy of Sciences of the United States of America (PNAS) provides a quantitative framework for understanding the impact of drugs and vaccines that lower viral load of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on the infectiousness of infected individuals, but also for rapid testing strategies.
Study: In vivo kinetics of SARS-CoV-2 infection and its relationship with a person’s infectiousness. Image Credit: Marcin Janiec / Shutterstock
A highly contagious SARS-CoV-2 is still spreading rapidly across the globe, causing coronavirus disease 2019 (COVID-19) that has resulted in more than five million deaths around the world as of December 2021. The virus can readily infect cells in the upper respiratory tract and reach a high viral load, enabling effective transmission.
But even though it is not entirely clear how viral load, infectiousness, and symptom onset are quantitatively related, the understanding of this relationship is pivotal for both non-pharmaceutical and pharmaceutical interventions on viral transmission and for the prediction of disease course.
Viral load has previously already been used as a surrogate for the infectiousness of the influenza virus and SARS-CoV-2. Moreover, mathematical modeling has already been pursued by different researchers. However, there were uncertainties in model parameter estimates – primarily because data was taken after symptom onset without knowing infection dates and early viral dynamics.
This is why a research group led by Dr. Ruian Ke from the Los Alamos National Laboratory and New Mexico Consortium in Los Alamos, New Mexico, aimed to estimate key within-host viral dynamic parameters by using much more precise modeling approaches.
A dynamic model of SARS-CoV-2 infection
![Fitting results of the innate response model to the VL data from two studies. (A) Fitting results to data from eight individuals in the Germany study [i.e., Wolfel et al. (3)]. The model (solid lines) was simulated using the best-fit individual parameter values estimated by a nonlinear mixed effect modeling approach (Tables 1 and 2). The symbols (red dots and circles) show the data from pharyngeal swabs. The circles indicate data points below the limit of detection (LoD). Vertical gray lines denote the time of symptom onset as reported in ref. 19. Horizontal dashed black lines show the LoD. (B) Fitting results to data from nine individuals in the NBA study as reported in Kissler et al. (20) with symbols and colors as in A.](https://d2jx2rerrg6sh3.cloudfront.net/images/news/ImageForNews_698521_16387645630109756.jpg "Fitting results of the innate response model to the VL data from two studies. (A) Fitting results to data from eight individuals in the Germany study [i.e., Wolfel et al. (3)]. The model (solid lines) was simulated using the best-fit individual parameter values estimated by a nonlinear mixed effect modeling approach (Tables 1 and 2). The symbols (red dots and circles) show the data from pharyngeal swabs. The circles indicate data points below the limit of detection (LoD). Vertical gray lines denote the time of symptom onset as reported in ref. 19. Horizontal dashed black lines show the LoD. (B) Fitting results to data from nine individuals in the NBA study as reported in Kissler et al. (20) with symbols and colors as in A.")
Fitting results of the innate response model to the VL data from two studies. (A) Fitting results to data from eight individuals in the Germany study [i.e., Wolfel et al. (3)]. The model (solid lines) was simulated using the best-fit individual parameter values estimated by a nonlinear mixed effect modeling approach (Tables 1 and 2). The symbols (red dots and circles) show the data from pharyngeal swabs. The circles indicate data points below the limit of detection (LoD). Vertical gray lines denote the time of symptom onset as reported in ref. 19. Horizontal dashed black lines show the LoD. (B) Fitting results to data from nine individuals in the NBA study as reported in Kissler et al. (20) with symbols and colors as in A.
In short, this research group has developed viral dynamic models of SARS-CoV-2 infection and fit them into data to appraise key within-host parameters, emphasizing within-host reproductive number and infected cell half-life. Then they have developed a model linking viral load to infectiousness.
Infectiousness was defined as the probability that an infected person sheds one or more infectious viral particles, subsequently resulting in a successful infection of the recipient for a typical contact of a relatively short time frame. Furthermore, three datasets on infectious virus cell culture positivity were used to model viral transmission.
Using data on viral load and the predicted infectiousness, the researchers have further included data on antigen and reverse transcription-polymerase chain reaction (RT-PCR) tests and compared their utility in determining infection and preventing transmission.
![The relationship between VL and host infectiousness. (A) A schematic of the probabilistic model describing the steps in a transmission event. A donor sheds both infectious and noninfectious viruses, of which some infectious viruses may reach a recipient during a close contact and establish an infection. (B) Best-fit of the three models [i.e., the linear model (gray), the power-law model (blue), and the saturation model (red)] to the data from Jaafar et al. (27), Jones et al. (28), and Kohmer et al. (29). The open circles denote the percentage of cell culture positivity reported, and vertical lines denote the 95% CIs calculated assuming a binomial distribution for the number of positive cultures. For the datasets from Jones et al. (28) and Kohmer et al. (29), VLs are binned into half-log10 intervals. Solid lines are used for models that describe the data well. (C) The predicted probability of transmission for a typical contact as a function of log10 VL given by the saturation model in Eq. 1 with θ=0.20,h=0.51, and](https://d2jx2rerrg6sh3.cloudfront.net/images/news/ImageForNews_698521_16387646259818463.jpg "The relationship between VL and host infectiousness. (A) A schematic of the probabilistic model describing the steps in a transmission event. A donor sheds both infectious and noninfectious viruses, of which some infectious viruses may reach a recipient during a close contact and establish an infection. (B) Best-fit of the three models [i.e., the linear model (gray), the power-law model (blue), and the saturation model (red)] to the data from Jaafar et al. (27), Jones et al. (28), and Kohmer et al. (29). The open circles denote the percentage of cell culture positivity reported, and vertical lines denote the 95% CIs calculated assuming a binomial distribution for the number of positive cultures. For the datasets from Jones et al. (28) and Kohmer et al. (29), VLs are binned into half-log10 intervals. Solid lines are used for models that describe the data well. (C) The predicted probability of transmission for a typical contact as a function of log10 VL given by the saturation model in Eq. 1 with θ=0.20,h=0.51, and")
The relationship between VL and host infectiousness. (A) A schematic of the probabilistic model describing the steps in a transmission event. A donor sheds both infectious and noninfectious viruses, of which some infectious viruses may reach a recipient during a close contact and establish an infection. (B) Best-fit of the three models [i.e., the linear model (gray), the power-law model (blue), and the saturation model (red)] to the data from Jaafar et al. (27), Jones et al. (28), and Kohmer et al. (29). The open circles denote the percentage of cell culture positivity reported, and vertical lines denote the 95% CIs calculated assuming a binomial distribution for the number of positive cultures. For the datasets from Jones et al. (28) and Kohmer et al. (29), VLs are binned into half-log10 intervals. Solid lines are used for models that describe the data well. (C) The predicted probability of transmission for a typical contact as a function of log10 VL given by the saturation model in Eq. 1 with θ=0.20,h=0.51, and Km=8.9×106 RNA copies (red) or by the power model in Eq. 2 with ϕ=2.4×10−5 and h=0.53 (blue). (D and E) The infectiousness profile for all individuals studied (lines in Upper) predicted by the infectious model assuming a saturation function (Eq. 1) or a power-law function (Eq. 2), respectively. (Lower) The relationship between the duration of the incubation period (x axis) and estimated presymptomatic area under the infectiousness curve. Irrespective of the model used, expected presymptomatic transmission is more likely in individuals with a longer incubation period.
A sublinear increase of infectiousness
The study has revealed how an individual’s infectiousness actually increases sublinearly with viral load and that the logarithm of the viral load in the upper respiratory tract truly represents a better surrogate of infectiousness.
For patients with known dates of infection and the beginning of symptoms, the researchers have found that protracted incubation periods had a much higher potential of pre-symptomatic viral transmission, which was consistent with some recent studies tackling similar research questions.
This modeling approach has also suggested that RT-PCR tests are a much better choice than antigen tests at both finding infected individuals and effectively reducing total infectiousness, assuming equal testing frequency. This is especially valid when testing is utilized as a tool for safe reopening workplaces, schools, and various events.
Predictive modeling for health policy
Overall, this model linking within-host viral load dynamics to infectiousness provides an indispensable tool for assessing non-pharmaceutical and pharmaceutical interventions and steering public health policy recommendations and decisions.
“Our modeling approach is well suited to quantify the impact of vaccination on the infectiousness of a person,” said the study authors in this PNAS paper. “These results demonstrate that the relationship between viral load reduction and infectiousness reduction is highly non-linear,” they further explain.
Additional research endeavors in this field that will appraise individual-level heterogeneity in the relationship between infectious viral shedding and viral load will aid in characterizing heterogeneity in individual infectiousness and give rise to much more specific predictions of the various testing strategies for SARS-CoV-2 transmission.
Journal reference:
Ke, R. et al. (2021). In vivo kinetics of SARS-CoV-2 infection and its relationship with a person’s infectiousness. Proceedings of the National Academy of Sciences of the United States of America (PNAS). https://doi.org/10.1073/pnas.2111477118, https://www.pnas.org/content/118/49/e2111477118
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