A mathematical model of the within-host kinetics of SARS-CoV-2 neutralizing antibodies following COVID-19 vaccination

Pillis, Lisette de; Caffrey, Rebecca; Chen, Ge; Dela, Mark D.; Eldevik, Leif; McConnell, Joseph; Shabahang, Shahrokh; Varvel, Stephen A.

doi:10.1016/j.jtbi.2022.111280

Cited by 8 publications

(13 citation statements)

References 28 publications

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“…where t ij denotes the number of days when the jth NAb observation for subject i occurred since first vaccine dose (for example, t 4,2 = 49 means the second NAb activity measurement for subject 4 happened 49 days after this subject received their first vaccine dose. ), t represents the mean number of days since the first vaccine dose, C i is an indicator variable denoting whether subject i is in the convalesced group (1) or not (0), and y ij denotes the NAb activity measurement for subject i at the jth time point. In addition, ϵ ij denotes the error term for the jth time point for subject i along with b 0i and b 1i representing the random effects of subject i; we assume the error term and random effects are normally distributed with mean 0, each with standard deviations ω ϵ , ω b0 , and ω b1 , respectively.…”

Section: Linear Mixed Effects Analysis Of Neutralizing Antibody Decaymentioning

confidence: 99%

“…Comparing this to the subject and population level equations in (1) Fig. 2 Mean curves for convalesced and naïve groups using NAb activity as the response over time.…”

Section: Linear Mixed Effects Analysis Of Neutralizing Antibody Decaymentioning

confidence: 99%

“…Here, D i is an indicator variable denoting whether subject i received the Moderna (1) or Pfizer (0) vaccine. The likelihood ratio test rejects the reduced model at the 5% significance level (χ 2 (8) = 18.718, p-value = 0.016), so including vaccine type is statistically significant in explaining the decay region of NAb activity progression.…”

Section: Impact Of Vaccine Type and Sex Covariates On Nab Progressionmentioning

confidence: 99%

“…Variable A 0 denotes the initial NAb level in the structural model, indicating that convalesced individuals start with higher initial NAb Comparing Naïve and Convalesced COVID-19 Vaccinated Groups Fig. 4 The structural model of [1] was trained on data from naïve subjects, but is appropriate to use for data from convalesced individuals as well. The RMSE of the model fit to data is no larger than the RMSE for the fit to data from naïve individuals.…”

Section: Non-linear Mixed Effects Analysis Of Neutralizing Antibody P...mentioning

confidence: 99%

“…What is novel here is the use of a particular mathematical model of NAb dynamics proposed by de Pillis et. al [1] as the structural component to the nonlinear mixed effects model. This mathematical model describes the evolution of NAb activity as a solution to a simple two-population system of ordinary differential equations with four subject-specific parameters that captures the high-level mechanistic dynamics of a vaccine-triggered immune response within an individual.…”

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confidence: 99%

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Comparing Neutralizing Antibody Activity Over Time Between Naive and Convalesced COVID-19 Vaccinated Individuals

de Pillis,

Caffrey,

Che

et al. 2024

Preprint

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Longitudinal data comprised of neutralizing antibody (NAb) activity measurements from subjects who received COVID-19 vaccinations were collected between November 2020 and April 2022. To detect differences between convalesced and naive groups with respect to the evolution of NAb activity since the subject's first COVID-19 vaccine, we initially fit a linear mixed effects model to only the decay section of NAb evolution. We conclude that NAb activity, when restricted to this region, behaves differently between these two groups, with the convalesced group generally having higher neutralizing antibody levels than the naive group. We then fit a nonlinear mixed effects model over the entire NAb progression using a system of ordinary differential equations described by dePillis et al. JTB 2023 as our structural component to the model. This analysis not only supports the claim that over the entire progression, NAb activity behaves differently for convalesced and naive groups, but aligns with the linear analysis in confirming that NAb decay is slower in the convalesced group than the naive group. Finally, we use the estimated parameters from the nonlinear mixed effects model to predict NAb progression for each subject from their last observed measurement to 100 days past this measurement.

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Section: Linear Mixed Effects Analysis Of Neutralizing Antibody Decaymentioning

confidence: 99%

“…Comparing this to the subject and population level equations in (1) Fig. 2 Mean curves for convalesced and naïve groups using NAb activity as the response over time.…”

Section: Linear Mixed Effects Analysis Of Neutralizing Antibody Decaymentioning

confidence: 99%

Section: Impact Of Vaccine Type and Sex Covariates On Nab Progressionmentioning

confidence: 99%

Section: Non-linear Mixed Effects Analysis Of Neutralizing Antibody P...mentioning

confidence: 99%

mentioning

confidence: 99%

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Comparing Neutralizing Antibody Activity Over Time Between Naive and Convalesced COVID-19 Vaccinated Individuals

de Pillis,

Caffrey,

Che

et al. 2024

Preprint

Self Cite

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Differences in virus and immune dynamics for SARS-CoV-2 Delta and Omicron infections by age and vaccination histories

Tan,

Anelone,

Tay

et al. 2024

BMC Infect Dis

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Vaccination against COVID-19 was integral to controlling the pandemic that persisted with the continuous emergence of SARS-CoV-2 variants. Using a mathematical model describing SARS-CoV-2 within-host infection dynamics, we estimate differences in virus and immunity due to factors of infecting variant, age, and vaccination history (vaccination brand, number of doses and time since vaccination). We fit our model in a Bayesian framework to upper respiratory tract viral load measurements obtained from cases of Delta and Omicron infections in Singapore, of whom the majority only had one nasopharyngeal swab measurement. With this dataset, we are able to recreate similar trends in URT virus dynamics observed in past within-host modelling studies fitted to longitudinal patient data.We found that Omicron had higher R0,within values than Delta, indicating greater initial cell-to-cell spread of infection within the host. Moreover, heterogeneities in infection dynamics across patient subgroups could be recreated by fitting immunity-related parameters as vaccination history-specific, with or without age modification. Our model results are consistent with the notion of immunosenescence in SARS-CoV-2 infection in elderly individuals, and the issue of waning immunity with increased time since last vaccination. Lastly, vaccination was not found to subdue virus dynamics in Omicron infections as well as it had for Delta infections.This study provides insight into the influence of vaccine-elicited immunity on SARS-CoV-2 within-host dynamics, and the interplay between age and vaccination history. Furthermore, it demonstrates the need to disentangle host factors and changes in pathogen to discern factors influencing virus dynamics. Finally, this work demonstrates a way forward in the study of within-host virus dynamics, by use of viral load datasets including a large number of patients without repeated measurements.

show abstract

Differences in virus and immune dynamics for SARS-CoV-2 Delta and Omicron infections by age and vaccination histories

Tan,

Anelone,

Tay

et al. 2024

Preprint

View full text Add to dashboard Cite

Vaccination against COVID-19 was integral to controlling the pandemic that persisted with the continuous emergence of SARS-CoV-2 variants. Using a mathematical model describing SARS-CoV-2 within-host infection dynamics, we estimate differences in virus and immunity due to factors of infecting variant, age, and vaccination history (vaccination brand, number of doses and time since vaccination). We fit our model in a Bayesian framework to upper respiratory tract viral load measurements obtained from cases of Delta and Omicron infections in Singapore, of whom the majority only had one nasopharyngeal swab measurement. With this dataset, we are able to recreate similar trends in URT virus dynamics observed in past within-host modelling studies fitted to longitudinal patient data. We found that Omicron had greater infection potential than Delta, indicating greater propensity to establish infection. Moreover, heterogeneities in infection dynamics across patient subgroups could be recreated by fitting immunity-related parameters as vaccination history-specific, with or without age modification. Our model results are consistent with the notion of immunosenescence in SARS-CoV-2 pathogenesis in elderly individuals, and the issue of waning immunity with increased time since last vaccination. Lastly, vaccination was not found to subdue virus dynamics in Omicron infections as well as it had for Delta infections. This study provides insight into the influence of vaccine-elicited immunity on SARS-CoV-2 within-host dynamics, and the interplay between age and vaccination history. Furthermore, it demonstrates the need to disentangle host factors and changes in pathogen to discern factors influencing virus dynamics. Finally, this work demonstrates a way forward in the study of within-host virus dynamics, by use of viral load datasets including a large number of patients without repeated measurements.

show abstract

A mathematical model of the within-host kinetics of SARS-CoV-2 neutralizing antibodies following COVID-19 vaccination

Cited by 8 publications

References 28 publications

Comparing Neutralizing Antibody Activity Over Time Between Naive and Convalesced COVID-19 Vaccinated Individuals

Comparing Neutralizing Antibody Activity Over Time Between Naive and Convalesced COVID-19 Vaccinated Individuals

Differences in virus and immune dynamics for SARS-CoV-2 Delta and Omicron infections by age and vaccination histories

Differences in virus and immune dynamics for SARS-CoV-2 Delta and Omicron infections by age and vaccination histories

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