From our initial data exploration via the regression analysis (S1 Table), we observed higher peak viremia in Delta infections, faster rate of virus clearance in Delta infections, and slower rate of virus clearance in older age groups, similar to the results of the within-host model. The mathematical model further allowed us to examine dynamics of both virus and immune dynamics during infection, and their interplay.
We have constructed a simple mathematical model describing the within-host dynamics of infection with SARS-CoV-2, fitted to URT viral load data collected in Singapore. We characterised heterogeneities in infection dynamics across vaccine histories and ages by fitting immunity-related parameters as vaccination history-specific, with or without age-modification. Moreover, by varying virus-related parameters by infecting VOC, it was possible for us to recreate differences between Delta and Omicron infections.
Resulting URT virus dynamics from model fitting showed rapid virus growth, early peak, followed by gradual decay in circulating virus. The shapes of our model fits for URT viremia (Fig. 2) are broadly similar to that observed in a human challenge trial with wild-type virus for both nasal and throat viral load trajectories(27). Despite us fitting our models to individual data where a majority of the individuals only had one nasopharyngeal swab taken, by estimating parameters at a group level, we were able to recreate similar trends in URT virus dynamics observed in other within-host models of URT SARS-CoV-2 infection fitted to longitudinal patient data(15, 17, 28). The Bayesian hierarchical approach we adopted made it possible for us to utilise our dataset which included a large number of individuals with only one measurement taken during acute infection. Hence, it is possible for our model to be used for other swab datasets with a large number of patients, but without repeated measurements allowing exploration of the impact on virus dynamics of a wide range of vaccination histories and ages
Model selection results showed that it was necessary to vary growth rate of immunity during infection (ω) by age and vaccination history to reproduce differences observed between patient subgroups (Table 3). As a result of this age modifier, growth rate of immunity (ω) decreased with increasing age for the same vaccination history, suggesting weakened immune function in older age groups (Fig. 4). These results provide supporting evidence for existing hypotheses on the role of immunosenescence in SARS-CoV-2 pathogenesis in older individuals(29–31). We further noted that for a given age group, growth rate of immunity (ω) remained higher for vaccinated groups compared to the unvaccinated regardless of time since vaccination. These results align with findings that older age groups showed greater increment in antibody responses following vaccination, although antibody titres were lower in older age groups than in younger individuals despite vaccination(32, 33). We found that clearance by immune response (γ) could be varied by vaccination history without the need for age modification (Table 3). There was a slight increase and variation in this clearance over time since vaccination before it stabilised from 60–90 days post vaccination and 90–180 days post vaccination for Delta and Omicron infections respectively (Fig. 3). Differences in immune clearance (γ) over time since vaccination are not as large as that observed in our results for growth rate of immunity (ω). This suggests that there are little changes in the function of clearing immunity over time since vaccination and instead, time since vaccination is perhaps more relevant to the activation of immunity given infection. However, this conclusion remains tentative with the lack of immunological measurements in our data. Overall, our model is able to recreate overall differences in parameter estimates for growth rate of immunity (ω) with differing vaccination history and age.
By considering time since last vaccine dose received as a means of subgrouping, we are able to capture differences in infection dynamics across time since vaccination subgroups that was possibly due to waning immunity. We found that both Delta and Omicron infections showed increasing growth rate of immunity during infection (ω) for the first 2 weeks post-vaccination before decreasing, then finally plateauing from approximately 60–90 days post-vaccination. For Delta and Omicron, growth rate of immunity (ω) at 0–7 days for a vaccine group and age subgroup is typically lower than that at 8–14 days or 15–21 days. These findings are consistent with studies of T-cell and antibody response after 2 doses of mRNA vaccines that showed increased levels after 21 days post-vaccination(34, 35). Furthermore, Gao et al. reported that antigen-specific effector T-cells contracted to approximately pre-vaccination levels by day 90 post-vaccination(35), with similar declining of antibody titres(36) observed in individuals who completed their primary series of vaccination. Waning of humoral response after third mRNA dose was also observed, albeit at a slower rate than after the second dose(5). Although we did not model specific components of immunity, trends observed for the generic clearing immunity included in our model appears to mimic these observations of the waning adaptive immune response. In the absence of measurements of the effector immune response we are unable to draw definitive conclusions regarding the reasons for this eventual decline in growth rate of immunity (ω).
Comparing Delta and Omicron infections, model results showed faster virus growth, earlier and lower virus peaks followed by slower virus decline for all Omicron infections (Fig. 2). We found Omicron infections to have higher R0, within values than Delta infections (Table 4), with higher estimates for virus infection rate of target cells (β) and modelled components of immunity, and lower estimates for natural clearance rate of free virus (c). These results corroborate with a previous study using a model of virus infection dynamics of Delta and Omicron variants in nasal and lung cell types, whose results showed Omicron to have greater fitness advantage in human nasal epithelial cells with higher target cell infection rate and faster growth rate of virus, but lower peak viral load than Delta(37). Although other studies have reported lower viral load for Omicron than Delta(38, 39), results in literature remain conflicting. Some studies have shown Delta and Omicron infections to have little difference in their viral load regardless of vaccination status(40, 41), while others have reported higher viral load for Omicron infections(42). However, these studies had not accounted for differences in incubation period of infected individuals. As such, their results compare viral load measurements for Delta and Omicron infections regardless of date of symptom onset, with measurements likely to have been taken at different timepoints of individual virus dynamics trajectories. A recent study of Delta and Omicron viral kinetics accounting for time since last infection or vaccination reported higher peak viral loads for Delta infections compared to Omicron (BA.1), similar to our results(43).
We found that vaccination altered URT viral dynamics more in Delta infections than Omicron. The difference in virus dynamics is especially apparent in the 3-dose mRNA vaccine groups that had lowered virus peak value and, in some cases, increased rate of virus decline for Delta infections (Fig. 2). There was no such discernible trend for 3-dose mRNA vaccine groups with Omicron infections, with URT viral load dynamics being similar regardless of vaccine brand. These results align with findings of other studies. Yang et al. found largely similar viral dynamics among individuals who were unvaccinated, received 2 doses of inactivated vaccine, and received 3 doses of inactivated vaccine during Omicron infection(44). A study on Delta and Omicron virus dynamics showed a greater difference in viral load of the 2-/3-dose vaccine groups compared to those unvaccinated for Delta infections compared to Omicron(38). However, Puhach et al. found that although vaccination decreased both RNA and infectious viral loads for Delta infections, the same was not observed for Omicron infections. The study showed that for Omicron infections, although 3-dose vaccinated individuals had lower infectious viral loads than 2-dose vaccinated individuals, RNA viral load of the two groups were largely similar(45). Our results show that vaccination was not able to subdue virus dynamics in Omicron infections as well as it had for Delta infections, motivating for a vaccine that is better able to reduce Omicron virus load while minimising side effects.
The model has several limitations. First, we fitted our models to nasopharyngeal viral load measurements obtained post-symptom onset. Due to the lack of data during the early stages of infection, assumptions regarding incubation period, virus production rate and uninfected target cell density affect estimates of infection rate of target cells (β). Sensitivity analysis showed that the early stages of infection in our model are sensitive to the assumed distributions of incubation period, corroborating with findings of Ke et al.(46). As such, in the absence of early-stage viral load data, we are limited in our ability to model variations in early virus dynamics between vaccination regimes and age groups, with our conclusions pertaining to early virus dynamics remaining tentative. To address this issue, further studies can be conducted with data including measurements taken prior to symptom onset.
Second, we are characterising infection in patients with a narrow range of symptoms. The clinical manifestations of disease experienced by the patients in our dataset were likely to be mild to moderate. Individuals in the dataset presented to clinics for confirmatory testing of SARS-CoV-2 infection based on nasopharyngeal PCR swabs. This implies that individuals perceived their symptoms, but these symptoms were not sufficiently severe for individuals to present to hospitals or other forms of emergency care. Hence when making inferences regarding differences between vaccinated and unvaccinated groups, and between vaccine groups, we note that we are studying breakthrough infections, and that vaccine efficacy might differ between vaccine groups.
Third, majority of individuals in our dataset were swabbed once, with swabs taken earlier in the course of infection, closer to the date of symptom onset. As a result, these individuals mostly contribute to data closer to the time of virus peak. Individuals with longitudinal samples were typically elderly, unvaccinated individuals, or individuals vaccinated with non-mRNA vaccines who had multiple swabs taken as per the swab protocol. Sensitivity analysis by model fitting showed Hence, it appears that the longitudinal samples assist in informing the virus decay phase, rather than biasing the model towards having slower virus decay. This is possibly due to patients in our dataset having experienced similar disease severity for infections with the same VOC.
Another limitation of this study is the simplicity of the model. Without measurements of the uninfected and infected target cell populations, and effector immune response, we are unable to consider more complex models of infection. For example, we could not explicitly model effector cell populations nor include more than one infection-clearing immune mechanism. Furthermore, we opted to account for age by incorporating it as a modifier to limit the number of parameters to be fitted in our model and preserving the model’s simplicity. Although this allowed us to clearly compare age effects for growth rate of immunity (ω) via the age modifier (θ), opting for this simpler model resulted in us being unable to capture age-dependent immune priming and waning.
Lastly, we assumed that the main mechanism by which immunity controls infection was infected cell clearance and did not include clearance of free virus by immunity in our model. As such, we are only modelling one arm of immunity, mainly the T-cell mechanisms for infected cell clearance. In our model results, we are unable to distinguish between infected cell clearance and clearance of free virus, as well as between clearance by immunity and natural clearance. Instead, we opted to model one mechanism for immune control of infection and fix the natural clearance rate of the component being cleared for the sake of model parsimony. Results from fitting an alternative model with immune clearance of free virus as the main mechanism showed model diagnostics to be poor with no convergence (S10 Fig). These results imply that infected cell clearance by immune response was more appropriate of a choice, given that our original model was able to recreate virus dynamics similar in shape to human challenge studies and past modelling work. However, it is possible that the alternative model had poor model diagnostics due to the lack of data on immunity-related components. Further studies could compare model fits for both models if such data is available alongside viral load measurements during infection.
By fitting a mathematical model of SARS-CoV-2 infection to Delta and Omicron infection data, in which information on patients’ vaccines received, age, and time since last vaccine dose is available, we were able to provide insights into the age effects on immunity, immunity waning, the role of different levels of vaccine-induced protection, and VOC-specific pathogenesis of SARS-CoV-2. Our work highlights the importance of age-targeted public health policy, updating immunity with booster doses, and the need for vaccines better targeted against Omicron infection. A possible extension to this work would involve the comparison of Omicron infections in individuals who received monovalent vaccines with those who received bivalent vaccines to investigate the effects of these vaccines on virus dynamics. Such work could consider infection with different Omicron sublineages if data is available, in order to examine differences in virus dynamics between Omicron variants.