Quantifying the Effects of Viral Load on Multistate COVID-19 Infection and Progression of Alpha and Omicron VOCs: A Bayesian Competing Markov Exponential Regression Model

doi:10.21203/rs.3.rs-3127298/v1

Download PDF

Research Article

Quantifying the Effects of Viral Load on Multistate COVID-19 Infection and Progression of Alpha and Omicron VOCs: A Bayesian Competing Markov Exponential Regression Model

https://doi.org/10.21203/rs.3.rs-3127298/v1

This work is licensed under a CC BY 4.0 License

Journal Publication

published 30 Oct, 2023

Read the published version in Stochastic Environmental Research and Risk Assessment →

You are reading this latest preprint version

We used a Bayesian competing four-state Markov model to explore how viral shedding in terms of cycle threshold (Ct) value makes relative contribution between persistent and non-persistent asymptomatic mode, and whether it affects the subsequent progression to show symptoms. The proposed model was applied to data from two large outbreaks on Alpha and Omicron variants of concern (VOCs) in Changhua, Taiwan. A multistate Markov exponential regression model was proposed for quantifying the odds ratio (OR) of viral shedding measured by cycle threshold (Ct). A Bayesian Markov Chain Monte Carlo (MCMC) method was used for estimating the parameters of the posterior distribution. The estimated results show that developing non-persistent asymptomatic mode relative to persistent asymptomatic mode was reduced by 14% (adjusted OR = 0.86, 95% CI: 0.81–0.92) per one increasing unit of Ct for Alpha VOC, whereas these figures were shrunk to 5% (aOR = 0.95, 95% CI: 0.93–0.98) for Omicron VOC. Similar significant gradient relationships were also observed between three viral load levels. Similar, but not statistically significant, dose-response effects of viral load on the progression to symptoms for non-persistent asymptomatic mode were observed. The application of statistical model helps elucidate the pathways of SARS-CoV-2 infectious process associated with viral shedding that demonstrate viral shedding plays a crucial role in determining the path of either non-persistent or persistent asymptomatic mode in a dose-response manner, which was more pronounced for the Alpha than the Omicron. Modelling such a multistate infectious process with two competing pathways would provide a new insight into the transmissibility and the duration of insidious infection before onset of symptom and the deployment of precision containment measures with a better use of the Ct value as virologic surveillance for projecting the individual epidemic course.

viral shedding

Alpha and Omicron VOCs

multistate model

contact tracing

It is well acknowledged that the main reason of Coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) mutants is attributed to silent infection before onset of symptom, which is often defined by two distinct phenotypes, including pre-symptomatic infected cases and asymptomatic infected cases (Alene et al. 2021, Arons et al. 2020, Buitrago-Garcia et al. 2022; Lee et al. 2020, Ma et al. 2021, Sah et al. 2021). The main difference between two phenotypes is that the pre-symptomatic phenotype will eventually lead to onset of symptom during the incubation period that is a conventional measure of infectious and transmissible property defined by the time of infection to onset of symptom whereas the asymptomatic phenotype will not manifest symptom until recovery. Accordingly, the pre-symptomatic cases are also named as non-persistent asymptomatic cases in contrast to persistent asymptomatic cases coined for asymptomatic cases (Buitrago-Garcia et al. 2022). In essence, there are two distinct pathways of the multiple-step infectious process of SARS-CoV-2 variant from the time of initial infection until either following non-persistent asymptomatic case or persistent asymptomatic without showing symptoms until recovery. Modelling such a multistate infectious process with two pathways would provide a new insight into the transmissibility and the duration of insidious infection before onset of symptom and the deployment of precision containment measures

It should be also noted that as both phenotypes are not distinguishable before onset of symptoms it is therefore imperative to make use of the reverse transcription polymerase chain reaction (RT-PCR) test for identifying non-persistent asymptomatic cases when they were in the presence of symptoms during quarantine and isolation period, which actually represents the transition from pre-symptomatic infectious phase to symptomatic infectious phase. As far as persistent asymptomatic cases are concerned, they will not manifest symptoms and therefore may not be detected if they are not offered with the RT-PCR test. Only when contact tracing and epidemic investigation of the close contacts with infectives resulting from different kinds of cluster infection would the RT-PCR test be offered for detecting both phenotypes together with quarantine and isolation.

It is reasoned that non-persistent asymptomatic cases would be more contagious than persistent asymptomatic cases in terms of viral shedding measured by the cyclic threshold (abbreviated as Ct) value of viral load (Chen et al. 2021, Wu et al. 2021). More importantly, the viral shedding also evolves dynamically in parallel with the development of non-persistent asymptomatic and persistent asymptomatic cases with time from initial infection, onset of symptom, and recovery. Nonetheless, such dynamic and quantitative effects of viral shedding on the two pathways of multistate infectious process as mentioned above is yet well studied. Accurately quantifying the effects of viral shedding on two pathways of multistate infectious process would provide a precision guidance for contact tracing and also the optimal schedule for quarantine and isolation. However, such a quantitative role of the state-dependent viral shedding may be also perturbed by demographic features, the type of cluster infection, and whether to have available and deliverable vaccination. The new approach is therefore required for accommodating these state-dependent covariates, with emphasis on the level of viral shedding, on such a multistate infectious process of COVID-19, including the risk of infection, the potential of being non-persistent asymptomatic or remaining persistent asymptomatic, and the median time of the progression from pre-symptomatic to symptomatic phase after the exposure to infected source case for contact persons.

To this end, we first developed a competing multistate Markov exponential regression model to fit in with the scenario of two pathways spanning from infection until onset of symptom or persistent asymptomatic case with each step of transition on which the viral shedding level and relevant covariates were superimposed in order to assess the significance of their state-dependent quantitative roles. We then applied the proposed model to Taiwan community-acquired outbreak data on both Alpha and Omicron variants of concern (VOCs) collected through contact tracing and epidemic investigation of two cohorts of close contacts with the detailed information on the dynamic of multistate infectious process accompanied with viral shedding detected through RT-PCR test and other relevant covariates through questionnaire on travel, occupation, contact, and cluster. The state-dependent quantitative roles of viral shedding level together with demographic features, the type of cluster infection, and vaccination were accurately estimated for both Alpha and Omicron VOCs.

2.1 Model Specification

The dynamics of multistate infectious process are framed and designed by the competing Markov process with state-specific covariates as shown in Fig. 1. These multiple time events are modeled from uninfected state to infected state cases (the first step) estimated by the infected parameter denoted by λ after close contact with infected persons and then go through two pathways (the second step), one for the potential of developing symptoms through pre-symptomatic phase for non-persistent asymptomatic cases denoted by π and the potential of remaining persistent asymptomatic until recovery denoted by 1-π. The third step is pertaining to the progression rate from pre-symptomatic phase to symptomatic phase denoted by λ₂ only for non-persistent asymptomatic cases that can be further converted into the median time to develop symptoms. Relevant covariates with emphasis on the main independent variable viral shedding level are superimposed on the second and third step of transition in the gray box of Fig. 1. Based on this multistate design, the first was to estimate the overall infected rate and the specific incidence rates by age, gender, the type of cluster infection, and vaccination. The second was then to estimate the incidence rate of being pre-symptomatic (non-persistent asymptomatic) or being persistent asymptomatic by the reparameterization of using both λ and π as shown in Fig. 1. The effects of the viral shedding level on the potential of following the pathway of being non-persistent asymptomatic or being persistent asymptomatic were further assessed. The third was to estimate the progression from pre-symptomatic phase to symptoms with adjustment for demographic features, the type of cluster infection, and vaccination status.

2.2 Data on Contact Tracing Cohort

Data on two community-acquired outbreak cohorts between May 14 and July 24, 2021 (the Alpha period) and between April 1 and May 16, 2022 (the Omicron period) in Changhua, the middle county of Taiwan, were used for analysis. We collected information on age, sex, viral shedding level (Ct value), date of exposure, PCR testing, date of showing symptom, the type of cluster infection, and vaccination status through the outbreak investigation. Note that the type of cluster infection among Alpha VOC included two major types in the light of index case. The first type of index case is pertaining to a fruit dealer who accounted for around 40% Alpha VOC in Changhua in 2021. The transmission chains from this cluster was mostly from household members (see Supplementary Fig. 1). The second type of index case was a Mahjong player. Such a cluster was representative of one kind of social gathering infection. Contact tracing for identifying further infected cases among contact persons was through the index case of each cluster according to information on the date of exposure. It should be noted that the vaccine policy was not widely administered during the period of Alpha outbreak in Changhua. In addition, information on the type of cluster infection was only available during the early Omicron period as there were too many cases and too many chains regarding the transmission mode of the spread of Omicron later on. Therefore, the entire community residents were regarded as the close contact cohort when we estimated the infected rate of Omicron. The type of cluster infection could not be specified as that collected from the outbreak of Alpha VOC. This study was approved by the Ethical Committee of Taipei Medical University (TMU-JIRB No.: N202007018).

Figure 2 shows how information provided for the estimation of parameters in Fig. 1 with the detailed flowchart of following up the contact tracing cohort. It begins with the date of exposure to infective (t₀) among the contacted persons and the date of RT-PCR test at the date of tracing (t₁). Those contacts with positive RT-PCRT result upon the presence of symptoms were pursuant to infected-pre-symptomatic-symptomatic pathway and provide information on the time of infection at t₀ and from infection to onset of symptomatic during t₁-t₀. Note that such information failed to provide additional information on the exact time of the transition from pre-symptomatic phase to symptomatic phase during t₁-t₀ (see the Box (A) of Fig. 2). This unknow time point will be integrated out from multiple integrals in the formula of the transition probability from time of infection until the onset of symptom during t₁-t₀. Those RT-PCR positive contacts upon the RT-PCR test but without symptoms were isolated with surveillance. They had two possible outcomes, the presence of symptom at t_s before the end of isolation (Box (B) of Fig. 2) and the absence of symptom until recovery at t_r (Box (C) of Fig. 2). In addition to the origin of infection time at t₀, the former not only provides information on the potential of being non-persistent asymptomatic case (π) but also dynamic transitions from infection to pre-symptomatic phase during t₁-t₀ and from pre-symptomatic to symptomatic phase between t_s and t₁. The latter type followed up the pathway leading to persistent asymptomatic state from infection until recovery during t_r-t₀ and provide information on infection rate and the potential of being persistent asymptomatic case (1-π) (Box (C) of Fig. 2). Those with the negative result of RT-PCR at t₁ were quarantined. Once they showed symptoms they were requested to confirm with RT-PCR test. Positive results suggest the pathway of non-persistent asymptomatic cases with very informative dynamic transitions in two periods as seen in the Box (D) of Fig. 2 similar to the Box (B) of Fig. 2. Those in the absence of symptoms or with negative RT-PCR results of showing symptoms before the end of isolation were classified as uninfected with the censoring information during t_u-t₀ (Box (E) of Fig. 2). Note that the date of contact tracing and RT-PCR test with positive result provide information on infection rate (λ) among the cohort of those contact tracing subjects.

2.3 Statistical Analysis

We estimated parameters involved in the competing multi-state Markov model delineated in Fig. 1 following the previously proposed Markov processes applied to establish the precision strategies of screening, quarantine, and isolation for imported COVID-19 cases in Taiwan (Chen et al. 2022, Jen et al. 2022). These include the infection rate (λ), the potential of following the non-persistent pathway (π), and the subsequent progression from pre-symptomatic to symptomatic phase (λ₂), further converting into the median time of such a progression. We modeled the effect of the viral shedding level on the pathway of either from pre-symptomatic (non-persistent asymptomatic) to symptomatic phase or persistent asymptomatic state. As the viral shedding of SARS-CoV-2 may affect the possibility of developing symptoms, we treated the Ct value at time when the patients were confirmed infected as a covariate. The effect of viral shedding on each state transition was first dealt with the continuous and decile distribution of Ct value and was further categorized as low (Ct≥25), medium (18≤Ct < 25) and high level (Ct < 18) in the light of conventional classification. Other relevant covariates considered in our model included sex, age, the type of cluster infection (only for Alpha VOC), and vaccination (only for Omicron VOC). We applied the Markov exponential regression model to estimate the effect of these relevant covariates (Hart et al. 2022). The proportion hazards regression from was applied to infection rate (λ) and the subsequent progression from pre-symptomatic to symptomatic phase (λ₂), and the logistic regression model from was applied to the potential of being non-persistent asymptomatic (π).

Bayesian Markov Chain Monte Carlo (MCMC) method based on a random-walk Metropolis sampling scheme with the normal proposal distribution was applied to derive the joint posterior distribution of the abovementioned parameters from a multidimensional space to support the maximum likelihood function detailed in the Supplementary Materials. Basically, non-information prior distributions were used, including gamma distributions for infected parameter (λ) and the shape parameter for time from pre-symptomatic to symptomatic phase following log-logistic distribution (Jen et al, 2022), and the normal distribution for regression coefficients which link the correlated covariates to infection parameter (λ) and the potential of being non-persistent asymptomatic (π). Regarding inference about the transition from pre-symptomatic to symptomatic phase of Omicron outbreak in Changhua, May 2022, we borrowed the prior information from an earlier smaller outbreak in a northern County, January 2022, because the latter had a more detailed contact tracing when the outbreak size was small then. The MCMC sampling started with 5000 burn-in period followed by 20,000 sampling iterations to derive the posterior distribution of all parameters. Reparameterization of posterior samples corresponding to each transition were used to make inference about the mean estimates and the corresponding 95% credible intervals of adjusted odds ratios. All analyses were performed with SAS version 9.4 (SAS Institute Inc., Cary, NC, USA).

3.1 Descriptive Results of the Alpha and Omicron VOC outbreak

Following the flowchart of Fig. 2 with different types of information provided for estimating the infection rate, the potential of either pathways, and the transition rate from pre-symptomatic to symptomatic phase, a total of 8,018 subject were under contact tracing after Alpha community-required outbreak had occurred in Changhua between May and July, 2021. There were 269 cases out of 8,018 contacts confirmed by RT-PCR test at the date of tracing. Of 269, 80 RT-PCR test positives were accompanied with symptoms at the date of test. They are therefore defined as non-persistent symptomatic cases following the pre-symptomatic-symptomatic pathway with information delineated in the Box (A) of Fig. 2. A total of 103 RT-PCR positives were ascertained as non-persistent asymptomatic cases as there had been absence of symptoms at the date of RT-PCR and epidemic investigation but had onset of symptoms later during quarantine and isolation. Information provided for modelling is depicted in the Box (B) of Fig. 2. The remaining 24 RT-PCR positives were defined as persistent asymptomatic as they had never manifested symptom until the recovery with information specified in the Box (C) of Fig. 2. As far as RT-PCR negative contacts at the date of contact tracing were concerned, 62 presented with symptoms and confirmed as RT-PCR positive after follow-up during quarantine and isolation are defined as non-persistent asymptomatic cases with information depicted in Box (D) of Fig. 2 similar to Box (B) of Fig. 2 but with different time epochs. Those with negative RT-PCR and in the absence of symptoms were defined as uninfected with information as descried in the Box (E) of Fig. 2. Descriptive results and data regarding Omicron VOC were derived in a similar manner. Information on cases corresponding to Box (A)-(D) for Omicron are detailed in Fig. 2.

Table 1 shows the distributions of sex, age, the type of cluster infeciton, vaccination status, and the viral shedding for confirmed cases and contacts for both Alpha and Omicron VOCs. It should be noted that there were specific 8018 contacts under tracing as community-acquired outbreaks of Alpha VOC had been limited to several types of cluster infection, including fruit dealer, mahjong players, and others. However, contacts for Omicron VOC infection included the underlying population due to its high transmission and the relaxation of non-pharmaceutical interventions leading to an increasing contact rate with high social mobility. The risk of infection was at increased risk for those aged 65 years compared with the young generation for Alpha VOC infection whereas the opposite was noted for Omicron VOC infection. Of all confirmed cases, those detected as RT-PCR positive accompanied with the manifestation of symptoms (Box (A) of Fig. 2) were more likely to have high viral load (low Ct) level than those persistent asymptomatic cases (Box (C) of Fig. 2). It is very interesting to note that viral load level was the highest in symptomatic cases followed by non-persistent asymptomatic (pre-symptomatic) cases, and persistent asymptomatic cases. Among 269 cases, there were two major clusters with distinct contact patterns, the fruit dealer and mahjong players.

Table 1

The baseline characteristics for confirmed cases by symptom from the contact tracing cohorts under Alpha and Omicron VOCs
Dominant variant Variable Level	Contact persons	Confirmed Cases	Asymptomatic		Symptomatic
Dominant variant Variable Level	Contact persons	Confirmed Cases	Persistent	Non-persistent	Symptomatic
Alpha VOC*[n, (risk per 100 contacts)]
Subtotal	8018	269 (3.35)	24 (0.30)	103 (1.28)	142 (1.77)
Viral load (Ct value)
Median (Q1, Q3)	-	18.1 (15.0, 23.2)	26.1 (19.1, 31.0)	18.2 (15.0, 25.0)	17.6 (14.6, 21.0)
≥25	-	57	13 (22.8)	26 (45.6)	18 (31.6)
18–25	-	82	7 (8.5)	28 (34.2)	47 (57.3)
<18	-	130	4 (3.1)	49 (37.7)	77 (59.2)
Sex
Female	4379	154 (3.52)	15 (0.34)	60 (1.37)	79 (1.80)
Male	3639	115 (3.16)	9 (0.25)	43 (1.18)	63 (1.73)
Age
< 20	1084	35 (3.23)	7 (0.65)	14 (1.29)	14 (1.29)
20–64	5565	163 (2.93)	12 (0.22)	62 (1.11)	89 (1.60)
> 64	1247	71 (5.69)	5 (0.40)	27 (2.17)	39 (3.13)
Cluster
Fruit Dealer	2766	112 (4.05)	9 (0.33)	53 (1.92)	50 (1.81)
Others	5252	157 (2.99)	15 (0.29)	50 (0.95)	92 (1.75)
Omicron VOC*[n, (risk per 10,000 residents)]
Subtotal	1,288,561	1118 (8.68)	265 (2.06)	30 (0.23)	807 (6.26)
Viral load (Ct value)
Median (Q1, Q3)	-	17.0 (14.0, 21.0)	18.0 (14.0, 23.0)	22.0 (17.0, 28.0)	16.0 (14.0, 20.0)
≥25	-	131	47 (37.6)	11 (8.8)	67 (53.6)
18–25	-	278	67 (24.3)	9 (3.2)	200 (72.5)
<18	-	531	105 (19.8)	7 (1.3)	418 (78.9)
NK	-	178	46 (26.9)	3 (1.8)	122 (71.3)
Sex
Female	635,484	573 (9.02)	128 (2.01)	14 (0.22)	425 (6.69)
Male	653,077	545 (8.35)	137 (2.10)	16 (0.24)	382 (5.85)
Age
< 20	222,351	328 (14.75)	75 (3.37)	10 (0.45)	241 (10.84)
20–64	837,685	706 (8.43)	168 (2.01)	16 (0.19)	511 (6.10)
> 64	228,525	84 (3.68)	22 (0.96)	4 (0.18)	55 (2.41)
Vaccination
0 or 1 dose	298,395	335 (11.23)	77 (2.58)	14 (0.47)	240 (8.04)
2 + doses	990,166	783 (7.91)	188 (1.90)	16 (0.16)	567 (5.73)
^# Risk of being infection of Alpha VOC (per 100) and Omicron VOC (per 10000) by age, sex, cluster type, and vaccination status, and proportion of disease profile by Ct level among confirmed cases
* 16 cases infected with Omicron VOC had missing data on symptoms
NK: not known

3.2 Estimated Results of Multistate Infectious Process

The expected incident cases for persistent asymptomatic and non-persistent asymptomatic cases given the underlying contacts were 24.9 (95% CI: 15.6–35.1) and 250.9 (95% CI: 219.8–282.0), respectively (Table 2). Median infectiousness time from non-persistent asymptomatic to symptomatic phase was 4.1 days (95% CI: 3.3–4.8) for Alpha and 1.22 for Omicron (95% CI: 1.12–1.33). The proportion of persistent asymptomatic cases was 9.0% (95% CI: 5.8–12.7%) for Alpha and 24.3% (95% CI: 21.8–26.8%) for Omicron.

Table 2

The estimated incidence rate of being symptomatic and asymptomatic, and progression from pre-symptoms to symptomatic COVID-19 of Alpha and Omicron VOC in Changhua
	Alpha	Omicron
Incident cases
Presymptomatic pathway	250.9 (219.8–282.0)	849.1 (792.3–906.0)
Asymptomatic pathway	24.9 (15.6–35.1)	271.4 (240.4-303.7)
Proportion of persistent asymptomatic case (%)	9.02 (5.83–12.67)	24.25 (21.83–26.75)
Median time to develop symptoms (days)	4.07 (3.33–4.84)	1.22 (1.12–1.33)

3.3 Viral-load-dependent and Covariate-specific State Transition

3.3.1 Alpha VOC

Table 3 shows the estimated results of univariate analysis regarding the crude odds ratio of being infected, the crude odds ratio of the potential of being non-persistent asymptomatic versus persistent asymptomatic, and the crude odds ratio of the transition to symptomatic phase for non-persistent asymptomatic case. As far as the most important predictor of viral shedding expressed by Ct value is concerned, the odds of being non-persistent asymptomatic as opposed to persistent asymptomatic in the second step for Alpha VOC was reduced by 14% per one increasing unit of Ct (odds ratio (OR) = 0.86, 95% CI: 0.80–0.91) and 31% (OR = 0.69, 95% CI: 0.58–0.83) per ascending decile of Ct. In the light of the conventional classification of viral load, the estimated results show that high (< 18) and medium (18–25) viral shedding of source cases were approximately ten times (OR = 10.25, 95% CI: 3.17–34.53) and three times (OR = 3.32, 95% CI: 1.30–8.98) to be non-persistent asymptomatic rather than stay as asymptomatic before recovery. Regarding the progression from pre-symptomatic to symptomatic phase, the higher the Ct value, the slower the transition rate. An increasing unit of Ct and an ascending decile of Ct reduced 2% and 3% of the transition rate. However, these estimated results were not statistically significant. The odds ratios of the transition rate from pre-symptomatic to symptomatic phase were 1.80 (95% CI: 0.72–4.11) for the lowest level (Ct < 18) and 4.10 (95% CI: 1.50-11.45) for the medium level (Ct 18–25) compared with Ct > 25.

Table 3

The crude effects of viral shedding on the risk of disease progression with univariate analysis for Alpha and Omicron VOCs, Changhua
	Being infected	Being symptomatic	Progression from pre-symptomatic to symp.
Alpha VOC
Ct level (continuous)	-	0.86 (0.80–0.91)	0.98 (0.93–1.03)
Ct level (per ascending decile)	-	0.69 (0.58–0.83)	0.97 (0.87–1.10)
Ct level (vs 25+)
<18	-	10.25 (3.17–34.53)	1.80 (0.72–4.11)
18–25	-	3.32 (1.30–8.98)	4.10 (1.50-11.45)
Sex (vs Female)
Male	0.91 (0.72–1.16))	1.29 (0.49–3.13)	1.02 (0.53–1.95)
Age (vs < 20)
20–64	0.86 (0.59–1.25)	2.95 (1.06–8.44)	1.38 (0.52–3.50)
65+	1.52 (1.03–2.31)	3.18 (0.85–10.91)	2.77 (1.00-8.47)
Fruit dealer cluster vs others	1.35 (1.07–1.75)	1.22 (0.49–3.04)	0.32 (0.17–0.66)
Omicron VOC*
Ct level (continuous)	-	0.95 (0.92–0.97)	0.97 (0.84–1.12)
Ct level (per ascending decile)	-	0.90 (0.85–0.94)	0.84 (0.51–1.29)
Ct level (vs 25+)
<18	-	2.42 (1.49–3.66)	1.21 (0.60–2.48)
18–25	-	2.01 (1.20–3.21)	1.46 (0.74–3.09)
Sex (vs Female)
Male	0.92 (0.83–1.03)	0.83 (0.63–1.11)	2.04 (1.12–3.68)
Age (vs < 20)
20–64	0.57 (0.51–0.65)	0.93 (0.68–1.27)	1.11 (0.48–2.55)
65+	0.25 (0.20–0.32)	0.77 (0.43–1.33)	1.02 (0.40–2.42)
Vaccination (vs 0 or 1 dose)
2 and more doses	0.70 (0.62–0.80)	0.95 (0.70–1.28)	1.26 (0.56–3.11)
* Informative prior for parameters related to the progression from pre-symptomatic and symptomatic was borrowed from an early community-outbreak of 190 domestic cases of Omicron VOC in Taoyuan, Jan 2022

In addition to viral shedding, the elderly aged 65 years or older had 52% higher risk of being infected (RR = 1.52, 95% CI: 1.03–2.31) and 218% more likely to become symptomatic (OR = 3.18, 95% CI: 0.85–10.91) compared with young subjects aged 20 years or below but not statistically significant. The middle-aged subjects (20–64 years old) did not show a higher infection rate than young subjects. However, once infected, they were at greater risk of developing symptoms by 195% (OR = 2.95, 95% CI: 1.06–8.44). The result also shows that there was lacking of difference between males and females on the risk of infection, the odds of being non-persistent asymptomatic, and the transition rate from pre-symptomatic to symptomatic phase. Besides, the odds of being infected was higher in fruit dealer cluster compared with other clusters (OR = 1.35, 95% CI: 1.07–1.75). Its effects on the potential of being non-persistent asymptomatic and the transition rate from pre-symptomatic to symptomatic phase were not statistically significant.

Table 4 shows the multivariate results with adjustment for significant covariates in the univariate analyses. The odds of being non-persistent asymptomatic as opposed to persistent asymptomatic in the second step for Alpha VOC was reduced by 14% per one increasing unit of Ct (adjusted odds ratio (aOR) = 0.86, 95% CI: 0.81–0.92) and 29% (aOR = 0.71, 95% CI: 0.58–0.87) per one ascending decile of Ct after adjustment for other covariates. High (< 18) (aOR = 8.02, 95% CI: 3.29-20) and medium (18–25) (aOR = 3.03, 95% CI: 1.10–9.06) viral shedding of source cases were associated with higher risk of being non-persistent asymptomatic versus staying as asymptomatic until recovery. An increasing unit of Ct and an ascending decile of Ct reduced 2% of the transition rate from pre-symptomatic to symptomatic phase. Again, these estimated results were not statistically significant. The odds ratios of the transition rate from pre-symptomatic to symptomatic phase were 1.69 (95% CI: 0.74–3.97) for the lowest level (Ct < 18) and 3.25 (95% CI: 1.10–8.98) for the medium level (Ct 18–25) compared with Ct > 25.

Table 4

The adjusted effects of viral shedding on the risk of disease progression with multivariate analysis for Alpha and Omicron VOCs, Changhua
	Being infected	Being symptomatic	Progression from pre-symptomatic to symp.
Alpha VOC
Ct level (continuous)	-	0.86 (0.81–0.92)	0.98 (0.93–1.03)
Ct level (per ascending decile)	-	0.71 (0.58–0.87)	0.98 (0.87–1.11)
Ct level (vs 25+)
<18	-	8.02 (3.29–20.02)	1.69 (0.74–3.97)
18–25	-	3.03 (1.10–9.06)	3.25 (1.10–8.98)
Age (vs < 20) ^#
20–64	0.89 (0.62–1.31)	2.37 (0.80–6.56)	NS
65+	1.58 (1.06–2.36)	2.70 (0.85–10.66)	NS
Fruit dealer cluster vs others^#	1.32 (1.05–1.71)	NS	0.37 (0.17–0.73)
Omicron VOC*
Ct level (continuous)	-	0.95 (0.93–0.98)	0.98 (0.83–1.14)
Ct level (per ascending decile)	-	0.91 (0.86–0.96)	0.86 (0.56–1.30)
Ct level (vs 25+)
<18	-	2.36 (1.57–3.48)	1.41 (0.62–3.90)
18–25	-	1.78 (1.15–2.72)	1.53 (0.69–3.13)
2 doses vaccination (vs 0–1 dose) ^#	0.70 (0.61–0.80)	NS	NS
^# Estimated results in the model with categorical Ct levels
* Informative prior for parameters related to the progression from pre-symptomatic and symptomatic was borrowed from an early community-outbreak of 190 domestic cases of Omicron VOC in Taoyuan, Jan 2022

The elderly aged 65 years or older (aOR = 1.58, 95% CI: 1.06–2.36) and fruit dealer cluster (aOR = 1.32, 95% CI: 1.05–1.71) had higher risks of being infected than the counterparts. There was lacking of statistical significant effects of other transitions with respect to age, gender, and the type of cluster infection.

3.3.2 Omicron

The same trend regarding the effect of viral shedding was noted for Omicron but the effect sizes were smaller as shown at the lower panel of Table 3. The corresponding figures were attenuated to 5% (OR = 0.95, 95% CI: 0.92–0.97) reduction in the potential of being non-persistent asymptomatic pathway per one increasing unit of Ct and 10% (OR = 0.90, 95% CI: 0.85–0.94) per one ascending decile of Ct for Omicron. The estimated OR for being non-persistent asymptomatic for high (< 18) and medium (18–25) viral shedding of source cases were 2.42 (95% CI: 1.49–3.66) and 2.01 (95% CI: 1.20–3.21) compared with low viral shedding group. In analogous to Alpha VOC, the higher the Ct value, the slower the transition rate from pre-symptomatic to symptomatic phase. An increasing unit of Ct and an ascending decile of Ct reduced 3% and 16% of the transition rate. However, these estimated results were not statistically significant. The estimated results of multivariate analysis as shown in the lower panel of Table 4 yielded the similar findings as noted in the univariate analysis.

Different from the estimated results for Alpha VOC, we estimated the effects of age, gender, and vaccination on the risk of infection, the potential of being non-persistent asymptomatic versus persistent asymptomatic, and the transition rate from pre-symptomatic to symptomatic phase. Only the effect of vaccination on the reduction of infection was statistically significant (aOR = 0.70 (95% CI:0.61–0.80)).

3.4 Dynamics of Multistate Infectious Process by Viral Shedding Level and Relevant Covariates

In the light of the estimated parameters as shown in Table 2, Fig. 3(a) shows the dynamics of three states after infection defined in the competing multistate Markov process for Alpha VOC with time (day) since infection. Pre-symptomatic state increased with time until the peak and then decreased after then. Followed by the ebb of pre-symptomatic state, the chance of symptomatic state increased with time in the light of pre-symptomatic-symptomatic pathway. The chance of persistent asymptomatic state following the other pathway also increased with time according to infection rate and the proportion of persistent asymptomatic case. These dynamic curves are further presented with each personal Ct value in continuous scale by the application of the parameters estimated from Table 4. Ct-guided personalized dynamic multistate infectious process can be derived as shown in Fig. 3(b). The lower the Ct value, the more likely to lie on the top of curve. Figure 3(c) and (d) present a series of similar personalized dynamic multistate infectious process curves guided by Ct values in conjunction with age group and two types of cluster infection. It can be clearly seen that those aged 65 years or older were more likely to have higher risk of the evolution of each state than those aged 65 years or below. Those belonging to the fruit dealer (mainly through household transmission) of the cluster infection had particularly higher risk for being non-persistent asymptomatic. Note that personalized Ct-guided curves were well distinct with good discrimination within age group and the type of cluster infection.

Figures 4(a)-(c) show a series of similar dynamic curves for Omicron VOC with the same trend as Alpha VOC. However, the pattern of the Omicron VOC was different from that of Alpha VOC. The ebb of pre-symptomatic phase for Omicron VOC was more abrupt than that for Alpha VOC. This means the day for reaching the peak of pre-symptomatic phase for Omicron VOC was much shorter than that for Alpha VOC. Those with primary or booster vaccination had lower chance of being each state as shown in Fig. 4(c). It should be also noted that personalized Ct-guided curves were well distinct with good discrimination stratified by vaccination status.

4.1 Main Findings on Dose-response Effect of Viral Load Level Assessed by the competing Multistate Markov Exponential Regression Model

The current study proposed a new competing multistate Markov process for modelling dynamic multistate infectious process from the first step of initial infection after exposure to infective sources among close contacts, the second step of two pathways regarding the potential of being non-persistent persistent asymptomatic before onset of symptom or staying persistent asymptomatic until recovery, and the third subsequent transition of from pre-symptomatic to symptomatic phase only for non-persistent asymptomatic case in both periods of Alpha and Omicron VOC. The Markov exponential regression model was further used to regress each transition on respective effects of viral load in continuous, decile, and three categories of CT value with adjustment for relevant state-specific covariates including age and the type of cluster infection for Alpha VOC and vaccination status for Omicron VOC. The novelty of the proposed model and the resultant findings is three-fold. First, the proposed new model in contrast to the conventional epidemic model can differentiate non-persistent type from persistent type among asymptomatic cases and also decompose the parameter of incubation period (the duration between time of infection and time of symptom onset) into infection rate, the potential of either pathways for two asymptomatic cases, and the transition from pre-symptomatic to symptomatic phase for non-persistent asymptomatic type. Second, viral load level plays a key role in the potential of being non-persistent asymptomatic or persistent asymptomatic in a dose-response manner. The higher the viral load level (the lower Ct value), the more likely to follow non-persistent asymptomatic pathway and the less likely to stay as persistent asymptomatic cases until recovery. The magnitude of such a dose-response relationship was more remarkable for Alpha VOC than Omicron VOC. The effects of relevant covariates such age, the type of cluster infection, and vaccination on each transition, particularly the initial infection, were also assessed and deemed as the controlled variables when the main effect of viral load was assessed. Third, the findings on the dose-response effects of viral load and other covariates provide a new insight into personalized dynamic multistate curves for supporting the use of continuous Ct value as virologic surveillance for projecting individualized epidemic trajectory. Each of three features is discussed as follows.

4.2 Modelling Competing Multistate Markov Infectious Process with Data on Active Case Finding

In contrast to the conventional epidemic model like SEIR model that often provides the epidemic trajectory of infectious process on population level, the competing multistate Markov infectious process is proposed for estimating relevant parameters as indicated in Table 3 (the risk of infection, the potential of either asymptomatic pathways, and the subsequent progression to symptomatic cases) by fitting the proposed model to six types of follow-up data on active case finding under contact tracing as shown in Fig. 2. The risk of infection multiplied by the potential of either pathways (π and 1-π) given total person days yielded incident non-persistent asymptomatic cases and persistent asymptomatic cases for Alpha and Omicron VOC, respectively. The progression or the median time from pre-symptomatic to symptomatic phase following non-persistent asymptomatic is not the same as but related to the parameters of infectiousness on pre-symptomatic transmission such as generation time, serial intervals, and incubation period. Our findings on the median time from pre-symptomatic to symptomatic phase for both Alpha and Omicron VOC were also consistent with the previous results of generation time although we did not have provide information on Delta VOC. Previous studies showed that the mean intrinsic generation time was shorter for the delta variant than the Alpha variant (Wu et al. 2014). Omicron was further proved to have a shorter general time and serial interval than Delta (Abbott et al. 2022, Backer et al. 2022, Ito et al. 2022, Kremer et al. 2022).

4.3 Distinguishing non-persistent asymptomatic and persistent asymptomatic pathway

In spite of previous studies already addressing the distribution of Ct value on the profile of infectiousness on symptomatic transmission before onset of symptoms on population level (Hay et al. 2021), it is still unclear how such infectious properties are quantitatively affected by viral shedding on individual level. Namely, the quantitative role of viral load played in the incubation period is yet well elucidated. The most intractable to do so is pertaining to two indistinguishable infectious phenotypes, non-persistent asymptomatic case and persistent asymptomatic case, before onset of symptom and also the subsequent progression from pre-symptomatic phase to symptomatic phase of the former. To assess respective effects of viral load on such a multistate infectious process, the present study proposed a Markov exponential regression model to quantitatively assess the relative contribution of viral shedding to the potential of either pathways with or without developing symptom and also the effect of viral shedding on the subsequent pre-symptomatic-symptomatic progression for non-persistent asymptomatic case with simultaneous adjustment for other covariates affecting the risk of initial infection. Both Alpha and Omicron have the findings in common that high viral shedding level made significant contribution to having higher odds of the pathway leading to non-persistent asymptomatic cases relative to the pathway of staying as persistent asymptomatic cases but viral shedding may play a minor role in the subsequent pre-symptomatic-symptomatic transition. The ability to distinguish ether pathways provides a new insight into the use of Ct as virologic surveillance for individualized epidemic trajectory of infectiousness profile on pre-symptomatic transmission and the potential of being persistent asymptomatic.

4.4 Personalized Dynamic Multistate Infectious Process

To the best of our knowledge, it is the first time for the field of infectious epidemiology to extensively use viral load level measured by Ct level through RT-PCR test as an indicator for guiding active case finding during contact tracing and providing quarantine and isolation for reducing pre-symptomatic transmission during the surveillance of emerging infectious disease such as COVID-19 caused by SARS-CoV-2 infection. The distribution of Ct value has been used to predict the epidemic trajectory of the SEIR model on population level (Hay et al. 2021). The previous studies showed high viral load detected at time of symptom onset and decreased monotonically after symptom (He et al. 2020). The high viral load could become the high transmission correlate (Marc et al. 2021). Reduced viral load could considerably decrease secondary attack rate. However, the dynamic of infectious process in the light of Ct value at the individual level has been yet studied. By quantifying the effect of viral load on the potential of either pathways and transition from pre-symptomatic to symptomatic phase with the proposed Markov exponential regression model, personalized dynamic curves of passing through pre-symptomatic state, progressing to symptomatic state, and staying as persistent asymptomatic by Ct vale can be derived at the individual level. The benefit of personalized dynamic curves is three-fold. First, personalized dynamic curves provide a precision surveillance for active case finding during the early outbreak of contact tracing. Second, they also guide precision control measures such as personal hygiene or facial mask for reducing pre-symptomatic transmission at individual level. Third, they also provide precision guidance of timely administration of anti-viral therapy such as Paxlovid for averting severe cases.

4.5 Relevant Covariates

The two major types of cluster infection included household-based transmission identified as the fruit dealer (index case) cluster type and social-activity-based transmission in a community-acquired outbreak. Compared with social-activity-based transmission type, the cluster with household-based transmission was more likely to have the potential of following pre-symptomatic-symptomatic pathway as opposed to the pathway of being persistent asymptomatic. Our finding was consistent with the result of higher risk infection in household due to the close and frequent contact (Madewell et al. 2020). Regarding sex and age, the result revealed low Ct-value and the elderly were more likely to have the potential of following pre-symptomatic-symptomatic pathway rather than staying as persistent asymptomatic but there was no difference between males and females. The longer median time for developing symptoms was observed in those with medium or high Ct-values and in the elderly but all these findings were not statistically significant.

As far as vaccination is concerned, it is well known that the occurrence and progression of pre-symptomatic of COVID-19 would be affected by vaccination. However, during the epidemic period by Alpha VOC attack in Taiwan, most susceptible subjects did not have vaccination protection but relied only on non-pharmaceutical interventions. Vaccination indeed o plays a role in viral shedding. The previous study in Singapore showed difference in viral load between the vaccinated and unvaccinated after the onset of symptom for Delta variant (Chia et al. 2021). However, little is known about the viral load in progression and occurrence of symptom caused by Omicron. We revealed that the lower Ct value was also associated with the symptom development after taking vaccination into consideration in Omicron VOC. The less odds of developing symptom in the vaccinated group compared with the unvaccinated group was noted in Omicron infected cases.

The study has limitations. The generalizability based on the current evidence need to be verified as data were only derived from community-acquired outbreak of one county in Taiwan. In addition, availability of data only allowed us to model Alpha and Omicron VOC. Note that such a dose-response relationship between viral load and multistate infectious process for other VOCs needs further validated by using more external data. Although personalized dynamic multistate infectious curve in relation to Ct value of viral load was derived the Ct value measured in different states is still one-shot value for each individual rather than the repeated measurement of the same individual. How to incorporate the dynamic viral shedding of the same individual into the proposed Markov exponential regression model is an ongoing subject in the near future.

In conclusion, the current demonstrates that the viral shedding caused by SARS-CoV-2 variant plays a key role in determining the pathway of either non-persistent asymptomatic or persistent asymptomatic cases in a dose-response manner but minor role in the subsequent progression to symptomatic phase. The higher the viral load (the lower Ct value), the higher odds of following the non-persistent asymptomatic pathway and the effect size was larger for the Alpha VOC than the Omicron VOC even making allowance for vaccination status. All the findings on the dose-response effects of viral load together with relevant state-specific covariates provide a new insight into the development of personalized dynamic multistate curves for supporting the use of continuous Ct value as virologic surveillance for projecting individualized epidemic trajectory.

Funding

This study was supported by the Ministry of Science and Technology, Taiwan. (111-2118-M-002 -004 -MY2; 111-2321-B-002-017; 111-2118-M-038 -002 -MY2; 111-2118-M-038 -001 -MY2). The funders had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

Author Contributions

YPY and THC conceptualized and design the study. AMY was responsible for data analysis and the drafting of the manuscript. AMY, CYH, and TYL was responsible for statistical analysis. TYL and SLC were in charge of the data collection and management. YPY, AMY, CYH, THC and SLC interpreted results and revised the manuscript. All authors agreed the findings and provided input on the revision of the manuscript.

Abbott S, Sherratt K, Gerstung M, Funk S. Estimation of the test to test distribution as a proxy for generation interval distribution for the Omicron variant in England. medRxiv preprint doi: 10.1101/2022.01.08.22268920.
Alene M, Yismaw L, Assemie MA, et al. Magnitude of asymptomatic COVID-19 cases throughout the course of infection: A systematic review and meta-analysis. PLoS One. 2021;16(3):e0249090. doi:10.1371/journal.pone.0249090
Arons MM, Hatfield KM, Reddy SC, et al; Public Health–Seattle and King County and CDC COVID-19 Investigation Team. Presymptomatic SARS-CoV-2 Infections and Transmission in a Skilled Nursing Facility. N Engl J Med. 2020;382(22):2081-2090. doi: 10.1056/NEJMoa2008457.
Backer JA, Eggink D, Andeweg SP, Veldhuijzen IK, van Maarseveen N, Vermaas K, Vlaemynck B, Schepers R, van den Hof S, Reusken CB, Wallinga J. Shorter serial intervals in SARS-CoV-2 cases with Omicron BA.1 variant compared with Delta variant, the Netherlands, 13 to 26 December 2021. Euro Surveill 2022;27(6):2200042. doi: 10.2807/1560-7917.ES.2022.27.6.2200042.
Buitrago-Garcia D, Ipekci AM, Heron L, et al. Occurrence and transmission potential of asymptomatic and presymptomatic SARS-CoV-2 infections: Update of a living systematic review and meta-analysis. PLoS Med 2022;19:e1003987. doi: 10.1371/journal.pmed.1003987.
Chia PY, Ong SWX, Chiew CJ, Ang LW, Chavatte JM, Mak TM, Cui L, Kalimuddin S, Chia WN, Tan CW, Chai LYA, Tan SY, Zheng S, Lin RTP, Wang L, Leo YS, Lee VJ, Lye DC, Young BE. Virological and serological kinetics of SARS-CoV-2 Delta variant vaccine breakthrough infections: a multicentre cohort study. Clin Microbiol Infect. 2021 Nov 23:S1198-743X(21)00638-8.
Chen Y, Li P, Ding Y, et al. Epidemiological feature, viral shedding, and antibody seroconversion among asymptomatic SARS-CoV-2 carriers and symptomatic/presymptomatic COVID-19 patients. J Infect Public Health. 2021;14:845-851. doi: 10.1016/j.jiph.2021.05.003.
Chen SL, Jen GH, Hsu CY, Yen AM, Lai CC, Yeh YP, Chen TH. A new approach to modeling pre-symptomatic incidence and transmission time of imported COVID-19 cases evolving with SARS-CoV-2 variants. Stoch Environ Res Risk Assess. 2023;37(1):441-452. doi: 10.1007/s00477-022-02305-z.
Hay JA, Kennedy-Shaffer L, Kanjilal S, Lennon NJ, Gabriel SB, Lipsitch M, Mina MJ. Estimating epidemiologic dynamics from cross-sectional viral load distributions. Science 2021;373(6552):eabh0635. doi: 10.1126/science.abh0635.
Hart WS, Miller E, Andrews NJ, et al. Generation time of the alpha and delta SARS-CoV-2 variants: an epidemiological analysis [published online ahead of print, 2022 Feb 14]. Lancet Infect Dis. 2022;S1473-3099(22)00001-9. doi:10.1016/S1473-3099(22)00001-9.
He X, Lau EHY, Wu P, Deng X, Wang J, Hao X, et al. Temporal dynamics in viral shedding and 369 transmissibility of COVID-19. Nat Med. 2020;26(5):672-5.
Ito K, Piantham C, Nishiura H. Estimating relative generation times and reproduction numbers of Omicron BA.1 and BA.2 with respect to Delta variant in Denmark. Math Biosci Eng 2022;19(9):9005-9017. doi: 10.3934/mbe.2022418.
Kremer C, Braeye T, Proesmans K, André E, Torneri A, Hens N. Serial Intervals for SARS-CoV-2 Omicron and Delta Variants, Belgium, November 19-December 31, 2021. Emerg Infect Dis 2022;28(8):1699-1702. doi: 10.3201/eid2808.220220.
Jen GH, Yen AM, Hsu CY, Chen SL, Chen TH. A pre-symptomatic incubation model for precision strategies of screening, quarantine, and isolation based on imported COVID-19 cases in Taiwan. Sci Rep. 2022;12(1):6053. Published 2022 Apr 11. doi:10.1038/s41598-022-09863-w
Lee S, Kim T, Lee E, et al. Clinical Course and Molecular Viral Shedding Among Asymptomatic and Symptomatic Patients With SARS-CoV-2 Infection in a Community Treatment Center in the Republic of Korea. JAMA Intern Med. 2020;180(11):1447-1452. doi:10.1001/jamainternmed.2020.3862
Ma Q, Liu J, Liu Q, et al. Global Percentage of Asymptomatic SARS-CoV-2 Infections Among the Tested Population and Individuals With Confirmed COVID-19 Diagnosis: A Systematic Review and Meta-analysis. JAMA Netw Open. 2021;4(12):e2137257. Published 2021 Dec 1. doi:10.1001/jamanetworkopen.2021.37257
Madewell ZJ, Yang Y, Longini IM, Halloran ME, Dean NE. Household Transmission of SARS-CoV-2: A Systematic Review and Meta-analysis. JAMA Netw Open. 2020;3(12):e2031756.
Marc A, Kerioui M, Blanquart F, Bertrand J, Mitjà O, Corbacho-Monné M, et al. Quantifying 364 the relationship between SARS-CoV-2 viral load and infectiousness. Elife. 2021;10
Sah P, Fitzpatrick MC, Zimmer CF, et al. Asymptomatic SARS-CoV-2 infection: A systematic review and meta-analysis. Proc Natl Acad Sci U S A. 2021;118(34):e2109229118. doi:10.1073/pnas.2109229118
Wu P, Liu F, Chang Z, et al. Assessing Asymptomatic, Presymptomatic, and Symptomatic Transmission Risk of Severe Acute Respiratory Syndrome Coronavirus 2. Clin Infect Dis. 2021;73(6):e1314-e1320. doi: 10.1093/cid/ciab271.
Wu YY, Yen MF, Yu CP, Chen HH. Risk assessment of multistate progression of breast tumor with state-dependent genetic and environmental covariates. Risk Anal 2014; 34(2): 367-379. https://doi: 10.1111/risa.12116.

No competing interests reported.

202306302SupplementaryMaterials.docx

Download PDF

Journal Publication

published 30 Oct, 2023

Read the published version in Stochastic Environmental Research and Risk Assessment →

Editorial decision: Major revision
02 Jul, 2023
Editor assigned by journal
02 Jul, 2023
Submission checks completed at journal
30 Jun, 2023
First submitted to journal
30 Jun, 2023

You are reading this latest preprint version

Quantifying the Effects of Viral Load on Multistate COVID-19 Infection and Progression of Alpha and Omicron VOCs: A Bayesian Competing Markov Exponential Regression Model

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Materials and Methods

2.1 Model Specification

2.2 Data on Contact Tracing Cohort

2.3 Statistical Analysis

3. Results

3.1 Descriptive Results of the Alpha and Omicron VOC outbreak

3.2 Estimated Results of Multistate Infectious Process

3.3 Viral-load-dependent and Covariate-specific State Transition

3.3.1 Alpha VOC

3.3.2 Omicron

3.4 Dynamics of Multistate Infectious Process by Viral Shedding Level and Relevant Covariates

4. Discussion

4.2 Modelling Competing Multistate Markov Infectious Process with Data on Active Case Finding

4.3 Distinguishing non-persistent asymptomatic and persistent asymptomatic pathway

4.4 Personalized Dynamic Multistate Infectious Process

4.5 Relevant Covariates

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1