key: cord-0714399-adjez0sy
authors: Aguiar, Maíra; Van-Dierdonck, Joseba Bidaurrazaga; Mar, Javier; Stollenwerk, Nico
title: The role of mild and asymptomatic infections on COVID-19 vaccines performance: a modeling study
date: 2021-11-16
journal: J Adv Res
DOI: 10.1016/j.jare.2021.10.012
sha: a208f98c00f385fcafae35ded782e317105354dc
doc_id: 714399
cord_uid: adjez0sy

INTRODUCTION: Different COVID-19 vaccine efficacies are reported, with remarkable effectiveness against severe disease. The so called sterilizing immunity, occurring when vaccinated individuals cannot transmit the virus, is still being evaluated. It is also unclear to what extent people with no symptoms or mild infection transmit the disease, and estimating their contribution to outbreaks is challenging. OBJECTIVE: With an uneven roll out of vaccination, the purpose of this study is to investigate the role of mild and asymptomatic infections on COVID-19 vaccine performance as vaccine efficacy and vaccine coverage vary. METHODS: We use an epidemiological SHAR (Susceptible-Hospitalized-Asymptomatic-Recovered) model framework to evaluate the effects of vaccination in different epidemiological scenarios of coverage and efficacy. Two vaccination models, the vaccine [Formula: see text] protecting against severe disease, and the vaccine [Formula: see text] , protecting against infection as well as severe disease, are compared to evaluate the reduction of overall infections and hospitalizations. RESULTS: Vaccine performance is driven by the ability of asymptomatic or mild disease cases transmitting the virus. Vaccines protecting against severe disease but failing to block transmission might not be able to reduce significantly the severe disease burden during the initial stage of a vaccination roll out programme, with an eventual increase on the number of overall infections in a population. CONCLUSION: The different COVID-19 vaccines currently in use have features placing them closer to one or the other of these two extreme cases, [Formula: see text] and [Formula: see text] , and insights on the importance of asymptomatic infection in a vaccinated population are of a major importance for the future planning of vaccination programmes. Our results give insights on how to best combine the use of the available COVID-19 vaccines, optimizing the reduction of hospitalizations.

erence to V 2 is desirable, even with a smaller efficacy, a conscientious strategy 85 to administrate simultaneously each vaccine type is needed to optimize hos-86 pitalization reductions, knowing that efficacies are also varying according to 87 vaccination doses schedules. 88 This paper is structured as follows. The second section contains the descrip- analysis in a Bayesian framework). 128 We distinguish the naive susceptible S individuals prone to natural infec-129 tion and vaccinated susceptible individuals S v with a reduced risk of severe 130 disease, but still able to transmit the virus when becoming mild or asymp-131 tomatic infected. Here, the hospitalization ratio η in this natural infectivity ηβ 132 changes with vaccine uptake r · ηβ, whereas the mild/asymptomatic infection 133 rate (1 − η)β is assumed to not be efficiently reduced (in the extreme case, no 134 reduction at all). 135 The dynamical system of the SHARV 1 model is given by

with the term in the dynamics of the asymptomatic infected easily simplified (1−η) 

The dynamical system of the SHARV 2 model is given by

Vaccine performance analysis: a conceptual study 155 For analytical insights into the behaviour of the models with vaccination com-156 pared to the non-vaccination scenario, we consider the dynamics of the disease 157 compartments, here in the V 1 case, 

and

for vaccine V 1 , but with specific variables y and z all the three models can be 175 analyzed with the same formulation.

The matrix B is explicitly given below (omitting the factor S 0 N since initially 177 S 0 ≈ N , and note that the infection rate β carries S 0 N in case S 0 is significantly 178 lower than N )

along with matrix G as that can be used for a first inspection of vaccine effects.

To apply the analysis closer to the present epidemiological scenario of COVID- 191 19, we analyze the models including import as (H + φA + N ) in the force 192 of infection and keep the community spreading below exponential growth [16] .

Hence we have the dynamical system given by

with matrix J = B − G decomposed into eigenvalue matrix Λ and eigenvector

with I as unit matrix, and stationary value x * = −T Λ −1 T −1 = J −1 ρ with the 198 results given by 

and

with κ := ηy + φ(1 − η)z.

The analysis for the vaccine V 2 is done similarly to the analysis for vaccine 205 V 1 , obtaining slightly altered vaccination variables y 2 = 1 − c · k (as for the 206 previous case V 1 ) and z 2 = y 2 = 1 − c · k.

The effective infection rate obtained from the growth rates of all three mod-208 els can be written using the same formulation. For the SHARV 1 model we

while for the SHARV 2 model

since z 2 = y 2 . Finally for the basic SHAR model without vaccination, where

as result.

The reduction of the effective infection rate due to the vaccine V 2 type is 215 given by

while for V 1 we obtain a slightly more complex situation given by

defining an expression f (φ, η) := φ/(η + φ(1 − η)). With a similar result as 218 for V 2 , the first term is identical but then reduced by an additional term pro-219 portional to c · κ, which is dependent on the SHAR specific parameters η, the 

For the basic SHAR model with import and eventual waning immunity 

while for vaccine V 2 we have the altered transitions

to complete the formal description of the stochastic processes. The stochastic The stationary value for hospitalizations and overall infections are given 291 by Equation (14) and Equation (15) vary the infectivity of asymptomatic/mild cases to be smaller (φ < 1) or larger 305 (φ > 1) than the infectivity of severe/hospitalized cases and we discuss the role 306 of asymptomatic infection on vaccine performance.

By assuming a small infectivity of asymptomatic cases relative to severe 308 cases, φ = 0.2, we observe a very small difference on the performance of V 1 and 309 V 2 (see Fig. 2 In detail, for the φ = 0.8 scenario shown in Fig. 2 b) we have, for vaccine 316 coverage over 60%, some overlapping region of V 1 and V 2 , where a higher effica-317 cious V 1 , which protects against severe disease without blocking transmission 318 completely, can reduce hospitalizations more than a lower efficacious V 2 , which 319 protects against disease and infection. For the φ = 1.1 scenario shown in Fig. 2   320 c), where mild/asymptomatic cases are transmitting slightly more than severe 321 cases, this effect nearly disappears.

Finally, for the φ = 1.245 scenario shown in Fig. 2 d) , where mild/asympto-323 matic cases are assumed to transmit approximately 25% more than severe/hospi- population. 328 We continue with our analysis, now to also evaluate the reduction in the 329 overall infections. Similarly to the analysis above, we show for some intermedi-330 ate cases of φ, below unit and above unit, how the overall number of infected 331 I * = H * + A * change with vaccination coverage. In Fig. 3 a) and Fig. 3 b) 332 we plot the ratio of overall infections with and without vaccination, I * (c, k)/I * 0 .

In the same way as in Fig. 2 , results obtained for V 1 are shown in yellow and In this section, we present the first numerical experiment for this conceptual performance against new variants of concern (VOCs) and variants of interest 374 (VOIs) are discussed in the Section below.

While Fig. 4a ) shows a small decrease of reported severe cases (in red) 376 as vaccination coverage increases, a significant increase of confirmed cases are 377 also observed (yellow), as described in Table 1, for example, for the scenario   378 where asymptomatic cases contribution to the force of infection is considered 379 to be larger than symptomatic cases, once they are identified and isolated. Our variants also wained significantly [29] .

This is an ongoing work, with information on COVID-19 vaccine efficacies 411 to be updated frequently and included into the refined modeling framework 412 as needed [14] . Considerations of different variants of concern and variants of nevertheless, still an ample space for further evaluations, including additional 467 stochastic effects as described e.g. in [16, 17, 28] . In this study we consider the • COVID-19 vaccines with different efficacies are reported to be effective against severe disease.

• Vaccine sterilizing immunity is still being evaluated.

• We investigate COVID-19 vaccine performance as vaccine efficacy and vaccine coverage vary.

• Vaccine performance is driven by the ability of asymptomatic infections transmitting the virus.

• Planned strategy to use different COVID-19 vaccines will optimize hospitalization reductions. 

World Health Organization. Coronavirus Disease (COVID-19) Situ-509 ation Reports. Weekly epidemiological update on

Coronavirus Disease (COVID-19) Situa-513 tion Reports. Weekly epidemiological update on COVID-19 -19 Octo-514 ber 2021

Condition-specific mortality risk

Model-558 ing COVID-19 vaccine efficacy and coverage towards herd-immunity in 559 the Basque Country, Spain

Reproduc-562 tion ratio and growth rates: Measures for an unfolding pandemic

The inter-565 play between subcritical fluctuations and import: understanding COVID-566 19 epidemiology dynamics

Critical fluctuations in epi-569 demic models explain COVID-19 post-lockdown dynamics. Scientific Re-570 ports

Modelling COVID 19 in the Basque Country from intro-575 duction to control measure response

Dengvaxia Efficacy Dependency 578 on Serostatus: A Closer Look at More Recent Data

Dengvaxia: age as sur-581 rogate for serostatus. The Lancet Infectious Diseases

The Impact of Serotype Cross-584

Protection on Vaccine Trials: DENVax as a Case Study

Stationary solution of master equations in 587 the large-system-size limit

Intervention-Based Stochastic Disease Eradication

Hopf and torus 593 bifurcations, torus destruction and chaos in population biology

A general method for numerically simulating 596 the stochastic time evolution of coupled chemical reactions

Monte Carlo simulation of random walks 600 with residence time dependent transition probability rates

Population Biology and Criticality: 604 From critical birth-death processes to self-organized criticality in mutation 605 pathogen systems

BNT162b2 COVID-19 vaccine up to 6 months in a large integrated health 608 system in the USA: a retrospective cohort study. The Lancet

Product-specific COVID-19 vaccine effectiveness against secondary infec-612 tion in close contacts