Modelling COVID-19 Vaccine Breakthrough Infections in Highly Vaccinated Israel - the effects of waning immunity and third vaccination dose

In August 2021, a major wave of the SARS-CoV-2 Delta variant erupted in the highly vaccinated population of Israel. The Delta variant has a transmission advantage over the Alpha variant, and thus replaced it in approximately two months. The outbreak led to an unexpectedly large proportion of breakthrough infections (BTI)-- a phenomenon that received worldwide attention. The BTI proportion amongst cases in the age group of 60+ years reached levels as high as ~85% in August 2021. Most of the Israeli population, especially those 60+ age, received their second dose of the vaccination, four months before the invasion of the Delta variant. Hence, either the vaccine induced immunity dropped significantly or the Delta variant possesses immunity escaping abilities. In this work, we analyzed and model age-structured cases, vaccination coverage, and vaccine BTI data obtained from the Israeli Ministry of Health, to help understand the epidemiological factors involved in the outbreak. We propose a mathematical model which captures a multitude of factors, including age structure, the time varying vaccine efficacy, time varying transmission rate, BTIs, reduced susceptibility and infectivity of vaccinated individuals, protection duration of the vaccine induced immunity, and the vaccine distribution. We fitted our model to the cases among vaccinated and unvaccinated, for <60 and 60+ age groups, to address the aforementioned factors. We found that the transmission rate was driven by multiple factors including the invasion of Delta variant and the mitigation measures. Through a model reconstruction of the reproductive number R0(t), it was found that the peak transmission rate of the Delta variant was 1.96 times larger than the previous Alpha variant. The model estimated that the vaccine efficacy dropped significantly from >90% to ~40% over 6 months, and that the immunity protection duration has a peaked Gamma distribution (rather than exponential). We further performed model simulations quantifying the important role of the third vaccination booster dose in reducing the levels of breakthrough infections. This allowed us to explore "what if" scenarios should the booster not have been rolled out. Application of this framework upon invasion of new pathogens, or variants of concern, can help elucidate important factors in the outbreak dynamics and highlight potential routes of action to mitigate their spread.

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Re-emergence of respiratory syncytial virus following the COVID-19 pandemic in the United States: a modeling study

10.1101/2021.07.19.21260817 ◽

2021 ◽

Author(s):

Zhe Zheng ◽

Virginia E. Pitzer ◽

Eugene D. Shapiro ◽

Louis J. Bont ◽

Daniel M. Weinberger

Keyword(s):

New York ◽

Respiratory Syncytial Virus ◽

Transmission Rate ◽

Age Distribution ◽

Age Groups ◽

Pediatric Intensive Care ◽

The United States ◽

Mitigation Measures ◽

Hospital Capacity ◽

Syncytial Virus

Importance: Respiratory syncytial virus (RSV) is a leading cause of hospitalizations in young children. RSV largely disappeared in 2020 due to precautions taken because of the COVID-19 pandemic. Projecting the timing and intensity of the re-emergence of RSV and the age groups affected is crucial for planning for the administration of prophylactic antibodies and anticipating hospital capacity. Objective: To project the potential timing and intensity of re-emergent RSV epidemics in different age groups. Design, Setting, Participants: Mathematical models were used to reproduce the annual RSV epidemics before the COVID-19 pandemic in New York and California. These models were modified to project the trajectory of RSV epidemics in 2020-2025 under different scenarios with varying stringency of mitigation measures for SARS-CoV-2: 1) constant low RSV transmission rate from March 2020 to March 2021; 2) an immediate decrease in RSV transmission in March 2020 followed by a gradual increase in transmission until April 2021; 3) a decrease in non-household contacts from April to July 2020. Simulations also evaluated factors likely to impact the re-emergence of RSV epidemics, including introduction of virus from out-of-state sources and decreased transplacentally acquired immunity in infants. Main Outcomes and Measures: The primary outcome of this study was defined as the predicted number of RSV hospitalizations each month in the entire population. Secondary outcomes included the age distribution of hospitalizations among children <5 years of age, incidence of any RSV infection, and incidence of RSV lower respiratory tract infection (LRI). Results: In the 2021-2022 RSV season, we expect that the lifting of mitigation measures and build-up of susceptibility will lead to a larger-than-normal RSV outbreak. We predict an earlier-than-usual onset in the upcoming RSV season if there is substantial external introduction of RSV. Among children 1-4 years of age, the incidence of RSV infections could be twice that of a typical RSV season, with infants <6 months of age having the greatest seasonal increase in the incidence of both severe RSV LRIs and hospitalizations. Conclusions and Relevance: Pediatric departments, including pediatric intensive care units, should be alert to large RSV outbreaks. Enhanced surveillance is required for both prophylaxis administration and hospital capacity management.

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Modeling robust COVID-19 intensive care unit occupancy thresholds for imposing mitigation to prevent exceeding capacities

10.1101/2021.06.27.21259530 ◽

2021 ◽

Author(s):

Manuela Runge ◽

Reese A.K. Richardson ◽

Patrick Clay ◽

Arielle Eagan ◽

Tobias M Holden ◽

...

Keyword(s):

Intensive Care ◽

Compartmental Model ◽

Census Data ◽

Transmission Rate ◽

The United States ◽

Quantitative Approach ◽

Mitigation Measures ◽

Reproductive Number ◽

Pharmaceutical Interventions ◽

Selection Of

In managing COVID-19 with non-pharmaceutical interventions, occupancy of intensive care units (ICU) is often used as an indicator to inform when to intensify mitigation and thus reduce SARS-CoV-2 transmission, strain on ICUs, and deaths. However, ICU occupancy thresholds at which action should be taken are often selected arbitrarily. We propose a quantitative approach using mathematical modeling to identify ICU occupancy thresholds at which mitigation should be triggered to avoid exceeding the ICU capacity available for COVID-19 patients. We used a stochastic compartmental model to simulate SARS-CoV-2 transmission and disease progression, including critical cases that would require intensive care. We calibrated the model for the United States city of Chicago using daily COVID-19 ICU and hospital census data between March and August 2020. We projected ICU occupancies from September to May 2021 under two possible levels of transmission increase. The effect of combined mitigation measures was modeled as a decrease in the transmission rate that took effect when projected ICU occupancy reached a specified threshold. We found that mitigation did not immediately eliminate the risk of exceeding ICU capacity. Delaying action by 7 days increased the probability of exceeding ICU capacity by 10-60% and this increase could not be counteracted by stronger mitigation. Even under modest transmission increase, a threshold occupancy no higher than 60% was required when mitigation reduced the reproductive number Rt to just below 1. At higher transmission increase, a threshold of at most 40% was required with mitigation that reduced Rt below 0.75 within the first two weeks after mitigation. Our analysis demonstrates a quantitative approach for the selection of ICU occupancy thresholds that considers parameter uncertainty and compares relevant mitigation and transmission scenarios. An appropriate threshold will depend on the location, number of ICU beds available for COVID-19, available mitigation options, feasible mitigation strengths, and tolerated durations of intensified mitigation.

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Transmission dynamics reveal the impracticality of COVID-19 herd immunity strategies

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2008087117 ◽

2020 ◽

Vol 117 (41) ◽

pp. 25897-25903 ◽

Cited By ~ 2

Author(s):

Tobias S. Brett ◽

Pejman Rohani

Keyword(s):

Transmission Rate ◽

Herd Immunity ◽

Age Groups ◽

Extended Period ◽

Target Population ◽

Transmission Model ◽

Social Distancing ◽

The United Kingdom ◽

Age Structured ◽

Nonpharmaceutical Interventions

The rapid growth rate of COVID-19 continues to threaten to overwhelm healthcare systems in multiple countries. In response, severely affected countries have had to impose a range of public health strategies achieved via nonpharmaceutical interventions. Broadly, these strategies have fallen into two categories: 1) “mitigation,” which aims to achieve herd immunity by allowing the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus to spread through the population while mitigating disease burden, and 2) “suppression,” aiming to drastically reduce SARS-CoV-2 transmission rates and halt endogenous transmission in the target population. Using an age-structured transmission model, parameterized to simulate SARS-CoV-2 transmission in the United Kingdom, we assessed the long-term prospects of success using both of these approaches. We simulated a range of different nonpharmaceutical intervention scenarios incorporating social distancing applied to differing age groups. Our modeling confirmed that suppression of SARS-CoV-2 transmission is possible with plausible levels of social distancing over a period of months, consistent with observed trends. Notably, our modeling did not support achieving herd immunity as a practical objective, requiring an unlikely balancing of multiple poorly defined forces. Specifically, we found that 1) social distancing must initially reduce the transmission rate to within a narrow range, 2) to compensate for susceptible depletion, the extent of social distancing must be adaptive over time in a precise yet unfeasible way, and 3) social distancing must be maintained for an extended period to ensure the healthcare system is not overwhelmed.

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Modelling the effect of vertical transmission in the dynamics of HIV/AIDS in an age-structured population

The South Pacific Journal of Natural and Applied Sciences ◽

10.1071/sp03016 ◽

2003 ◽

Vol 21 (1) ◽

pp. 82 ◽

Cited By ~ 2

Author(s):

J. Y. T. Mugisha ◽

L. S. Luboobi

Keyword(s):

Vertical Transmission ◽

Equilibrium Points ◽

Age Groups ◽

Endemic Equilibrium ◽

Mass Action ◽

Basic Reproductive Number ◽

Reproductive Number ◽

First Case ◽

Age Structured ◽

Hiv Aids

We use a continuous age-structured model of McKendrick-von-Foerster type to derive a two-age groups HIV/AIDS epidemic model. In the analysis of the model, keen interest is put on the role of vertical transmission in the dynamics of the spread of the epidemic. The model is analysed in two scenarios: the case when the force of infection is a constant and the case when we have it as a mass action. In the first case, the only possible equilibrium is the endemic equilibrium. In this situation, we show that if all babies born to infected mothers are HIV-free we have the basic reproductive number R0 = 0 and as such the epidemic will die out. In the second case, we show that both the disease-free and endemic equilibrium points exist. We also derive conditions for their stability.

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Application of an Age-Structured Deterministic Endemic Model for Disease Control in Nigeria

10.1101/2020.03.28.20046300 ◽

2020 ◽

Author(s):

A. O. Victor ◽

H. K. Oduwole

Keyword(s):

Equilibrium State ◽

Disease Control ◽

Transmission Rate ◽

Rate Of Change ◽

Reproductive Number ◽

Model Framework ◽

Structured Population ◽

Age Structured ◽

Model Equations ◽

Disease Free

ABSTRACTThis paper focuses on the development and analysis of the endemic model for disease control in an aged-structured population in Nigeria. Upon the model framework development, the model equations were transformed into proportions with rate of change of the different compartments forming the model, thereby reducing the model equations from twelve to ten homogenous ordinary differential equations. The model exhibits two equilibria, the endemic state and the disease-free equilibrium state while successfully achieving a Reproductive Number R0 = 0.The deterministic endemic susceptible-exposed-infected-removed-undetectable=untransmissible-susceptible (SEIRUS) model is analyzed for the existence and stability of the disease-free equilibrium state. We established that a disease-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number 0 ≤ R0 < 1. Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect treatment rate and the net transmission rate on recovery for both juvenile and adult sub-population in an age-structured population.

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Az alapellátásban kezelt COVID–19-fertőzött gyermekek tünettani és epidemiológiai jellemzői

Orvosi Hetilap ◽

10.1556/650.2021.32360 ◽

2021 ◽

Vol 162 (44) ◽

pp. 1751-1760

Author(s):

Éva Karászi ◽

Beáta Onozó ◽

Adrienn Sütő ◽

Katalin Kutas ◽

Beáta Szalóczi ◽

...

Keyword(s):

Respiratory Symptoms ◽

Transmission Rate ◽

Age Distribution ◽

Age Groups ◽

Mitigation Measures ◽

Third Wave ◽

Virus Variant ◽

The Third ◽

Household Transmission ◽

Epidemiological Characteristics

Összefoglaló. Bevezetés: A COVID–19-pandémia kapcsán számos tanulmány vizsgálta a tünetek gyakoriságát és a járványterjedés jellemzőit gyermekkorban, kevés azonban az alapellátás adatait összefoglaló publikáció. Közleményünkben 12 házi gyermekorvosi praxis 545 SARS-CoV-2-fertőzött betegének adatait elemeztük a 2. (n = 293) és a 3. (n = 252) járványhullámban. Célkitűzés: A gyermekkori fertőzések tünettanának és epidemiológiai jellemzőinek összehasonlítása korcsoportok és járványhullámok között. Módszer: Valamennyi alapellátó praxis egységes retrospektív adatgyűjtést végzett ugyanazon paraméterek regisztrálásával. Eredmények: A 10 év alatti betegekben a láz, a nátha és a köhögés dominált (30–50%), míg a 10 év felettiekben magas arányban regisztráltunk általános tüneteket is (30–40% fejfájás, gyengeség, szaglászavar). A 2. hullámban a 11–18 évesek (68%), a 3. hullámban a 0–10 évesek (53%) voltak többségben. A 3. hullámban szignifikánsan emelkedett a légúti tünetek előfordulása, az általános tünetek gyakorisága jelentősen csökkent, és szignifikánsan nőtt a családon belüli expozíció aránya (36% vs. 58%) a 2. hullámmal összehasonlítva. A gyermekről családtagra történő továbbterjedés 24% és 16% volt a két járványhullámban, és mértékét az életkor befolyásolta. Megbeszélés: A klinikai kép az életkorral és a feltételezett vírusvariánssal mutatott összefüggést: 10 év alatt a légúti tünetek domináltak, 10 év felett szignifikánsan több általános tünetet regisztráltunk a 0–10 évesekhez képest. A 3. járványhullámban az alfa-variáns terjedésével gyakoribbá váltak a légúti tünetek, az iskolabezárások következtében megváltozott az életkori megoszlás, és megemelkedett a családi expozíció okozta fertőzések aránya. A fertőzés továbbadása háztartáson belül mindkét hullámban alacsony maradt. Következtetés: A COVID–19 klinikai megjelenését és terjedési jellemzőit jelentősen befolyásolta az érintett gyermekpopuláció életkori összetétele, a cirkuláló vírusvariáns és az aktuális korlátozó intézkedések. Orv Hetil. 2021; 162(44): 1751–1760. Summary. Introduction: During the COVID-19 pandemic, a large number of publications examined the frequency of symptoms and the mode of transmission in childhood but only a few community-based studies have been published. In our paper, 545 pediatric COVID-19 patients’ data were collected by 12 primary care pediatricians in the second (n = 293) and third (n = 252) waves of the pandemic. Objective: To compare the frequency of symptoms and household transmission in different age groups and between the two waves. Method: Patients’ data and disease characteristics were recorded retrospectively in the same manner by all participating pediatricians. Results: In patients of <10 years of age, fever, rhinorrhea and cough were registered the most frequently (30–50%), in contrast to patients of >10 years, where high frequency of general symptoms was found (30–40% headache, weakness, anosmia). In the third wave, the ratio of the age group 11–18 years declined from 68% to 47%, the frequency of respiratory symptoms increased significantly, while the ratio of general symptoms decreased. Household exposition was more frequent in the third wave (36% vs. 58%), while the transmission rate from children to family members was 24% and 16%, respectively, and it varied with age. Discussion: Clinical manifestation showed relation to age and virus variant: the older age associated with higher frequency of general symptoms and the spread of the alpha variant led to the predominance of respiratory symptoms over general complaints. Prolonged school closures affected the age distribution and increased the frequency of household exposition. Secondary household transmission remained low. Conclusion: Clinical and epidemiological characteristics of pediatric COVID-19 disease were highly influenced by age, dominant virus variant and mitigation measures. Orv Hetil. 2021; 162(44): 1751–1760.

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Optimizing influenza vaccine policies for controlling 2009-like pandemics and regular outbreaks

PeerJ ◽

10.7717/peerj.6340 ◽

2019 ◽

Vol 7 ◽

pp. e6340 ◽

Cited By ~ 2

Author(s):

Sheng-I Chen ◽

Chia-Yuan Wu ◽

Yu-Hsuan Wu ◽

Min-Wei Hsieh

Keyword(s):

Vaccine Efficacy ◽

Compartmental Model ◽

Vaccine Coverage ◽

Transmission Rate ◽

Vaccination Campaign ◽

Age Group ◽

Current Policy ◽

Vaccination Programs ◽

Vaccine Distribution ◽

Different Levels

Background This study examined the effectiveness of various vaccine policies against influenza. The transmission rate was calculated by use of the time-series influenza-like illness case during the year of 2009 and recent epidemics in Taiwan. Methods We developed a stochastic compartmental model to analyze the transmission of influenza, where the population was stratified by location and age group, and the vaccine distribution was considered using the current policy. The simulation study compared the previous vaccine policy and a new policy with expanded coverage and various lengths of the vaccination campaign. The sensitivity analysis investigated different levels of vaccine efficacy to confirm the robustness of the recommended policies. Results Doubling vaccine coverage can decrease the number of infections effectively in the regular epidemic scenario. However, a peak of infections occurs if the duration of implementing vaccination is too long. In the 2009-like pandemic scenario, both increasing vaccine doses and reducing the program’s duration can mitigate infections, although the early outbreak restricts the effectiveness of vaccination programs. Conclusions The finding indicates that only increasing vaccine coverage can reduce influenza infections. To avoid the peak of infections, it is also necessary to execute the vaccination activity immediately. Vaccine efficacy significantly impacts the vaccination policy’s performance. When vaccine efficacy is low, neither increasing vaccination doses nor reducing vaccination timeframe prevents infections. Therefore, the variation in vaccine efficacy should be taken into account when making immunization policies against influenza.

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Lockdown Measures and their Impact on Single- and Two-age-structured Epidemic Model for the COVID-19 Outbreak in Mexico

10.1101/2020.08.11.20172833 ◽

2020 ◽

Author(s):

Jesús Cuevas-Maraver ◽

Panayotis Kevrekidis ◽

Qian-Yong Chen ◽

George Kevrekidis ◽

Víctor Villalobos-Daniel ◽

...

Keyword(s):

Time Series ◽

Age Groups ◽

Optimization Procedure ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Ode Model ◽

Age Structured ◽

And Behavior ◽

The Impact

The role of lockdown measures in mitigating COVID-19 in Mexico is investigated using a comprehensive nonlinear ODE model. The model includes both asymptomatic and presymptomatic populations with the latter leading to sickness (with recovery, hospitalization and death possibilities). We consider the situation involving the imposed application of partial social distancing measures in the time series of interest and find optimal parametric fits to the time series of deaths (only), as well as to that of deaths and cumulative infections. We discuss the merits and disadvantages of each approach, we interpret the parameters of the model and assess the realistic nature of the parameters resulting from the optimization procedure. Importantly, we explore a model involving two sub-populations (younger and older than a specific age), to more accurately reflect the observed impact as concerns symptoms and behavior in different age groups. For definitiveness and to separate people that are (typically) in the active workforce, our partition of population is with respect to members younger vs. older than the age of 65. The basic reproductive number of the model is computed for both the single- and the two-population variant. Finally, we consider what would be the impact on the number of deaths and cumulative infections upon imposition of partial lockdown (involving only the older population) and full lockdown (involving the entire population).

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COVID-19 herd immunity strategies: walking an elusive and dangerous tightrope

10.1101/2020.04.29.20082065 ◽

2020 ◽

Cited By ~ 5

Author(s):

Tobias S Brett ◽

Pejman Rohani

Keyword(s):

Transmission Rate ◽

Herd Immunity ◽

Age Groups ◽

Target Population ◽

Transmission Model ◽

Social Distancing ◽

Long Duration ◽

Age Structured ◽

The Uk ◽

Public Health Strategies

AbstractThe rapid growth in cases of COVID-19 has threatened to overwhelm healthcare systems in multiple countries. In response, severely affected countries have had to consider a range of public health strategies achieved by implementing non-pharmaceutical interventions. Broadly, these strategies have fallen into two categories: i) “mitigation”, which aims to achieve herd immunity by allowing the SARS-CoV-2 virus to spread through the population while mitigating disease burden, and ii) “suppression”, aiming to drastically reduce SARS-CoV-2 transmission rates and halt endogenous transmission in the target population. Using an age-structured transmission model, parameterised to simulate SARS-CoV-2 transmission in the UK, we assessed the prospects of success using both of these approaches. We simulated a range of different non-pharmaceutical intervention scenarios incorporating social distancing applied to differing age groups. We found that it is possible to suppress SARS-CoV-2 transmission if social distancing measures are sustained at a sufficient level for a period of months. Our modelling did not support achieving herd immunity as a practical objective, requiring an unlikely balancing of multiple poorly-defined forces. Specifically, we found that: i) social distancing must initially reduce the transmission rate to within a narrow range, ii) to compensate for susceptible depletion, the extent of social distancing must be vary over time in a precise but unfeasible way, and iii) social distancing must be maintained for a long duration (over 6 months).

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Dynamics of the COVID-19 epidemic in Ireland under mitigation

BMC Infectious Diseases ◽

10.1186/s12879-021-06433-9 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Bernard Cazelles ◽

Benjamin Nguyen-Van-Yen ◽

Clara Champagne ◽

Catherine Comiskey

Keyword(s):

Transmission Rate ◽

Vaccination Campaign ◽

Virus Transmission ◽

Reporting Rate ◽

Mitigation Measures ◽

Third Wave ◽

The European Union ◽

Hospital Data ◽

Prevalence Survey ◽

Epidemic Curve

Abstract Background In Ireland and across the European Union the COVID-19 epidemic waves, driven mainly by the emergence of new variants of the SARS-CoV-2 have continued their course, despite various interventions from governments. Public health interventions continue in their attempts to control the spread as they wait for the planned significant effect of vaccination. Methods To tackle this challenge and the observed non-stationary aspect of the epidemic we used a modified SEIR stochastic model with time-varying parameters, following Brownian process. This enabled us to reconstruct the temporal evolution of the transmission rate of COVID-19 with the non-specific hypothesis that it follows a basic stochastic process constrained by the available data. This model is coupled with Bayesian inference (particle Markov Chain Monte Carlo method) for parameter estimation and utilized mainly well-documented Irish hospital data. Results In Ireland, mitigation measures provided a 78–86% reduction in transmission during the first wave between March and May 2020. For the second wave in October 2020, our reduction estimation was around 20% while it was 70% for the third wave in January 2021. This third wave was partly due to the UK variant appearing in Ireland. In June 2020 we estimated that sero-prevalence was 2.0% (95% CI: 1.2–3.5%) in complete accordance with a sero-prevalence survey. By the end of April 2021, the sero-prevalence was greater than 17% due in part to the vaccination campaign. Finally we demonstrate that the available observed confirmed cases are not reliable for analysis owing to the fact that their reporting rate has as expected greatly evolved. Conclusion We provide the first estimations of the dynamics of the COVID-19 epidemic in Ireland and its key parameters. We also quantify the effects of mitigation measures on the virus transmission during and after mitigation for the three waves. Our results demonstrate that Ireland has significantly reduced transmission by employing mitigation measures, physical distancing and lockdown. This has to date avoided the saturation of healthcare infrastructures, flattened the epidemic curve and likely reduced mortality. However, as we await for a full roll out of a vaccination programme and as new variants potentially more transmissible and/or more infectious could continue to emerge and mitigation measures change silent transmission, challenges remain.

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