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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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Manaus, a city of 2.2 million population, the capital of Amazonas state of Brazil was hit badly by two waves of COVID-19 with more than 10,000 severe acute respiratory syndrome deaths by the end of February 2021. It was estimated that the first wave infected over three quarters of the population in Manaus based on routine blood donor data, and the second wave was largely due to reinfection with a new variant named P1 strain. In this work, we revisit these claims, and discuss biological constraints. In particular, we model the two waves with a two-strain model without a significant proportion of reinfections.
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In susceptible-exposed-infectious-recovered (SEIR) epidemic models, with the exponentially distributed duration of exposed/infectious statuses, the mean generation interval (GI, time lag between infections of a primary case and its secondary case) equals the mean latent period (LP) plus the mean infectious period (IP). It was widely reported that the GI for COVID-19 is as short as 5 days. However, many works in top journals used longer LP or IP with the sum (i.e., GI), e.g., > 7 days. This discrepancy will lead to overestimated basic reproductive number, and exaggerated expectation of infectious attack rate and control efficacy, since all these quantities are functions of basic reproductive number. We argue that it is important to use suitable epidemiological parameter values.
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In late March 2020, SARS-CoV-2 arrived in Manaus, Brazil, and rapidly developed into a large-scale epidemic that collapsed the local health system, and resulted in extreme death rates. Several key studies reported that [~]76% of residents of Manaus were infected (attack rate AR[~=]76%) by October 2020, suggesting protective herd immunity had been reached. Despite this, in November an unexpected second wave of COVID-19 struck again, and proved to be larger than the first creating a catastrophe for the unprepared population. It has been suggested that this could only be possible if the second wave was driven by reinfections. Here we use novel methods to model the epidemic from mortality data, evaluate the impact of interventions, in order to provide an alternative explanation as to why the second wave appeared. The method fits a "flexible" reproductive number R0(t) that changes over the epidemic, and found AR[~=]30-34% by October 2020, for the first wave, which is far less than required for herd immunity, yet in-line with recent seroprevalence estimates. The two-strain model provides an accurate fit to observed epidemic datasets, and finds AR[~=]70% by March 2021. Using genomic data, the model estimates transmissibility of the new P.1 virus lineage, as 1.9 times as transmissible as the non-P1. The model thus provides a reasonable explanation for the two-wave dynamics in Manaus, without the need to rely on reinfections which until now have only been found in small numbers in recent surveillance efforts. SignificanceThis paper explores the concept of herd immunity and approaches for assessing attack rate during the explosive outbreak of COVID-19 in the city of Manaus, Brazil. The event has been repeatedly used to exemplify the epidemiological dynamics of the disease and the phenomenon of herd immunity, as claimed to be achieved by the end of the first wave in October 2020. A novel modelling approach reconstructs these events, specifically in the presence of interventions. The analysis finds herd immunity was far from being attained, and thus a second wave was readily possible, as tragically occurred in reality. Based on genomic data, the multi-strain model gives insights on the new highly transmissible variant of concern P.1 and role of reinfection.
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As of 1 March 2020, Iran has reported 987 COVID-19 cases and including 54 associated deaths. At least six neighboring countries (Bahrain, Iraq, Kuwait, Oman, Afghanistan and Pakistan) have reported imported COVID-19 cases from Iran. We used air travel data and the cases from Iran to other Middle East countries and estimated 16533 (95% CI: 5925, 35538) COVID-19 cases in Iran by 25 February, before UAE and other Gulf Cooperation Council countries suspended inbound and outbound flights from Iran.
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The novel coronavirus disease 2019 (COVID-19) outbreak in Republic of Korea has caused 3736 cases and 18 deaths by 1 March 2020. We modeled the transmission process in Republic of Korea with a stochastic model and estimated the basic reproduction number R0 as 2.6 (95%CI: 2.3-2.9) and 3.2 (95%CI: 2.9-3.5), under the assumption that the exponential growth starting 31 January and 5 February, 2020, respectively. Estimates of dispersion term (k) were larger than 10 significantly, which implies few super-spreading events..
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BackgroundsIn December 2019, a novel coronavirus (COVID-19) pneumonia hit Wuhan, Hubei Province, China and spread to the rest of China and overseas. The emergence of this virus coincided with the Spring Festival Travel Rush in China. It is possible to estimate total number of cases of COVID-19 in Wuhan, by 23 January 2020, given the cases reported in other cities and population flow data between cities. MethodsWe built a model to estimate the total number of cases in Wuhan by 23 January 2020, based on the number of cases detected outside Wuhan city in China, with the assumption that if the same screening effort used in other cities applied in Wuhan. We employed population flow data from different sources between Wuhan and other cities/regions by 23 January 2020. The number of total cases was determined by the maximum log likelihood estimation. FindingsFrom overall cities/regions data, we predicted 1326 (95% CI: 1177, 1484), 1151 (95% CI: 1018, 1292) and 5277 (95% CI: 4732, 5859) as total cases in Wuhan by 23 January 2020, based on different source of data from Changjiang Daily newspaper, Tencent, and Baidu. From separate cities/regions data, we estimated 1059 (95% CI: 918, 1209), 5214 (95% CI: 4659, 5808) as total cases in Wuhan in Wuhan by 23 January 2020, based on different sources of population flow data from Tencent and Baidu. ConclusionSources of population follow data and methods impact the estimates of local cases in Wuhan before city lock down.
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The novel coronavirus disease 2019 (COVID-19) outbreak on the Diamond Princess ship has caused over 634 cases as of February 20, 2020. We model the transmission process on the ship with a stochastic model and estimate the basic reproduction number at 2.2 (95%CI: 2.1-2.4). We estimate a large dispersion parameter than other coronaviruses, which implies that the virus is difficult to go extinction. The epidemic doubling time is at 4.6 days (95%CI: 3.0-9.3), and thus timely actions were crucial. The lesson learnt on the ship is generally applicable in other settings.
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BackgroundsThe emerging virus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has caused a large outbreak of novel coronavirus disease (COVID-19) in Wuhan, China since December 2019. Based on the publicly available surveillance data, we identified 21 transmission chains in Hong Kong and estimated the serial interval (SI) of COVID-19. MethodsIndex cases were identified and reported after symptoms onset, and contact tracing was conducted to collect the data of the associated secondary cases. An interval censored likelihood framework is adopted to fit a Gamma distribution function to govern the SI of COVID-19. FindingsAssuming a Gamma distributed model, we estimated the mean of SI at 4.4 days (95%CI: 2.9-6.7) and SD of SI at 3.0 days (95%CI: 1.8-5.8) by using the information of all 21 transmission chains in Hong Kong. ConclusionThe SI of COVID-19 may be shorter than the preliminary estimates in previous works. Given the likelihood that SI could be shorter than the incubation period, pre-symptomatic transmission may occur, and extra efforts on timely contact tracing and quarantine are recommended in combating the COVID-19 outbreak.
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BackgroundsAn ongoing outbreak of a novel coronavirus (2019-nCoV) pneumonia hit a major city of China, Wuhan, December 2019 and subsequently reached other provinces/regions of China and countries. We present estimates of the basic reproduction number, R0, of 2019-nCoV in the early phase of the outbreak. MethodsAccounting for the impact of the variations in disease reporting rate, we modelled the epidemic curve of 2019-nCoV cases time series, in mainland China from January 10 to January 24, 2020, through the exponential growth. With the estimated intrinsic growth rate ({gamma}), we estimated R0 by using the serial intervals (SI) of two other well-known coronavirus diseases, MERS and SARS, as approximations for the true unknown SI. FindingsThe early outbreak data largely follows the exponential growth. We estimated that the mean R0 ranges from 2.24 (95%CI: 1.96-2.55) to 3.58 (95%CI: 2.89-4.39) associated with 8-fold to 2-fold increase in the reporting rate. We demonstrated that changes in reporting rate substantially affect estimates of R0. ConclusionThe mean estimate of R0 for the 2019-nCoV ranges from 2.24 to 3.58, and significantly larger than 1. Our findings indicate the potential of 2019-nCoV to cause outbreaks.
