Effects of vaccination and non-pharmaceutical interventions and their lag times on the COVID-19 pandemic: Comparison of eight countries

Many countries implemented measures to control the COVID-19 pandemic, but the effects of these measures have varied greatly. We evaluated the effects of different policies, the prevalence of dominant variants (e.g., Delta), and vaccination on the characteristics of the COVID-19 pandemic in eight countries. We quantified the lag times of different non-pharmaceutical interventions (NPIs) and vaccination using a distributed lag non-linear model (DLNM). We also tested whether these lag times were reasonable by analyzing changes in daily cases and the effective reproductive number (Rt)over time. Our results indicated that the response to vaccination in countries with continuous vaccination programs lagged by at least 40 days, and the lag time for a response to NPIs was at least 14 days. A rebound was most likely to occur during the 40 days after the first vaccine dose. We also found that the combination of school closure, workplace closure, restrictions on mass gatherings, and stay-at-home requirements were successful in containing the pandemic. Our results thus demonstrated that vaccination was effective, although some regions were adversely affected by new variants and low vaccination coverage. Importantly, relaxation of NPIs soon after implementation of a vaccination program may lead to a rebound.

Caveats on COVID-19 herd immunity threshold: the Spain case

After a year of living with the COVID-19 pandemic and its associated consequences, hope looms on the horizon thanks to vaccines. The question is what percentage of the population needs to be immune to reach herd immunity, that is to avoid future outbreaks. The answer depends on the basic reproductive number, R0, a key epidemiological parameter measuring the transmission capacity of a disease. In addition to the virus itself, R0 also depends on the characteristics of the population and their environment. Additionally, the estimate of R0 depends on the methodology used, the accuracy of data and the generation time distribution. This study aims to reflect on the difficulties surrounding R0 estimation, and provides Spain with a threshold for herd immunity, for which we considered the different combinations of all the factors that affect the R0 of the Spanish population. Estimates of R0 range from 1.39 to 3.10 for the ancestral SARS-CoV-2 variant, with the largest differences produced by the method chosen to estimate R0. With these values, the herd immunity threshold (HIT) ranges from 28.1 to 67.7%, which would have made 70% a realistic upper bound for Spain. However, the imposition of the delta variant (B.1.617.2 lineage) in late summer 2021 may have expanded the range of R0 to 4.02–8.96 and pushed the upper bound of the HIT to 90%.

Dynamics of the Rumor-Spreading Model with Control Mechanism in Complex Network

The spread of rumors has a great impact on social order, people’s psychology, and life. In recent years, the application of rumor-spreading models in complex networks has received extensive attention. Taking the management and control of rumors by relevant departments in real life into account, the SIDRQ rumor-spreading model that combines forgetting mechanism, immune mechanism, and suspicion mechanism and guides on a uniform network is established in this paper. Then, the basic reproductive number of the system and the unique existence of the solution are discussed, and the stability of the system is analyzed using the basic reproductive number, Lyapunov function, and Lienard and Chipart theorem; furthermore, the basic reproductive number may not be able to deduce the stability of the system and a counterexample is given. Finally, the influence of different parameters on the spread of rumors is studied, and the validity of the theoretical results is verified.

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.

Modeling the recent outbreak of COVID-19 in India and its control strategies

The recent emergence of COVID-19 has drawn attention to the various methods of disease control. Since no proper treatment is available till date and the vaccination is restricted to certain age groups, also vaccine efficacy is still under progress, the emphasis has been given to the method of isolation and quarantine. This control is induced by tracing the contacts of the infectious individuals, putting them to the quarantine class and based on their symptoms, classifying them either as the susceptible or sick individuals and moving the sick individuals to the isolated class. To track the current pandemic situation of COVID-19 in India, we consider an extended Susceptible-Exposed-Quarantine-Infected-Isolated-Recovered (SEQ1IQ2R) compartmental model along with calculating its control reproductive number Rc. The disease can be kept in control if the value of Rc remains below one. This “threshold” value of Rc is used to optimize the period of quarantine, and isolation and have been calculated in order to eradicate the disease. The sensitivity analysis of Rc with respect to the quarantine and isolation period has also been done. Partial rank correlation coefficient method is applied to identify the most significant parameters involved in Rc. Based on the observed data, 7-days moving average curves are plotted for prelockdown, lockdown and unlock 1 phases. Following the trend of the curves for the infection, a generalized exponential function is used to estimate the data, and corresponding 95% confidence intervals are simulated to estimate the parameters. The effect of control measures such as quarantine and isolation are discussed. Following various mathematical and statistical tools, we systematically explore the impact of lockdown strategy in order to control the recent outbreak of COVID-19 transmission in India.

Bayesian Estimation of real-time Epidemic Growth Rates using Gaussian Processes: local dynamics of SARS-CoV-2 in England

Quantitative assessments of the recent state of an epidemic and short-term projections into the near future are key public health tools that have substantial policy impacts, helping to determine if existing control measures are sufficient or need to be strengthened. Key to these quantitative assessments is the ability to rapidly and robustly measure the speed with which the epidemic is growing or decaying. Frequently, epidemiological trends are addressed in terms of the (time-varying) reproductive number R. Here, we take a more parsimonious approach and calculate the exponential growth rate, r, using a Bayesian hierarchical model to fit a Gaussian process to the epidemiological data. We show how the method can be employed when only case data from positive tests are available, and the improvement gained by including the total number of tests as a measure of heterogeneous testing effort. Although the methods are generic, we apply them to SARS-CoV-2 cases and testing in England, making use of the available high-resolution spatio-temporal data to determine long-term patterns of national growth, highlight regional growth and spatial heterogeneity.

Transmission and containment of the SARS-CoV-2 Delta variant of concern in Guangzhou, China: A population-based study

Background The first community transmission of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Delta variant of concern (VOC) in Guangzhou, China occurred between May and June 2021. Herein, we describe the epidemiological characteristics of this outbreak and evaluate the implemented containment measures against this outbreak. Methodology/Principal findings Guangzhou Center for Disease Control and Prevention provided the data on SARS-CoV-2 infections reported between 21 May and 24 June 2021. We estimated the incubation period distribution by fitting a gamma distribution to the data, while the serial interval distribution was estimated by fitting a normal distribution. The instantaneous effective reproductive number (Rt) was estimated to reflect the transmissibility of SARS-CoV-2. Clinical severity was compared for cases with different vaccination statuses using an ordinal regression model after controlling for age. Of the reported local cases, 7/153 (4.6%) were asymptomatic. The median incubation period was 6.02 (95% confidence interval [CI]: 5.42–6.71) days and the means of serial intervals decreased from 5.19 (95% CI: 4.29–6.11) to 3.78 (95% CI: 2.74–4.81) days. The incubation period increased with age (P<0.001). A hierarchical prevention and control strategy against COVID-19 was implemented in Guangzhou, with Rt decreasing from 6.83 (95% credible interval [CrI]: 3.98–10.44) for the 7-day time window ending on 27 May 2021 to below 1 for the time window ending on 8 June and thereafter. Individuals with partial or full vaccination schedules with BBIBP-CorV or CoronaVac accounted for 15.3% of the COVID-19 cases. Clinical symptoms were milder in partially or fully vaccinated cases than in unvaccinated cases (odds ratio [OR] = 0.26 [95% CI: 0.07–0.94]). Conclusions/Significance The hierarchical prevention and control strategy against COVID-19 in Guangzhou was timely and effective. Authorised inactivated vaccines are likely to contribute to reducing the probability of developing severe disease. Our findings have important implications for the containment of COVID-19.

Understanding drivers of phylogenetic clustering and terminal branch lengths distribution in epidemics of Mycobacterium tuberculosis

Detecting factors associated with transmission is important to understand disease epidemics, and to design effective public health measures. Clustering and terminal branch lengths (TBL) analyses are commonly applied to genomic data sets of Mycobacterium tuberculosis (MTB) to identify sub-populations with increased transmission. Here, I used a simulation-based approach to investigate what epidemiological processes influence the results of clustering and TBL analyses, and whether difference in transmission can be detected with these methods. I simulated MTB epidemics with different dynamics (latency, infectious period, transmission rate, basic reproductive number R0, sampling proportion, and molecular clock), and found that all these factors, except the length of the infectious period and R0, affect the results of clustering and TBL distributions. I show that standard interpretations of this type of analyses ignore two main caveats: 1) clustering results and TBL depend on many factors that have nothing to do with transmission, 2) clustering results and TBL do not tell anything about whether the epidemic is stable, growing, or shrinking. An important consequence is that the optimal SNP threshold for clustering depends on the epidemiological conditions, and that sub-populations with different epidemiological characteristics should not be analyzed with the same threshold. Finally, these results suggest that different clustering rates and TBL distributions, that are found consistently between different MTB lineages, are probably due to intrinsic bacterial factors, and do not indicate necessarily differences in transmission or evolutionary success.

Transmission dynamic and backward bifurcation of Middle Eastern respiratory syndrome coronavirus

Middle East respiratory syndrome coronavirus (MERS-CoV) remains an emerging disease threat with regular human cases on the Arabian Peninsula driven by recurring camels to human transmission events. In this paper, we present a new deterministic model for the transmission dynamics of (MERS-CoV). In order to do this, we develop a model formulation and analyze the stability of the proposed model. The stability conditions are obtained in term of R0, we find those conditions for which the model become stable. We discuss basic reproductive number R0 along with sensitivity analysis to show the impact of every epidemic parameter. We show that the proposed model exhibits the phenomena of backward bifurcation. Finally, we show the numerical simulation of our proposed model for supporting our analytical work. The aim of this work is to show via mathematical model the transmission of MERS-CoV between humans and camels, which are suspected to be the primary source of infection.