Bayesian Inference of State-Level COVID-19 Basic Reproduction Numbers across the United States

Although many persons in the United States have acquired immunity to COVID-19, either through vaccination or infection with SARS-CoV-2, COVID-19 will pose an ongoing threat to non-immune persons so long as disease transmission continues. We can estimate when sustained disease transmission will end in a population by calculating the population-specific basic reproduction number , the expected number of secondary cases generated by an infected person in the absence of any interventions. The value of relates to a herd immunity threshold (HIT), which is given by . When the immune fraction of a population exceeds this threshold, sustained disease transmission becomes exponentially unlikely (barring mutations allowing SARS-CoV-2 to escape immunity). Here, we report state-level estimates obtained using Bayesian inference. Maximum a posteriori estimates range from 7.1 for New Jersey to 2.3 for Wyoming, indicating that disease transmission varies considerably across states and that reaching herd immunity will be more difficult in some states than others. estimates were obtained from compartmental models via the next-generation matrix approach after each model was parameterized using regional daily confirmed case reports of COVID-19 from 21 January 2020 to 21 June 2020. Our estimates characterize the infectiousness of ancestral strains, but they can be used to determine HITs for a distinct, currently dominant circulating strain, such as SARS-CoV-2 variant Delta (lineage B.1.617.2), if the relative infectiousness of the strain can be ascertained. On the basis of Delta-adjusted HITs, vaccination data, and seroprevalence survey data, we found that no state had achieved herd immunity as of 20 September 2021.

National-scale surveillance of emerging SARS-CoV-2 variants in wastewater

SARS-CoV-2 surveillance is crucial to identify variants with altered epidemiological properties. Wastewater-based epidemiology (WBE) provides an unbiased and complementary approach to sequencing individual cases. Yet, national WBE surveillance programs have not been widely implemented and data analyses remain challenging. We deep-sequenced 2,093 wastewater samples representing 95 municipal catchments, covering >57% of Austria's population, from December 2020 to September 2021. Our Variant Quantification in Sewage pipeline designed for Robustness (VaQuERo) enabled us to deduce variant abundance from complex wastewater samples and delineate the spatiotemporal dynamics of the dominant Alpha and Delta variants as well as regional clusters of other variants of concern. These results were cross validated by epidemiological records of >130,000 individual cases. Finally, we provide a framework to predict emerging variants de novo and infer variant-specific reproduction numbers from wastewater. This study demonstrates the power of national-scale WBE to support public health and promises particular value for countries without dense individual monitoring.

Estimation of age-stratified contact rates during the COVID-19 pandemic using a novel inference algorithm

Well parameterised epidemiological models including accurate representation of contacts, are fundamental to controlling epidemics. However, age-stratified contacts are typically estimated from pre-pandemic/peace-time surveys, even though interventions and public response likely alter contacts. Here we fit age-stratified models, including re-estimation of relative contact rates between age-classes, to public data describing the 2020-21 COVID-19 outbreak in England. This data includes age-stratified population size, cases, deaths, hospital admissions, and results from the Coronavirus Infection Survey (almost 9000 observations in all). Fitting stochastic compartmental models to such detailed data is extremely challenging, especially considering the large number of model parameters being estimated (over 150). An efficient new inference algorithm ABC-MBP combining existing Approximate Bayesian Computation (ABC) methodology with model-based proposals (MBP) is applied. Modified contact rates are inferred alongside time-varying reproduction numbers that quantify changes in overall transmission due to pandemic response, and age-stratified proportions of asymptomatic cases, hospitalisation rates and deaths. These inferences are robust to a range of assumptions including the values of parameters that cannot be estimated from available data. ABC-MBP is shown to enable reliable joint analysis of complex epidemiological data yielding consistent parametrisation of dynamic transmission models that can inform data-driven public health policy and interventions.

A Coupled Experimental and Statistical Approach for an Assessment of the Airborne Infection Risk in Event Locations

Operators of event locations are particularly affected by a pandemic. Resulting restrictions may cause uneconomical business. With previous models, only an incomplete quantitative risk assessments is possible, whereby no suitable restrictions can be derived. Hence, a mathematical and statistical model has been developed in order to link measurement data of substance dispersion in rooms with epidemiological data like incidences, reproduction numbers, vaccination rates and test qualities. This allows a first time overall assessment of airborne infection risks in large event locations. In these venues displacement ventilation concepts are often implemented. In this case simplified theoretical assumptions fail for the prediction of relevant airflows for infection processes. Thus, with locally resolving trace gas measurements and specific data of infection processes, individual risks can be computed more detailed. Via inclusion of many measurement positions, an assessment of entire event locations is possible. Embedding the overall model in a flexible application, daily updated epidemiological data allow latest calculations of expected new infections and individual risks of single visitors for a certain event. With this model, an instrument has been created that can help policymakers and operators to take appropriate measures and to check restrictions for their effect.

HIV/AIDS-Pneumonia Codynamics Model Analysis with Vaccination and Treatment

In this paper, we proposed and analyzed a realistic compartmental mathematical model on the spread and control of HIV/AIDS-pneumonia coepidemic incorporating pneumonia vaccination and treatment for both infections at each infection stage in a population. The model exhibits six equilibriums: HIV/AIDS only disease-free, pneumonia only disease-free, HIV/AIDS-pneumonia coepidemic disease-free, HIV/AIDS only endemic, pneumonia only endemic, and HIV/AIDS-pneumonia coepidemic endemic equilibriums. The HIV/AIDS only submodel has a globally asymptotically stable disease-free equilibrium if R 1 < 1 . Using center manifold theory, we have verified that both the pneumonia only submodel and the HIV/AIDS-pneumonia coepidemic model undergo backward bifurcations whenever R 2 < 1 and R 3 = max R 1 , R 2 < 1 , respectively. Thus, for pneumonia infection and HIV/AIDS-pneumonia coinfection, the requirement of the basic reproduction numbers to be less than one, even though necessary, may not be sufficient to completely eliminate the disease. Our sensitivity analysis results demonstrate that the pneumonia disease transmission rate β 2 and the HIV/AIDS transmission rate β 1 play an important role to change the qualitative dynamics of HIV/AIDS and pneumonia coinfection. The pneumonia infection transmission rate β 2 gives rises to the possibility of backward bifurcation for HIV/AIDS and pneumonia coinfection if R 3 = max R 1 , R 2 < 1 , and hence, the existence of multiple endemic equilibria some of which are stable and others are unstable. Using standard data from different literatures, our results show that the complete HIV/AIDS and pneumonia coinfection model reproduction number is R 3 = max R 1 , R 2 = max 1.386 , 9.69 = 9.69 at β 1 = 2 and β 2 = 0.2 which shows that the disease spreads throughout the community. Finally, our numerical simulations show that pneumonia vaccination and treatment against disease have the effect of decreasing pneumonia and coepidemic disease expansion and reducing the progression rate of HIV infection to the AIDS stage.

Modeling The Impact of Vaccination On COVID-19 And Its Delta Variant

Vaccination is an important means to fight against the spread of the SARS-CoV-2 virus and its variants. In this work, we propose a general susceptible-vaccinated-exposed-infected-hospitalized-removed (SVEIHR) model and derive its basic and effective reproduction numbers. We set Hong Kong as an example to prove the validity of our model. The model shows how the number of confirmed COVID-19 cases in Hong Kong during the second and third waves of the COVID-19 pandemic would have been reduced had vaccination been available then. We then investigate the relationships between various model parameters and the cumulative number of hospitalized COVID-19 cases in Hong Kong for the ancestral and Delta strains of the virus. Next, we compare the evolution of the SVEIHR model to the traditional “herd immunity” threshold where the proportion of vaccinated individuals is static and no further vaccination takes place after model initialization. Numerical results for Hong Kong demonstrate that the static herd immunity threshold corresponds to a cumulative hospitalization ratio of about one percent (assuming the current hospitalization rate of infected individuals is maintained). We also demonstrate that when the vaccination rate is high, the initial proportion of vaccinated individuals can be lowered for while still maintaining the same proportion of cumulative hospitalized individuals.

Potential severity, mitigation, and control of Omicron waves depending on pre-existing immunity and immune evasion

We assess the potential consequences of the upcoming SARS-CoV-2 waves caused by the Omicron variant. Our results suggest that even in those regions where the Delta variant is controlled at the moment by a combination of non-pharmaceutical interventions and population immunity, a significant Omicron wave can be expected. We stratify the population according to prior immunity status, and characterize the possible outbreaks depending on the population level of pre-existing immunity and the immune evasion capability of Omicron. We point out that two countries having similar effective reproduction numbers for the Delta variant can experience very different Omicron waves in terms of peak time, peak size and total number of infections among the high risk population.

SARS-CoV-2 variant dynamics across US states show consistent differences in effective reproduction numbers

Accurately estimating relative transmission rates of SARS-CoV-2 Variant of Concern and Variant of Interest viruses remains a scientific and public health priority. Recent studies have used the sample proportions of different variants from sequence data to describe variant frequency dynamics and relative transmission rates, but frequencies alone cannot capture the rich epidemiological behavior of SARS-CoV-2. Here, we extend methods for inferring the effective reproduction number of an epidemic using confirmed case data to jointly estimate variant-specific effective reproduction numbers and frequencies of co-circulating variants using case data and genetic sequences across states in the US from January to October 2021. Our method can be used to infer structured relationships between effective reproduction numbers across time series allowing us to estimate fixed variant-specific growth advantages. We use this model to estimate the effective reproduction number of SARS-CoV-2 Variants of Concern and Variants of Interest in the United States and estimate consistent growth advantages of particular variants across different locations.