A flexible age-dependent, spatially-stratified predictive model for the spread of COVID-19, accounting for multiple viral variants and vaccines.

BACKGROUND: After COVID-19 vaccines received approval, vaccination campaigns were launched worldwide. Initially, these were characterized by a shortage of vaccine supply, and specific risk groups were prioritized. Once supply was guaranteed and vaccination coverage saturated, the focus shifted from risk groups to anti-vaxxers, the under-aged population, and regions of low coverage. At the same time, hopes to reach herd immunity by vaccination campaigns were put into perspective by the emergence and spread of more contagious and aggressive viral variants. Particularly, concerns were raised that not all vaccines protect against the new-emerging variants. The objective of this study is to introduce a predictive model to quantify the effect of vaccination campaigns on the spread of SARS-CoV-2 viral variants. METHODS AND FINDINGS: The predictive model introduced here is a comprehensive extension of the one underlying the pandemic preparedness tool CovidSim 2.0 (http://covidsim.eu/). The model is age and spatially stratified, incorporates a finite (but arbitrary) number of different viral variants, and incorporates different vaccine products. The vaccines are allowed to differ in their vaccination schedule, vaccination rates, the onset of vaccination campaigns, and their effectiveness. These factors are also age and/or location dependent. Moreover, the effectiveness and the immunizing effect of vaccines are assumed to depend on the interaction of a given vaccine and viral variant. Importantly, vaccines are not assumed to immunize perfectly. Individuals can be immunized completely, only partially, or fail to be immunized against one or many viral variants. Not all individuals in the population are vaccinable. The model is formulated as a high-dimensional system of differential equations, which is implemented efficiently in the programming language Julia. As an example, the model was parameterized to reflect the epidemic situation in Germany until November 2021 and future dynamics of the epidemic under different interventions were predicted. In particular, without tightening contact reductions, a strong epidemic wave is predicted during December 2021 and January 2022. Provided the dynamics of the epidemic in Germany, in late 2021 administration of full-dose vaccination to all eligible individuals (e.g. by mandatory vaccination) would be too late to have a strong effect on reducing the number of infections in the fourth wave in Germany. However, it would reduce mortality. An emergency brake, i.e., an incidence-based stepwise lockdown, would be efficient to reduce the number of infections and mortality. Furthermore, to specifically account for mobility between regions, the model was applied to two German provinces of particular interest: Saxony, which currently has the lowest vaccine rollout in Germany and high incidence, and Schleswig-Holstein, which has high vaccine rollout and low incidence. CONCLUSIONS: A highly sophisticated and flexible but easy-to-parameterize model for the ongoing COVID-19 pandemic is introduced. The model is capable of providing useful predictions for the COVID-19 pandemic, and hence provides a relevant tool for epidemic decision-making. The model can be adjusted to any country, and the predictions can be used to derive the demand for hospital or ICU capacities.

The many definitions of multiplicity of infection.

The presence of multiple genetically different pathogenic variants within the same individual host is common in infectious diseases. Although this is neglected in some diseases, it is well recognized in others like malaria, where it is typically referred to as multiplicity of infection (MOI) or complexity of infection (COI). In malaria, with the advent of molecular surveillance, data is increasingly being available with enough resolution to capture MOI and integrate it into molecular surveillance strategies. The distribution of MOI on the population level scales with transmission intensities, while MOI on the individual level is a confounding factor when monitoring haplotypes of particular interests, e.g., those associated with drug-resistance. Particularly, in high-transmission areas, MOI leads to a discrepancy between the likelihood of a haplotype being observed in an infection (prevalence) and its abundance in the pathogen population (frequency). Despite its importance, MOI is not universally defined. Competing definitions vary from verbal ones to those based on concise statistical frameworks. Heuristic approaches to MOI are popular, although they do not mine the full potential of available data and are typically biased, potentially leading to misinferences. We introduce a formal statistical framework and suggest a concise definition of MOI and its distribution on the host-population level. We show how it relates to alternative definitions such as the number of distinct haplotypes within an infection or the maximum number of alleles detectable across a set of genetic markers. It is shown how alternatives can be derived from the general framework. Different statistical methods to estimate the distribution of MOI and pathogenic variants at the population level are discussed. The estimates can be used as plug-ins to reconstruct the most probable MOI of an infection and set of infecting haplotypes in individual infections. Furthermore, the relation between prevalence of pathogenic variants and their frequency (relative abundance) in the pathogen population in the context of MOI is clarified, with particular regard to seasonality in transmission intensities. The framework introduced here helps to guide the correct interpretation of results emerging from different definitions of MOI. Especially, it excels comparisons between studies based on different analytical methods.

A maximum-likelihood method to estimate haplotype frequencies and prevalence alongside multiplicity of infection from SNP data.

The introduction of genomic methods facilitated standardized molecular disease surveillance. For instance, SNP barcodes in Plasmodium vivax and Plasmodium falciparum malaria allows the characterization of haplotypes, their frequencies and prevalence to reveal temporal and spatial transmission patterns. A confounding factor is the presence of multiple genetically distinct pathogen variants within the same infection, known as multiplicity of infection (MOI). Disregarding ambiguous information, as usually done in ad-hoc approaches, leads to less confident and biased estimates. We introduce a statistical framework to obtain maximum-likelihood estimates (MLE) of haplotype frequencies and prevalence alongside MOI from malaria SNP data, i.e., multiple biallelic marker loci. The number of model parameters increases geometrically with the number of genetic markers considered and no closed-form solution exists for the MLE. Therefore, the MLE needs to be derived numerically. We use the Expectation-Maximization (EM) algorithm to derive the maximum-likelihood estimates, an efficient and easy-to-implement algorithm that yields a numerically stable solution. We also derive expressions for haplotype prevalence based on either all or just the unambiguous genetic information and compare both approaches. The latter corresponds to a biased ad-hoc estimate of prevalence. We assess the performance of our estimator by systematic numerical simulations assuming realistic sample sizes and various scenarios of transmission intensity. For reasonable sample sizes, and number of loci, the method has little bias. As an example, we apply the method to a dataset from Cameroon on sulfadoxine-pyrimethamine resistance in P. falciparum malaria. The method is not confined to malaria and can be applied to any infectious disease with similar transmission behavior. An easy-to-use implementation of the method as an R-script is provided.

Is increased mortality by multiple exposures to COVID-19 an overseen factor when aiming for herd immunity?

BACKGROUND: Governments across the globe responded with different strategies to the COVID-19 pandemic. While some countries adopted measures, which have been perceived controversial, others pursued a strategy aiming for herd immunity. The latter is even more controversial and has been called unethical by the WHO Director-General. Inevitably, without proper control measures, viral diversity increases and multiple infectious exposures become common, when the pandemic reaches its maximum. This harbors not only a potential threat overseen by simplified theoretical arguments in support of herd immunity, but also deserves attention when assessing response measures to increasing numbers of infection. METHODS AND FINDINGS: We extend the simulation model underlying the pandemic preparedness web interface CovidSim 1.1 (http://covidsim.eu/) to study the hypothetical effect of increased morbidity and mortality due to 'multi-infections', either acquired at by successive infective contacts during the course of one infection or by a single infective contact with a multi-infected individual. The simulations are adjusted to reflect roughly the situation in the USA. We assume a phase of general contact reduction ("lockdown") at the beginning of the epidemic and additional case-isolation measures. We study the hypothetical effects of varying enhancements in morbidity and mortality, different likelihoods of multi-infected individuals to spread multi-infections and different susceptibility to multi-infections in different disease phases. It is demonstrated that multi-infections lead to a slight reduction in the number of infections, as these are more likely to get isolated due to their higher morbidity. However, the latter substantially increases the number of deaths. Furthermore, simulations indicate that a potential second lockdown can substantially decrease the epidemic peak, the number of multi-infections and deaths. CONCLUSIONS: Enhanced morbidity and mortality due to multiple disease exposure is a potential threat in the COVID-19 pandemic that deserves more attention. Particularly it underlines another facet questioning disease management strategies aiming for herd immunity.

The impact of COVID-19 vaccination campaigns accounting for antibody-dependent enhancement.

BACKGROUND: COVID-19 vaccines are approved, vaccination campaigns are launched, and worldwide return to normality seems within close reach. Nevertheless, concerns about the safety of COVID-19 vaccines arose, due to their fast emergency approval. In fact, the problem of antibody-dependent enhancement was raised in the context of COVID-19 vaccines. METHODS AND FINDINGS: We introduce a complex extension of the model underlying the pandemic preparedness tool CovidSim 1.1 (http://covidsim.eu/) to optimize vaccination strategies with regard to the onset of campaigns, vaccination coverage, vaccination schedules, vaccination rates, and efficiency of vaccines. Vaccines are not assumed to immunize perfectly. Some individuals fail to immunize, some reach only partial immunity, and-importantly-some develop antibody-dependent enhancement, which increases the likelihood of developing symptomatic and severe episodes (associated with higher case fatality) upon infection. Only a fraction of the population will be vaccinated, reflecting vaccination hesitancy or contraindications. The model is intended to facilitate decision making by exploring ranges of parameters rather than to be fitted by empirical data. We parameterized the model to reflect the situation in Germany and predict increasing incidence (and prevalence) in early 2021 followed by a decline by summer. Assuming contact reductions (curfews, social distancing, etc.) to be lifted in summer, disease incidence will peak again. Fast vaccine deployment contributes to reduce disease incidence in the first quarter of 2021, and delay the epidemic outbreak after the summer season. Higher vaccination coverage results in a delayed and reduced epidemic peak. A coverage of 75%-80% is necessary to prevent an epidemic peak without further drastic contact reductions. CONCLUSIONS: With the vaccine becoming available, compliance with contact reductions is likely to fade. To prevent further economic damage from COVID-19, high levels of immunization need to be reached before next year's flu season, and vaccination strategies and disease management need to be flexibly adjusted. The predictive model can serve as a refined decision support tool for COVID-19 management.

Preventing COVID-19 spread in closed facilities by regular testing of employees-An efficient intervention in long-term care facilities and prisons?

BACKGROUND: Different levels of control measures were introduced to contain the global COVID-19 pandemic, many of which have been controversial, particularly the comprehensive use of diagnostic tests. Regular testing of high-risk individuals (pre-existing conditions, older than 60 years of age) has been suggested by public health authorities. The WHO suggested the use of routine screening of residents, employees, and visitors of long-term care facilities (LTCF) to protect the resident risk group. Similar suggestions have been made by the WHO for other closed facilities including incarceration facilities (e.g., prisons or jails), wherein parts of the U.S., accelerated release of approved inmates is taken as a measure to mitigate COVID-19. METHODS AND FINDINGS: Here, the simulation model underlying the pandemic preparedness tool CovidSim 1.1 (http://covidsim.eu/) is extended to investigate the effect of regularly testing of employees to protect immobile resident risk groups in closed facilities. The reduction in the number of infections and deaths within the risk group is investigated. Our simulations are adjusted to reflect the situation of LTCFs in Germany, and incarceration facilities in the U.S. COVID-19 spreads in closed facilities due to contact with infected employees even under strict confinement of visitors in a pandemic scenario without targeted protective measures. Testing is only effective in conjunction with targeted contact reduction between the closed facility and the outside world-and will be most inefficient under strategies aiming for herd immunity. The frequency of testing, the quality of tests, and the waiting time for obtaining test results have noticeable effects. The exact reduction in the number of cases depends on disease prevalence in the population and the levels of contact reductions. Testing every 5 days with a good quality test and a processing time of 24 hours can lead up to a 40% reduction in the number of infections. However, the effects of testing vary substantially among types of closed facilities and can even be counterproductive in U.S. IFs. CONCLUSIONS: The introduction of COVID-19 in closed facilities is unavoidable without a thorough screening of persons that can introduce the disease into the facility. Regular testing of employees in closed facilities can contribute to reducing the number of infections there, but is only meaningful as an accompanying measure, whose economic benefit needs to be assessed carefully.