Seroprevalence of SARS-CoV-2 IgG antibodies in the staff of the Slovak Academy of Sciences in response to COVID-19 and/or vaccination: situation in August 2021.

Cross-sectional seroprevalence study of SARS-CoV-2 IgG antibodies was accomplished in the Slovak Academy of Sciences to inform authorities of research institutions about the situation at their workplaces, to assess the risk of next exposure to SARS-CoV-2, and to guide decisions on institutional measures sustaining essential research in evolving epidemic situation. Study participants provided informed consent, anamnestic information, and self-collected dry blood spot samples that were analyzed by ELISA for SARS-CoV-2 S protein-specific IgG antibodies. Relative antibody levels detected in 1928 subjects showed seroprevalence of 84.13% and led to the following main findings consistent with the current knowledge: (1) mRNA-based vaccines induce better humoral response compared to adenovirus vaccines, (2) antibody levels reflect severity of COVID-19 symptoms, (3) post-COVID vaccination results in marked elevation of IgG levels particularly in asymptomatic and mild cases, (4) antibody levels decrease with increasing time elapsed from vaccination or COVID-19. In addition, data sorting to distinct research institutes and their clustering to three principal scientific sections of the Slovak Academy of Sciences revealed marked differences in seroprevalence, and allowed to identify workplaces with relatively high seropositivity and response rate that can potentially provide a safer working environment than those, where seroprevalence was low or unknown due to low participation. Thus, findings of this study can have direct implications on management decisions during the next pandemic development, with the necessity to keep in mind the phenomenon of time-dependent immunity waning and current spread of more contagious Delta variant of SARS-CoV-2. Keywords: SARS-CoV-2 coronavirus; COVID-19; spike protein; seroprevalence; antibodies; vaccination.

Spatial scales, patterns, and positivity trends of SARS-CoV-2 pandemics in mass rapid antigen testing in Slovakia.

We study geographical epidemic scales and patterns and positivity trends of SARS-CoV-2 pandemics in mass antigen testing in Slovakia in 2020. The observed test positivity was exponentially distributed with a long scale exponential spatial trend, and its characteristic correlation length was approximately 10 km. Spatial scales also play an important role in test positivity reduction between two consecutive testing rounds. While test positivity decreased in all counties, it increased in individual municipalities with low test positivity in the earlier testing round in a way statistically different from a mean-reversion process. Also, non-residents testing influences the mass testing results as test positivity of non-residents was higher than of residents when testing was offered only in municipalities with the highest positivity in previous rounds. Our results provide direct guidance for pandemic geographical data surveillance and epidemic response management.

Emerging algebraic growth trends in SARS-CoV-2 pandemic data.

We study the reported data from the SARS-CoV-2 pandemic outbreak in January-May 2020 in 119 countries. We observe that the time series of active cases in individual countries (the difference of the total number of confirmed infections and the sum of the total number of reported deaths and recovered cases) display a strong agreement with algebraic growth and at a later epidemic stage also with a combined algebraic growth with exponential decay. Our results are also formulated in terms of compartment-type mathematical models of epidemics. Within these models the universal scaling characterizing the observed regime in an advanced epidemic stage can be interpreted as an algebraic decay of the relative reproduction number R 0 as T M /t, where T M is a constant and t is the duration of the epidemic outbreak. We show how our findings can be applied to improve predictions of the reported pandemic data and estimate some epidemic parameters. Note that although the model shows a good agreement with the reported data, we do not make any claims about the real size of the pandemic, as the relationship of the observed reported data to the total number of individuals infected in the population is still unknown.

Existence of Traveling Waves for the Generalized F-KPP Equation.

Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatiotemporal spreading into areas occupied by the less advantageous genotypes. We study how these factors influence the speed of spreading in the case of two competing genotypes under the assumption that spatial variation of the total population is small compared to the spatial variation of the frequencies of the genotypes in the population. In that case, the dynamics of the frequency of one of the genotypes is approximately described by a generalized Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation. This generalized F-KPP equation with (nonlinear) frequency-dependent diffusion and advection terms admits traveling wave solutions that characterize the invasion of the dominant genotype. Our existence results generalize the classical theory for traveling waves for the F-KPP with constant coefficients. Moreover, in the particular case of the quadratic (monostable) nonlinear growth-decay rate in the generalized F-KPP we study in detail the influence of the variance in diffusion and mean displacement rates of the two genotypes on the minimal wave propagation speed.

Spatial Gene Frequency Waves Under Genotype-Dependent Dispersal.

Dispersal is a crucial factor in natural evolution, since it determines the habitat experienced by any population and defines the spatial scale of interactions between individuals. There is compelling evidence for systematic differences in dispersal characteristics within the same population, i.e., genotype-dependent dispersal. The consequences of genotype-dependent dispersal on other evolutionary phenomena, however, are poorly understood. In this article we investigate the effect of genotype-dependent dispersal on spatial gene frequency patterns, using a generalization of the classical diffusion model of selection and dispersal. Dispersal is characterized by the variance of dispersal (diffusion coefficient) and the mean displacement (directional advection term). We demonstrate that genotype-dependent dispersal may change the qualitative behavior of Fisher waves, which change from being "pulled" to being "pushed" wave fronts as the discrepancy in dispersal between genotypes increases. The speed of any wave is partitioned into components due to selection, genotype-dependent variance of dispersal, and genotype-dependent mean displacement. We apply our findings to wave fronts maintained by selection against heterozygotes. Furthermore, we identify a benefit of increased variance of dispersal, quantify its effect on the speed of the wave, and discuss the implications for the evolution of dispersal strategies.

Extension and Justification of Quasi-Steady-State Approximation for Reversible Bimolecular Binding.

The quasi-steady-state approximation (QSSA) is commonly applied in chemical kinetics without rigorous justification. We provide details of such a justification in the ubiquitous case of reversible two-step bimolecular binding in which molecules as an intermediate step of the reaction form a transient complex. First, we justify QSSA in the regime that agrees with the results in the literature and is characterized by max{R0, L0} ≪ K(m). Here, R0 and L0 are the initial concentrations of reacting receptor and ligand, respectively, and K(m) is the Michaelis constant. We also validate QSSA under an alternative condition that can be viewed as partially irreversible binding, and it does not require a tight bound on R0 and L0 but rather requires k2 + k₋2 ≪ k₋1. Here, k₋1 is the rate constant of decomposition of the transient complex to the ligand and the receptor, and k2 and k₋2 are the forward and the reverse rate constants of transformation of the complex to the product, respectively. Furthermore, we provide arguments that QSSA can also be accurate in a regime when max{R0, L0} ≈ K(m) and k2 + k₋2 ≈ k₋1 if |R0 - L0| ≪ K(m). The derived conditions may be of practical use as they provide weaker requirements for the validity of QSSA compared to the existing results.

Mathematical model of alternative mechanism of telomere length maintenance.

Biopolymer length regulation is a complex process that involves a large number of biological, chemical, and physical subprocesses acting simultaneously across multiple spatial and temporal scales. An illustrative example important for genomic stability is the length regulation of telomeres-nucleoprotein structures at the ends of linear chromosomes consisting of tandemly repeated DNA sequences and a specialized set of proteins. Maintenance of telomeres is often facilitated by the enzyme telomerase but, particularly in telomerase-free systems, the maintenance of chromosomal termini depends on alternative lengthening of telomeres (ALT) mechanisms mediated by recombination. Various linear and circular DNA structures were identified to participate in ALT, however, dynamics of the whole process is still poorly understood. We propose a chemical kinetics model of ALT with kinetic rates systematically derived from the biophysics of DNA diffusion and looping. The reaction system is reduced to a coagulation-fragmentation system by quasi-steady-state approximation. The detailed treatment of kinetic rates yields explicit formulas for expected size distributions of telomeres that demonstrate the key role played by the J factor, a quantitative measure of bending of polymers. The results are in agreement with experimental data and point out interesting phenomena: an appearance of very long telomeric circles if the total telomere density exceeds a critical value (excess mass) and a nonlinear response of the telomere size distributions to the amount of telomeric DNA in the system. The results can be of general importance for understanding dynamics of telomeres in telomerase-independent systems as this mode of telomere maintenance is similar to the situation in tumor cells lacking telomerase activity. Furthermore, due to its universality, the model may also serve as a prototype of an interaction between linear and circular DNA structures in various settings.