The SARS-CoV-2 pandemic led to the closure of nearly all K-12 schools in the United States of America in March 2020. Although reopening K-12 schools for in-person schooling is desirable for many reasons, officials also understand that risk reduction strategies and detection of cases must be in place to allow children to safely return to school. Furthermore, the consequences of reclosing recently reopened schools are substantial and impact teachers, parents, and ultimately the educational experience in children. Using a stratified Susceptible-Exposed-Infected-Removed model, we explore the influences of reduced class density, transmission mitigation (such as the use of masks, desk shields, frequent surface cleaning, or outdoor instruction), and viral detection on cumulative prevalence. Our model predicts that a combination of all three approaches will substantially reduce SARS-CoV-2 prevalence. The model also shows that reduction of class density and the implementation of rapid viral testing, even with imperfect detection, have greater impact than moderate measures for transmission mitigation.

The SARS-CoV-2 pandemic led to closure of nearly all K-12 schools in the United States of America in March 2020. Although reopening K-12 schools for in-person schooling is desirable for many reasons, officials understand that risk reduction strategies and detection of cases are imperative in creating a safe return to school. Furthermore, consequences of reclosing recently opened schools are substantial and impact teachers, parents, and ultimately educational experiences in children. To address competing interests in meeting educational needs with public safety, we compare the impact of physical separation through school cohorts on SARS-CoV-2 infections against policies acting at the level of individual contacts within classrooms. Using an age-stratified Susceptible-Exposed-Infected-Removed model, we explore influences of reduced class density, transmission mitigation, and viral detection on cumulative prevalence. We consider several scenarios over a 6-month period including (1) multiple rotating cohorts in which students cycle through in-person instruction on a weekly basis, (2) parallel cohorts with in-person and remote learning tracks, (3) the impact of a hypothetical testing program with ideal and imperfect detection, and (4) varying levels of aggregate transmission reduction. Our mathematical model predicts that reducing the number of contacts through cohorts produces a larger effect than diminishing transmission rates per contact. Specifically, the latter approach requires dramatic reduction in transmission rates in order to achieve a comparable effect in minimizing infections over time. Further, our model indicates that surveillance programs using less sensitive tests may be adequate in monitoring infections within a school community by both keeping infections low and allowing for a longer period of instruction. Lastly, we underscore the importance of factoring infection prevalence in deciding when a local outbreak of infection is serious enough to require reverting to remote learning.

Background and Objectives: Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in generating time-evolution trajectories for these systems because they can adequately capture the influence of random fluctuations and quantify rare events. We present a simple and flexible package, BioSimulator.jl, for implementing the Gillespie algorithm, τ-leaping, and related stochastic simulation algorithms. The objective of this work is to provide scientists across domains with fast, user-friendly simulation tools. Methods: We used the high-performance programming language Julia because of its emphasis on scientific computing. Our software package implements a suite of stochastic simulation algorithms based on Markov chain theory. We provide the ability to (a) diagram Petri Nets describing interactions, (b) plot average trajectories and attached standard deviations of each participating species over time, and (c) generate frequency distributions of each species at a specified time. Results: BioSimulator.jl’s as interface allows users to build models programmatically within Julia. A model is then passed to the simulate routine to generate simulation data. The built-in tools allow one to visualize results and compute summary statistics. Our examples highlight the broad applicability of our software to systems of varying complexity from ecology, systems biology, chemistry, and genetics. Conclusion: The user-friendly nature of BioSimulator.jl encourages the use of stochastic simulation, minimizes tedious programming efforts, and reduces errors during model specification.

Our understanding of population genetics comes primarily from studies of organisms with canonical life cycles and nuclear organization, either haploid or diploid, sexual, or asexual. Although this template yields satisfactory results for the study of animals and plants, the wide variety of genomic organizations and life cycles of unicellular eukaryotes can make these organisms behave differently in response to mutation, selection, and drift than predicted by traditional population genetic models. In this study, we show how each of these unique features of ciliates affects their evolutionary parameters in mutation-selection, selection-drift, and mutation-selection-drift situations. In general, ciliates are less efficient in eliminating deleterious mutations-these mutations linger longer and at higher frequencies in ciliate populations than in sexual populations--and more efficient in selecting beneficial mutations. Approaching this problem via analytical techniques and simulation allows us to make specific predictions about the nature of ciliate evolution, and we discuss the implications of these results with respect to the high levels of polymorphism and high rate of protein evolution reported for ciliates.

Birth-death processes are continuous-time Markov counting processes. Approximate moments can be computed by truncating the transition rate matrix. Using a coupling argument, we derive bounds for the total variation distance between the process and its finite approximation.