Reopening schools is an urgent priority as the COVID-19 pandemic drags on. To explore the risks associated with returning to in-person learning and the value of mitigation measures, we developed stochastic, network-based models of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission in primary and secondary schools. We find that a number of mitigation measures, alone or in concert, may reduce risk to acceptable levels. Student cohorting, in which students are divided into two separate populations that attend in-person classes on alternating schedules, can reduce both the likelihood and the size of outbreaks. Proactive testing of teachers and staff can help catch introductions early, before they spread widely through the school. In secondary schools, where the students are more susceptible to infection and have different patterns of social interaction, control is more difficult. Especially in these settings, planners should also consider testing students once or twice weekly. Vaccinating teachers and staff protects these individuals and may have a protective effect on students as well. Other mitigations, including mask wearing, social distancing, and increased ventilation, remain a crucial component of any reopening plan.
Reopening schools is an urgent priority as the COVID-19 pandemic drags on. To explore the risks associated with returning to in-person learning and the value of mitigation measures, we developed stochastic, network-based models of SARS-CoV-2 transmission in primary and secondary schools. We find that a number of mitigation measures, alone or in concert, may reduce risk to acceptable levels particularly when community prevalence is low. Student cohorting, in which students are divided into two separate populations that attend in-person classes on alternating schedules, can reduce both the likelihood and the size of outbreaks. Proactive testing of teachers and staff once or twice a week can help catch introductions early, before they spread widely through the school. In secondary schools, where the students are more susceptible to infection and have different patterns of social interaction, control is more difficult. Especially in these settings, planners should also consider testing students once or twice weekly. Vaccinating teachers and staff protects these individuals and---when vaccines block SARS-CoV-2 transmission in addition to symptoms---may also have a protective effect on students as well. Other mitigations, including mask-wearing, social distancing, and increased ventilation, remain a crucial component of any reopening plan.
During the initial stages of the COVID-19 pandemic, many workplaces and universities implemented institution-wide proactive testing programs of all individuals, irrespective of symptoms. These measures have proven effective in mitigating outbreaks. As a greater fraction of the population becomes vaccinated, we need to understand what continued benefit, if any, proactive testing can contribute. Here, we address this problem with two distinct modeling approaches: a simple analytical model and a more simulation using the SEIRS+ platform. Both models indicate that proactive testing remains useful until a threshold level of vaccination is reached. This threshold depends on the transmissibility of the virus and the scope of other control measures in place. If a community is able to reach the threshold level of vaccination, testing can cease. Otherwise, continued testing will be an important component of disease control. Because it is usually difficult or impossible to precisely estimate key parameters such as the basic reproduction number for a specific workplace or other setting, our results are more useful for understanding general trends than for making precise quantitative predictions.
Natural selection enriches genotypes that are well-adapted to their environment. Over successive generations, these changes to the frequencies of types accumulate information about the selective conditions. Thus, we can think of selection as an algorithm by which populations acquire information about their environment. Kimura (1961) pointed out that every bit of information that the population gains this way comes with a minimum cost in terms of unrealized fitness (substitution load). Due to the gradual nature of selection and ongoing mismatch of types with the environment, a population that is still gaining information about the environment has lower mean fitness than a counter-factual population that already has this information. This has been an influential insight, but here we find that experimental evolution of Escherichia coli with mutations in a RNA polymerase gene (rpoB) violates Kimura’s basic theory. To overcome the restrictive assumptions of Kimura’s substitution load and develop a more robust measure for the cost of selection, we turn to ideas from computational learning theory. We reframe the ‘learning problem’ faced by an evolving population as a population versus environment (PvE) game, which can be applied to settings beyond Kimura’s theory – such as stochastic environments, frequency-dependent selection, and arbitrary environmental change. We show that the learning theoretic concept of ‘regret’ measures relative lineage fitness and rigorously captures the efficiency of selection as a learning process. This lets us establish general bounds on the cost of information acquisition by natural selection. We empirically validate these bounds in our experimental system, showing that computational learning theory can account for the observations that violate Kimura’s theory. Finally, we note that natural selection is a highly effective learning process in that selection is an asymptotically optimal algorithm for the problem faced by evolving populations, and no other algorithm can consistently outperform selection in general. Our results highlight the centrality of information to natural selection and the value of computational learning theory as a perspective on evolutionary biology.
Genes that undergo horizontal gene transfer (HGT) evolve in different genomic backgrounds as they move between hosts, in contrast to genes that evolve under strict vertical inheritance. Despite the ubiquity of HGT in microbial communities, the effects of host-switching on gene evolution have been understudied. Here, we present a novel framework to examine the consequences of host-switching on gene evolution by probing the existence and form of host-dependent mutational effects. We started exploring the effects of HGT on gene evolution by focusing on an antibiotic resistance gene (encoding a beta-lactamase) commonly found on conjugative plasmids in Enterobacteriaceae pathogens. By reconstructing the resistance landscape for a small set of mutationally connected alleles in three enteric species (Escherichia coli, Salmonella enterica, and Klebsiella pneumoniae), we uncovered that the landscape topographies were largely aligned with very low levels of host-dependent mutational effects. By simulating gene evolution with and without HGT using the species-specific empirical landscapes, we found that evolutionary outcomes were similar despite HGT. These findings suggest that the adaptive evolution of a mobile gene in one species can translate to adaptation in another species. In such a case, vehicles of cross-species HGT such as plasmids enable a distributed form of genetic evolution across a bacterial community, where species can crowdsource adaptation from other community members. The role of evolutionary crowdsourcing on the evolution of bacteria merits further investigation.
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