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1. Toward Achieving a Vaccine-Derived Herd Immunity Threshold for COVID-19 in the U.S.

   https://doi.org/10.3389/fpubh.2021.709369  

   Gumel, Abba B. ; Iboi, Enahoro A. ; Ngonghala, Calistus N. ; Ngwa, Gideon A. ( July 2021 , Frontiers in Public Health)

   A novel coronavirus emerged in December of 2019 (COVID-19), causing a pandemic that inflicted unprecedented public health and economic burden in all nooks and corners of the world. Although the control of COVID-19 largely focused on the use of basic public health measures (primarily based on using non-pharmaceutical interventions, such as quarantine, isolation, social-distancing, face mask usage, and community lockdowns) initially, three safe and highly-effective vaccines (by AstraZeneca Inc., Moderna Inc., and Pfizer Inc.), were approved for use in humans in December 2020. We present a new mathematical model for assessing the population-level impact of these vaccines on curtailing themore »burden of COVID-19. The model stratifies the total population into two subgroups, based on whether or not they habitually wear face mask in public. The resulting multigroup model, which takes the form of a deterministic system of nonlinear differential equations, is fitted and parameterized using COVID-19 cumulative mortality data for the third wave of the COVID-19 pandemic in the United States. Conditions for the asymptotic stability of the associated disease-free equilibrium, as well as an expression for the vaccine-derived herd immunity threshold, are rigorously derived. Numerical simulations of the model show that the size of the initial proportion of individuals in the mask-wearing group, together with positive change in behavior from the non-mask wearing group (as well as those in the mask-wearing group, who do not abandon their mask-wearing habit) play a crucial role in effectively curtailing the COVID-19 pandemic in the United States. This study further shows that the prospect of achieving vaccine-derived herd immunity (required for COVID-19 elimination) in the U.S., using the Pfizer or Moderna vaccine, is quite promising. In particular, our study shows that herd immunity can be achieved in the U.S. if at least 60% of the population are fully vaccinated. Furthermore, the prospect of eliminating the pandemic in the U.S. in the year 2021 is significantly enhanced if the vaccination program is complemented with non-pharmaceutical interventions at moderate increased levels of compliance (in relation to their baseline compliance). The study further suggests that, while the waning of natural and vaccine-derived immunity against COVID-19 induces only a marginal increase in the burden and projected time-to-elimination of the pandemic, adding the impacts of therapeutic benefits of the vaccines into the model resulted in a dramatic reduction in the burden and time-to-elimination of the pandemic.« less
2. Control strategies for COVID-19 epidemic with vaccination, shield immunity and quarantine: A metric temporal logic approach

   https://doi.org/10.1371/journal.pone.0247660  

   Xu, Zhe ; Wu, Bo ; Topcu, Ufuk ( March 2021 , PLOS ONE)

   Borri, Alessandro (Ed.)

   Ever since the outbreak of the COVID-19 epidemic, various public health control strategies have been proposed and tested against the coronavirus SARS-CoV-2. We study three specific COVID-19 epidemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control; the SEIR model with shield immunity control; and the susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC) model with quarantine control. We express the control requirement in metric temporal logic (MTL) formulas (a type of formal specification languages) which can specify the expected control outcomes such as “ the deaths from the infection should never exceed one thousand per daymore »within the next three months ” or “ the population immune from the disease should eventually exceed 200 thousand within the next 100 to 120 days ”. We then develop methods for synthesizing control strategies with MTL specifications. To the best of our knowledge, this is the first paper to systematically synthesize control strategies based on the COVID-19 epidemic models with formal specifications. We provide simulation results in three different case studies: vaccination control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; shield immunity control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; and quarantine control for the COVID-19 epidemic with model parameters estimated from data in Wuhan, China. The results show that the proposed synthesis approach can generate control inputs such that the time-varying numbers of individuals in each category (e.g., infectious, immune) satisfy the MTL specifications. The results also show that early intervention is essential in mitigating the spread of COVID-19, and more control effort is needed for more stringent MTL specifications. For example, based on the model in Lombardy, Italy, achieving less than 100 deaths per day and 10000 total deaths within 100 days requires 441.7% more vaccination control effort than achieving less than 1000 deaths per day and 50000 total deaths within 100 days.« less
3. The pandemic exposes human nature: 10 evolutionary insights

   https://doi.org/10.1073/pnas.2009787117  

   Seitz, Benjamin M. ; Aktipis, Athena ; Buss, David M. ; Alcock, Joe ; Bloom, Paul ; Gelfand, Michele ; Harris, Sam ; Lieberman, Debra ; Horowitz, Barbara N. ; Pinker, Steven ; et al ( October 2020 , Proceedings of the National Academy of Sciences)

   Humans and viruses have been coevolving for millennia. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, the virus that causes COVID-19) has been particularly successful in evading our evolved defenses. The outcome has been tragic—across the globe, millions have been sickened and hundreds of thousands have died. Moreover, the quarantine has radically changed the structure of our lives, with devastating social and economic consequences that are likely to unfold for years. An evolutionary perspective can help us understand the progression and consequences of the pandemic. Here, a diverse group of scientists, with expertise from evolutionary medicine to cultural evolution, provide insightsmore »about the pandemic and its aftermath. At the most granular level, we consider how viruses might affect social behavior, and how quarantine, ironically, could make us susceptible to other maladies, due to a lack of microbial exposure. At the psychological level, we describe the ways in which the pandemic can affect mating behavior, cooperation (or the lack thereof), and gender norms, and how we can use disgust to better activate native “behavioral immunity” to combat disease spread. At the cultural level, we describe shifting cultural norms and how we might harness them to better combat disease and the negative social consequences of the pandemic. These insights can be used to craft solutions to problems produced by the pandemic and to lay the groundwork for a scientific agenda to capture and understand what has become, in effect, a worldwide social experiment.

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4. State-specific projection of COVID-19 infection in the United States and evaluation of three major control measures

   https://doi.org/10.1038/s41598-020-80044-3  

   Chen, Shi ; Li, Qin ; Gao, Song ; Kang, Yuhao ; Shi, Xun ( December 2020 , Scientific Reports)

   Most models of the COVID-19 pandemic in the United States do not consider geographic variation and spatial interaction. In this research, we developed a travel-network-based susceptible-exposed-infectious-removed (SEIR) mathematical compartmental model system that characterizes infections by state and incorporates inflows and outflows of interstate travelers. Modeling reveals that curbing interstate travel when the disease is already widespread will make little difference. Meanwhile, increased testing capacity (facilitating early identification of infected people and quick isolation) and strict social-distancing and self-quarantine rules are most effective in abating the outbreak. The modeling has also produced state-specific information. For example, for New York andmore »Michigan, isolation of persons exposed to the virus needs to be imposed within 2 days to prevent a broad outbreak, whereas for other states this period can be 3.6 days. This model could be used to determine resources needed before safely lifting state policies on social distancing.

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5. Modeling Epidemic Spread among a Commuting Population Using Transport Schemes

   https://doi.org/10.3390/math9161861  

   Calvetti, Daniela ; Hoover, Alexander P. ; Rose, Johnie ; Somersalo, Erkki ( August 2021 , Mathematics)

   null (Ed.)

   Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamicsmore »in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in the Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two.« less