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We reviewed the timeline of key policies for control of the coronavirus disease epidemic and determined their impact on the epidemic and hospital burden in South Korea. Using a discrete stochastic transmission model, we estimated that multilevel policies, including extensive testing, contact tracing, and quarantine, reduced contact rates by 90% and rapidly decreased the epidemic in Daegu and nationwide during February‒March 2020. Absence of these prompt responses could have resulted in a >10-fold increase in infections, hospitalizations, and deaths by May 15, 2020, relative to the status quo. The model suggests that reallocation of persons who have mild or asymptomatic cases to community treatment centers helped avoid overwhelming hospital capacity and enabled healthcare workers to provide care for more severely and critically ill patients in hospital beds and negative-pressure intensive care units. As small outbreaks continue to occur, contact tracing and maintenance of hospital capacity are needed.

IntroductionNew York City (NYC) was a global epicenter of COVID-19. Vaccines against COVID-19 became available in December 2020 with limited supply, resulting in the need for policies regarding prioritization. The next month, SARS-CoV-2 variants were detected that were more transmissible but still vaccine-susceptible, raising scrutiny of these policies. In particular, prioritization of higher-risk people could prevent more deaths per dose of vaccine administered but could also delay herd immunity if the prioritization introduced bottlenecks that lowered vaccination speed (the number of doses that could be delivered per day). We used mathematical modeling to examine the trade-off between prioritization and the vaccination speed.MethodsA stochastic, discrete-time susceptible-exposed-infected-recovered (SEIR) model with age- and comorbidity-adjusted COVID-19 outcomes (infections, hospitalizations, and deaths by July 1, 2021) was used to examine the trade-off between vaccination speed and whether or not vaccination was prioritized to individuals age 65+ and “essential workers,” defined as including first responders and healthcare, transit, education, and public safety workers. The model was calibrated to COVID-19 hospital admissions, hospital census, ICU census, and deaths in NYC. Vaccination speed was assumed to be 10,000 doses per day starting December 15th, 2020 targeting healthcare workers and nursing home populations, and to subsequently expand at alternative starting times and speeds. We compared COVID-outcomes across alternative expansion starting times (January 15th, January 21st, or February 1st) and speeds (20,000, 30,000, 50,000, 100,000, 150,000, or 200,000 doses per day for the first dose), as well as alternative prioritization options (“yes” versus “no” prioritization of essential workers and people age 65+). Model projections were produced with and without considering the emergence of a SARS-COV-2 variant with 56% greater transmissibility over January and February, 2021.ResultsIn the absence of a COVID-19 vaccine, the emergence of the more transmissible variant would triple the peak in infections, hospitalizations, and deaths and more than double cumulative infections, hospitalizations, and deaths. To offset the harm from the more transmissible variant would require reaching a vaccination speed of at least 100,000 doses per day by January 15th or 150,000 per day by January 21st. Prioritizing people ages 65+ and essential workers increased the number of lives saved per vaccine dose delivered: with the emergence of a more transmissible variant, 8,000 deaths could be averted by delivering 115,000 doses per day without prioritization or 71,000 doses per day with prioritization. If prioritization were to cause a bottleneck in vaccination speed, more lives would be saved with prioritization only if the bottleneck reduced vaccination speed by less than one-third of the maximum vaccine delivery capacity. These trade-offs between vaccination speed and prioritization were robust over a wide range of delivery capacity.ConclusionsThe emergence of a more transmissible variant of SARS-CoV-2 has the potential to triple the 2021 epidemic peak and more than double the 2021 COVID-19 burden in NYC. Vaccination could only offset the harm of the more transmissible variant if high speed were achieved in mid-to late January. Prioritization of COVID-19 vaccines to higher-risk populations saves more lives only if it does not create an excessive vaccine delivery bottleneck.

IntroductionNew York City (NYC) has the largest public school system in the United States (US). During the SARS-CoV-2 pandemic, NYC was the first major US city to open schools for in-person learning in the 2020-2021 academic year. Several policies were implemented to reduce the risk of in-school transmission, including infection control measures (facemasks, physical distancing, enhanced indoor ventilation, cohorting of small groups, and hand hygiene), option of all-remote instruction, alternative options for how class schedules would rotate in-person and remote instruction, daily symptom screening, and testing 10-20% of students and staff weekly or monthly depending on local case rates. We sought to determine which of these policies had the greatest impact on reducing the risk of in-school transmission.MethodsWe evaluated the impact of each policy by referring to global benchmarks for the secondary attack rate (SAR) of SARS-CoV-2 in school settings and by simulating the potential for transmission in NYC’s rotating cohort schedules, in which teachers could act as “bridges” across rotating cohorts. We estimated the impact of (1) infection control measures, (2) providing an option of all-remote instruction, (3) choice of class scheduling for in-person learners, (4) daily symptom screening, (5) testing to curtail transmission, and (6) testing to identify school outbreaks. Each policy was assessed independently of other policies, with the exception of symptom screening and random testing, which were assessed both independently and jointly.ResultsAmong the policies analyzed, the greatest transmission reduction was associated with the infection control measures, followed by small class cohorts with an option for all-remote instruction, symptom screening, and finally randomly testing 10-20% of school attendees. Assuming adult staff are the primary source of within-school SARS-CoV-2 transmission, weekly testing of staff could be at least as effective as symptom screening, and potentially more so if testing days occur in the beginning of the workweek with results available by the following day. A combination of daily symptom screening and testing on the first workday of each week could reduce transmission by 70%.ConclusionsAdherence to infection control is the highest priority for safe school re-opening. Further transmission reduction can be achieved through small rotating class cohorts with an option for remote learning, widespread testing at the beginning of the work week, and daily symptom screening and self-isolation. Randomly testing 10-20% of attendees weekly or monthly does not meaningfully curtail transmission and may not detect outbreaks before they have spread beyond a handful of individuals. School systems considering re-opening during the SARS-CoV-2 pandemic or similarly virulent respiratory disease outbreaks should consider these relative impacts when setting policy priorities.

Summary Background Advances in HIV prevention methods offer promise to accelerate declines in incidence, but how these methods can be deployed to have the best effect on the heterogeneous landscape and drivers of the pandemic remains unclear. We postulated that use of epidemic heterogeneity to inform the allocation of resources for combination HIV prevention could enhance the impact of HIV funding across sub-Saharan Africa. Methods We developed a compartmental mathematical model of HIV transmission and disease progression by risk group to subnational resolution in 18 countries, capturing 80% of the adult HIV burden in sub-Saharan Africa. Adults aged 15–49 years were grouped by risk of HIV acquisition and transmission, and those older than 50 years were assumed to have negligible risk. For each top-level administrative division, we calibrated the model to historical data for HIV prevalence, sexual behaviours, treatment scale-up, and demographics. We then evaluated four strategies for allocation of prevention funding over a 15 year period from 2016 to 2030, which exploited epidemic differences between subnational regions to varying degrees. Findings For a $US20 billion representative expenditure over the 15 year period, scale-up of prevention along present funding channels could avert 5·3 million infections relative to no scale-up. Prioritisation of key populations could avert 3·7 million more infections than present funding channels, and additional prioritisation by within-country geography could avert 400 000 more infections. Removal of national constraints could avert a further 600 000 infections. Risk prioritisation has greater marginal impact than geographical prioritisation across multiple expenditure levels. However, targeting by both risk and geography is best for total impact and could achieve gains of up to three times more than present channels. A shift from the present pattern to the optimum pattern would rebalance resources towards more cost-effective interventions and emerging epidemics. Interpretation If domestic and international funders were to align strategically to build an aggregate funding pattern that is guided by the epidemiology of HIV, and particularly by the emerging understanding of local dynamics and epidemic drivers, more cost-effective and impactful HIV prevention investments could be achieved across sub-Saharan Africa. Funding The Bill & Melinda Gates Foundation.

BackgroundZimbabwe adopted voluntary medical male circumcision (VMMC) as a priority HIV prevention strategy in 2007 and began implementation in 2009. We evaluated the costs and impact of this VMMC program to date and in future.MethodsThree mathematical models describing Zimbabwe's HIV epidemic and program evolution were calibrated to household survey data on prevalence and risk behaviors, with circumcision coverage calibrated to program-reported VMMCs. We compared trends in new infections and costs to a counterfactual without VMMC. Input assumptions were agreed in workshops with national stakeholders in 2015 and 2017.ResultsThe VMMC program averted 2,600-12,200 infections (among men and women combined) by the end of 2016. This impact will grow as circumcised men are protected lifelong, and onward dynamic transmission effects, which protect women via reduced incidence and prevalence in their male partners, increase over time. If other prevention interventions remain at 2016 coverages, the VMMCs already performed will avert 24,400-69,800 infections (2.3-5% of all new infections) through 2030. If coverage targets are achieved by 2021 and maintained, the program will avert 108,000-171,000 infections (10-13% of all new infections) by 2030, costing $2,100-3,250 per infection averted relative to no VMMC. Annual savings from averted treatment needs will outweigh VMMC maintenance costs once coverage targets are reached. If Zimbabwe also achieves ambitious UNAIDS targets for scaling up treatment and prevention efforts, VMMC will reduce the HIV incidence remaining at 2030 by one-third, critically contributing to the UNAIDS goal of 90% incidence reduction.ConclusionsVMMC can substantially impact Zimbabwe's HIV epidemic in the coming years; this investment will save costs in the longer term.

A recent hypothesis has proposed a glucose-lactate metabolic symbiosis between adjacent hypoxic and oxygenated regions of a developing tumour, and proposed a treatment strategy to target this symbiosis. However, in vivo experimental support remains inconclusive. Here we develop a minimal spatial mathematical model of glucose-lactate metabolism to examine, in principle, whether metabolic symbiosis is plausible in human tumours, and to assess the potential impact of inhibiting it. We find that symbiosis is a robust feature of our model system---although on the length scale at which oxygen supply is diffusion-limited, its occurrence requires very high cellular metabolic activity---and that necrosis in the tumour core is reduced in the presence of symbiosis. Upon simulating therapeutic inhibition of lactate uptake, we predict that targeted treatment increases the extent of tissue oxygenation without increasing core necrosis. The oxygenation effect is correlated strongly with the extent of wildtype hypoxia and only weakly with wildtype symbiotic behaviour, and therefore may be promising for radiosensitisation of hypoxic, lactate-consuming tumours even if they do not exhibit a spatially well-defined symbiosis. Finally, we conduct a set of in vitro experiments on the U87 glioblastoma cell line to facilitate preliminary speculation as to where highly malignant tumours might fall in our parameter space, and find that these experiments suggest a weakly symbiotic regime for U87 cells, which raises the new question of what relationship exists between symbiosis---if indeed it occurs in vivo---and tumour malignancy.

We model the metabolism and behaviour of a developing cancer tumour in the context of its microenvironment, with the aim of elucidating the consequences of altered energy metabolism. Of particular interest is the Warburg Effect, a widespread preference in tumours for cytosolic glycolysis rather than oxidative phosphorylation for glucose breakdown, as yet incompletely understood. We examine a candidate explanation for the prevalence of the Warburg Effect in tumours, the acid-mediated invasion hypothesis, by generalising a canonical non-linear reaction-diffusion model of acid-mediated tumour invasion to consider additional biological features of potential importance. We apply both numerical methods and a non-standard asymptotic analysis in a travelling wave framework to obtain an explicit understanding of the range of tumour behaviours produced by the model and how fundamental parameters govern the speed and shape of invading tumour waves. Comparison with conclusions drawn under the original system--a special case of our generalised system--allows us to comment on the structural stability and predictive power of the modelling framework.

Summary Background Many ways of preventing HIV infection have been proposed and more are being developed. We sought to construct a strategic approach to HIV prevention that would use limited resources to achieve the greatest possible prevention impact through the use of interventions available today and in the coming years. Methods We developed a deterministic compartmental model of heterosexual HIV transmission in South Africa and formed assumptions about the costs and effects of a range of interventions, encompassing the further scale-up of existing interventions (promoting condom use, male circumcision, early antiretroviral therapy [ART] initiation for all [including increased HIV testing and counselling activities], and oral pre-exposure prophylaxis [PrEP]), the introduction of new interventions in the medium term (offering intravaginal rings, long-acting injectable antiretroviral drugs) and long term (vaccine, broadly neutralising antibodies [bNAbs]). We examined how available resources could be allocated across these interventions to achieve maximum impact, and assessed how this would be affected by the failure of the interventions to be developed or scaled up. Findings If all interventions are available, the optimum mix would place great emphasis on the following: scale-up of male circumcision and early ART initiation with outreach testing, as these are available immediately and assumed to be low cost and highly efficacious; intravaginal rings targeted to sex workers; and vaccines, as these can achieve a large effect if scaled up even if imperfectly efficacious. The optimum mix would rely less on longer term developments, such as long-acting antiretroviral drugs and bNAbs, unless the costs of these reduced. However, if impossible to scale up existing interventions to the extent assumed, emphasis on oral PrEP, intravaginal rings, and long-acting antiretroviral drugs would increase. The long-term effect on the epidemic is most affected by scale-up of existing interventions and the successful development of a vaccine. Interpretation With current information, a strategic approach in which limited resources are used to maximise prevention impact would focus on strengthening the scale-up of existing interventions, while pursuing a workable vaccine and developing other approaches that can be used if further scale-up of existing interventions is limited. Funding Bill & Melinda Gates Foundation.