Sequential allocation of vaccine to control an infectious disease.

The problem of optimally allocating a limited supply of vaccine to control a communicable disease has broad applications in public health and has received renewed attention during the COVID-19 pandemic. This allocation problem is highly complex and nonlinear. Decision makers need a practical, accurate, and interpretable method to guide vaccine allocation. In this paper we develop simple analytical conditions that can guide the allocation of vaccines over time. We consider four objectives: minimize new infections, minimize deaths, minimize life years lost, or minimize quality-adjusted life years lost due to death. We consider an SIR model with interacting population groups. We approximate the model using Taylor series expansions, and develop simple analytical conditions characterizing the optimal solution to the resulting problem for a single time period. We develop a solution approach in which we allocate vaccines using the analytical conditions in each time period based on the state of the epidemic at the start of the time period. We illustrate our method with an example of COVID-19 vaccination, calibrated to epidemic data from New York State. Using numerical simulations, we show that our method achieves near-optimal results over a wide range of vaccination scenarios. Our method provides a practical, intuitive, and accurate tool for decision makers as they allocate limited vaccines over time, and highlights the need for more interpretable models over complicated black box models to aid in decision making.

Effectiveness of Policies for Addressing the US Opioid Epidemic: A Model-Based Analysis from the Stanford-Lancet Commission on the North American Opioid Crisis.

BACKGROUND: The U.S. opioid crisis has been exacerbated by COVID-19 and the spread of synthetic opioids (e.g., fentanyl). METHODS: We model the effectiveness of reduced prescribing, drug rescheduling, prescription monitoring programs (PMPs), tamper-resistant drug reformulation, excess opioid disposal, naloxone availability, syringe exchange, pharmacotherapy, and psychosocial treatment. We measure life years, quality-adjusted life years (QALYs), and opioid-related deaths over five and ten years. FINDINGS: Under the status quo, our model predicts that approximately 547,000 opioid-related deaths will occur from 2020 to 2024 (range 441,000 - 613,000), rising to 1,220,000 (range 996,000 - 1,383,000) by 2029. Expanding naloxone availability by 30% had the largest effect, averting 25% of opioid deaths. Pharmacotherapy, syringe exchange, psychosocial treatment, and PMPs are uniformly beneficial, reducing opioid-related deaths while leading to gains in life years and QALYs. Reduced prescribing and increasing excess opioid disposal programs would reduce total deaths, but would lead to more heroin deaths in the short term. Drug rescheduling would increase total deaths over five years as some opioid users escalate to heroin, but decrease deaths over ten years. Combined interventions would lead to greater increases in life years, QALYs, and deaths averted, although in many cases the results are subadditive. INTERPRETATION: Expanded health services for individuals with opioid use disorder combined with PMPs and reduced opioid prescribing would moderately lessen the severity of the opioid crisis over the next decade. Tragically, even with improved public policies, significant morbidity and mortality is inevitable.

Optimal allocation of limited vaccine to minimize the effective reproduction number.

We examine the problem of allocating a limited supply of vaccine for controlling an infectious disease with the goal of minimizing the effective reproduction number Re. We consider an SIR model with two interacting populations and develop an analytical expression that the optimal vaccine allocation must satisfy. With limited vaccine supplies, we find that an all-or-nothing approach is optimal. For certain special cases, we determine the conditions under which the optimal Re is below 1. We present an example of vaccine allocation for COVID-19 and show that it is optimal to vaccinate younger individuals before older individuals to minimize Re if less than 59% of the population can be vaccinated. The analytical conditions we develop provide a simple means of determining the optimal allocation of vaccine between two population groups to minimize Re.

Effectiveness of Face Masks in Reducing the Spread of COVID-19: A Model-Based Analysis.

BACKGROUND: The World Health Organization and US Centers for Disease Control and Prevention recommend that both infected and susceptible people wear face masks to protect against COVID-19. METHODS: We develop a dynamic disease model to assess the effectiveness of face masks in reducing the spread of COVID-19, during an initial outbreak and a later resurgence, as a function of mask effectiveness, coverage, intervention timing, and time horizon. We instantiate the model for the COVID-19 outbreak in New York, with sensitivity analyses on key natural history parameters. RESULTS: During the initial epidemic outbreak, with no social distancing, only 100% coverage of masks with high effectiveness can reduce the effective reproductive number Re below 1. During a resurgence, with lowered transmission rates due to social distancing measures, masks with medium effectiveness at 80% coverage can reduce Re below 1 but cannot do so if individuals relax social distancing efforts. Full mask coverage could significantly improve outcomes during a resurgence: with social distancing, masks with at least medium effectiveness could reduce Re below 1 and avert almost all infections, even with intervention fatigue. For coverage levels below 100%, prioritizing masks that reduce the risk of an infected individual from spreading the infection rather than the risk of a susceptible individual from getting infected yields the greatest benefit. LIMITATIONS: Data regarding COVID-19 transmission are uncertain, and empirical evidence on mask effectiveness is limited. Our analyses assume homogeneous mixing, providing an upper bound on mask effectiveness. CONCLUSIONS: Even moderately effective face masks can play a role in reducing the spread of COVID-19, particularly with full coverage, but should be combined with social distancing measures to reduce Re below 1.[Box: see text].

Optimal allocation of limited vaccine to control an infectious disease: Simple analytical conditions.

When allocating limited vaccines to control an infectious disease, policy makers frequently have goals relating to individual health benefits (e.g., reduced morbidity and mortality) as well as population-level health benefits (e.g., reduced transmission and possible disease eradication). We consider the optimal allocation of a limited supply of a preventive vaccine to control an infectious disease, and four different allocation objectives: minimize new infections, deaths, life years lost, or quality-adjusted life years (QALYs) lost due to death. We consider an SIR model with n interacting populations, and a single allocation of vaccine at time 0. We approximate the model dynamics to develop simple analytical conditions characterizing the optimal vaccine allocation for each objective. We instantiate the model for an epidemic similar to COVID-19 and consider n=2 population groups: one group (individuals under age 65) with high transmission but low mortality and the other group (individuals age 65 or older) with low transmission but high mortality. We find that it is optimal to vaccinate younger individuals to minimize new infections, whereas it is optimal to vaccinate older individuals to minimize deaths, life years lost, or QALYs lost due to death. Numerical simulations show that the allocations resulting from our conditions match those found using much more computationally expensive algorithms such as exhaustive search. Sensitivity analysis on key parameters indicates that the optimal allocation is robust to changes in parameter values. The simple conditions we develop provide a useful means of informing vaccine allocation decisions for communicable diseases.