Vaccination for communicable endemic diseases: optimal allocation of initial and booster vaccine doses.

For some communicable endemic diseases (e.g., influenza, COVID-19), vaccination is an effective means of preventing the spread of infection and reducing mortality, but must be augmented over time with vaccine booster doses. We consider the problem of optimally allocating a limited supply of vaccines over time between different subgroups of a population and between initial versus booster vaccine doses, allowing for multiple booster doses. We first consider an SIS model with interacting population groups and four different objectives: those of minimizing cumulative infections, deaths, life years lost, or quality-adjusted life years lost due to death. We solve the problem sequentially: for each time period, we approximate the system dynamics using Taylor series expansions, and reduce the problem to a piecewise linear convex optimization problem for which we derive intuitive closed-form solutions. We then extend the analysis to the case of an SEIS model. In both cases vaccines are allocated to groups based on their priority order until the vaccine supply is exhausted. Numerical simulations show that our analytical solutions achieve results that are close to optimal with objective function values significantly better than would be obtained using simple allocation rules such as allocation proportional to population group size. In addition to being accurate and interpretable, the solutions are easy to implement in practice. Interpretable models are particularly important in public health decision making.

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.

Surveillance for endemic infectious disease outbreaks: Adaptive sampling using profile likelihood estimation.

Outbreaks of an endemic infectious disease can occur when the disease is introduced into a highly susceptible subpopulation or when the disease enters a network of connected individuals. For example, significant HIV outbreaks among people who inject drugs have occurred in at least half a dozen US states in recent years. This motivates the current study: how can limited testing resources be allocated across geographic regions to rapidly detect outbreaks of an endemic infectious disease? We develop an adaptive sampling algorithm that uses profile likelihood to estimate the distribution of the number of positive tests that would occur for each location in a future time period if that location were sampled. Sampling is performed in the location with the highest estimated probability of triggering an outbreak alarm in the next time period. The alarm function is determined by a semiparametric likelihood ratio test. We compare the profile likelihood sampling (PLS) method numerically to uniform random sampling (URS) and Thompson sampling (TS). TS was worse than URS when the outbreak occurred in a location with lower initial prevalence than other locations. PLS had lower time to outbreak detection than TS in some but not all scenarios, but was always better than URS even when the outbreak occurred in a location with a lower initial prevalence than other locations. PLS provides an effective and reliable method for rapidly detecting endemic disease outbreaks that is robust to this uncertainty.

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.

Target-Based Care: An Intervention to Reduce Variation in Postoperative Length of Stay.

OBJECTIVES: To derive care targets and evaluate the impact of displaying them at the point of care on postoperative length of stay (LOS). STUDY DESIGN: A prospective cohort study using 2 years of historical controls within a freestanding, academic children's hospital. Patients undergoing benchmark cardiac surgery between May 4, 2014, and August 15, 2016 (preintervention) and September 6, 2016, to September 30, 2018 (postintervention) were included. The intervention consisted of displaying at the point of care targets for the timing of extubation, transfer from the intensive care unit (ICU), and hospital discharge. Family satisfaction, reintubation, and readmission rates were tracked. RESULTS: The postintervention cohort consisted of 219 consecutive patients. There was a reduction in variation for ICU (difference in SD -2.56, P < .01) and total LOS (difference in SD -2.84, P < .001). Patients stayed on average 0.97 fewer days (P < .001) in the ICU (median -1.01 [IQR -2.15, -0.39]), 0.7 fewer days (P < .001) on mechanical ventilation (median -0.54 [IQR -0.77, -0.50]), and 1.18 fewer days (P < .001) for the total LOS (median -2.25 [IQR -3.69, -0.15]). Log-transformed multivariable linear regression demonstrated the intervention to be associated with shorter ICU LOS (ß coefficient -0.19, SE 0.059, P < .001), total postoperative LOS (ß coefficient -0.12, SE 0.052, P = .02), and ventilator duration (ß coefficient -0.21, SE 0.048, P < .001). Balancing metrics did not differ after the intervention. CONCLUSIONS: Target-based care is a simple, novel intervention associated with reduced variation in LOS and absolute LOS across a diverse spectrum of complex cardiac surgeries.

Health outcomes and cost-effectiveness of diversion programs for low-level drug offenders: A model-based analysis.

BACKGROUND: Cycles of incarceration, drug abuse, and poverty undermine ongoing public health efforts to reduce overdose deaths and the spread of infectious disease in vulnerable populations. Jail diversion programs aim to divert low-level drug offenders toward community care resources, avoiding criminal justice costs and disruptions in treatment for HIV, hepatitis C virus (HCV), and drug abuse. We sought to assess the health benefits and cost-effectiveness of a jail diversion program for low-level drug offenders. METHODS AND FINDINGS: We developed a microsimulation model, calibrated to King County, Washington, that captured the spread of HIV and HCV infections and incarceration and treatment systems as well as preexisting interventions such as needle and syringe programs and opiate agonist therapy. We considered an adult population of people who inject drugs (PWID), people who use drugs but do not inject (PWUD), men who have sex with men, and lower-risk heterosexuals. We projected discounted lifetime costs and quality-adjusted life years (QALYs) over a 10-year time horizon with and without a jail diversion program and calculated resulting incremental cost-effectiveness ratios (ICERs) from the health system and societal perspectives. We also tracked HIV and HCV infections, overdose deaths, and jail population size. Over 10 years, the program was estimated to reduce HIV and HCV incidence by 3.4% (95% CI 2.7%-4.0%) and 3.3% (95% CI 3.1%-3.4%), respectively, overdose deaths among PWID by 10.0% (95% CI 9.8%-10.8%), and jail population size by 6.3% (95% CI 5.9%-6.7%). When considering healthcare costs only, the program cost $25,500/QALY gained (95% CI $12,600-$48,600). Including savings from reduced incarceration (societal perspective) improved the ICER to $6,200/QALY gained (95% CI, cost-saving $24,300). Sensitivity analysis indicated that cost-effectiveness depends on diversion program participants accessing community programs such as needle and syringe programs, treatment for substance use disorder, and HIV and HCV treatment, as well as diversion program cost. A limitation of the analysis is data availability, as fewer data are available for diversion programs than for more established interventions aimed at people with substance use disorder. Additionally, like any model of a complex system, our model relies on simplifying assumptions: For example, we simplified pathways in the healthcare and criminal justice systems, modeled an average efficacy for substance use disorder treatment, and did not include costs associated with homelessness, unemployment, and breakdown in family structure. CONCLUSIONS: We found that diversion programs for low-level drug offenders are likely to be cost-effective, generating savings in the criminal justice system while only moderately increasing healthcare costs. Such programs can reduce incarceration and its associated costs, and also avert overdose deaths and improve quality of life for PWID, PWUD, and the broader population (through reduced HIV and HCV transmission).