Resource allocation for epidemic control over short time horizons

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.

A bed allocation model for pandemic situation considering general demand: A case study of Iran

Pandemics place a new type of demand from patients affected by the pandemic, imposing significant strain on hospital departments, particularly the intensive care unit. A crucial challenge during pandemics is the imbalance in addressing the needs of both pandemic patients and general patients. Often, the community's focus shifts toward the pandemic patients, causing an imbalance that can result in severe issues. Simultaneously considering both demands, pandemic-related and general healthcare needs, has been largely overlooked. In this article, we propose a bi-objective mathematical model for locating temporary hospitals and allocating patients to existing and temporary hospitals, considering both demand types during pandemics. Hospital departments, such as emergency beds, serve both demand types, but due to infection risks, accommodating a pandemic patient and a general patient in the same department is not feasible. The first objective function is to minimize the bed shortages considering both types of demands, whereas the second objective is cost minimization, which includes the fixed and variable costs of temporary facilities, the penalty cost of changing the allocation of existing facilities (between general and pandemic demand), the cost of adding expandable beds to existing facilities, and the service cost for different services and beds. To show the applicability of the model, a real case study has been conducted on the COVID-19 pandemic in the city of Qom, Iran. Comparing the model results with real data reveals that using the proposed model can increase demand coverage by 16%.

Risk-based allocation of COVID-19 personal protective equipment under supply shortages

The COVID-19 outbreak put healthcare systems across the globe under immense pressure to meet the unprecedented demand for critical supplies and personal protective equipment (PPE). The traditional cost-effective supply chain paradigm failed to respond to the increased demand, putting healthcare workers (HCW) at a much higher infection risk relative to the general population. Recognizing PPE shortages and high infection risk for HCWs, the World Health Organization (WHO) recommends allocations based on ethical principles. In this paper, we model the infection risk for HCWs as a function of usage and use it as the basis for distribution planning that balances government procurement decisions, hospitals' PPE usage policies, and WHO ethical allocation guidelines. We propose an infection risk model that integrates PPE allocation decisions with disease progression estimates to quantify infection risk among HCWs. The proposed risk function is used to derive closed-form allocation decisions under WHO ethical guidelines in both deterministic and stochastic settings. The modelling is then extended to dynamic distribution planning. Although nonlinear, we reformulate the resulting model to make it solvable using off-the-shelf software. The risk function successfully accounts for virus prevalence in space and in time and leads to allocations that are sensitive to the differences between regions. Comparative analysis shows that the allocation policies lead to significantly different levels of infection risk, especially under high virus prevalence. The best-outcome allocation policy that aims to minimize the total infected cases outperforms other policies under this objective and that of minimizing the maximum number of infections per period.

Asymptotic Analysis of Optimal Vaccination Policies

Targeted vaccination policies can have a significant impact on the number of infections and deaths in an epidemic. However, optimising such policies is complicated, and the resultant solution may be difficult to explain to policy-makers and to the public. The key novelty of this paper is a derivation of the leading-order optimal vaccination policy under multi-group susceptible-infected-recovered dynamics in two different cases. Firstly, it considers the case of a small vulnerable subgroup in a population and shows that (in the asymptotic limit) it is optimal to vaccinate this group first, regardless of the properties of the other groups. Then, it considers the case of a small vaccine supply and transforms the optimal vaccination problem into a simple knapsack problem by linearising the final size equations. Both of these cases are then explored further through numerical examples, which show that these solutions are also directly useful for realistic parameter values. Moreover, the findings of this paper give some general principles for optimal vaccination policies which will help policy-makers and the public to understand the reasoning behind optimal vaccination programs in more generic cases.

COVID-19: Data-Driven optimal allocation of ventilator supply under uncertainty and risk

This study presents a new risk-averse multi-stage stochastic epidemics-ventilator-logistics compartmental model to address the resource allocation challenges of mitigating COVID-19. This epidemiological logistics model involves the uncertainty of untested asymptomatic infections and incorporates short-term human migration. Disease transmission is also forecasted through a new formulation of transmission rates that evolve over space and time with respect to various non-pharmaceutical interventions, such as wearing masks, social distancing, and lockdown. The proposed multi-stage stochastic model overviews different scenarios on the number of asymptomatic individuals while optimizing the distribution of resources, such as ventilators, to minimize the total expected number of newly infected and deceased people. The Conditional Value at Risk (CVaR) is also incorporated into the multi-stage mean-risk model to allow for a trade-off between the weighted expected loss due to the outbreak and the expected risks associated with experiencing disastrous pandemic scenarios. We apply our multi-stage mean-risk epidemics-ventilator-logistics model to the case of controlling COVID-19 in highly-impacted counties of New York and New Jersey. We calibrate, validate, and test our model using actual infection, population, and migration data. We also define a new region-based sub-problem and bounds on the problem and then show their computational benefits in terms of the optimality and relaxation gaps. The computational results indicate that short-term migration influences the transmission of the disease significantly. The optimal number of ventilators allocated to each region depends on various factors, including the number of initial infections, disease transmission rates, initial ICU capacity, the population of a geographical location, and the availability of ventilator supply. Our data-driven modeling framework can be adapted to study the disease transmission dynamics and logistics of other similar epidemics and pandemics.

Designing an optimal sequence of non-pharmaceutical interventions for controlling COVID-19

The COVID-19 pandemic has had an unprecedented impact on global health and the economy since its inception in December, 2019 in Wuhan, China. Non-pharmaceutical interventions (NPI) like lockdowns and curfews have been deployed by affected countries for controlling the spread of infections. In this paper, we develop a Mixed Integer Non-Linear Programming (MINLP) epidemic model for computing the optimal sequence of NPIs over a planning horizon, considering shortages in doctors and hospital beds, under three different lockdown scenarios. We analyse two strategies - centralised (homogeneous decisions at the national level) and decentralised (decisions differentiated across regions), for two objectives separately - minimization of infections and deaths, using actual pandemic data of France. We linearize the quadratic constraints and objective functions in the MINLP model and convert it to a Mixed Integer Linear Programming (MILP) model. A major result that we show analytically is that under the epidemic model used, the optimal sequence of NPIs always follows a decreasing severity pattern. Using this property, we further simplify the MILP model into an Integer Linear Programming (ILP) model, reducing computational time up to 99%. Our numerical results show that a decentralised strategy is more effective in controlling infections for a given severity budget, yielding up to 20% lesser infections, 15% lesser deaths and 60% lesser shortages in healthcare resources. These results hold without considering logistics aspects and for a given level of compliance of the population.

Optimizing Living Material Delivery During the COVID-19 Outbreak

The coronavirus disease 2019 (COVID-19) epidemic has spread worldwide, posing a great threat to human beings. The stay-home quarantine is an effective way to reduce physical contacts and the associated COVID-19 transmission risk, which requires the support of efficient living materials (such as meats, vegetables, grain, and oil) delivery. Notably, the presence of potential infected individuals increases the COVID-19 transmission risk during the delivery. The deliveryman may be the medium through which the virus spreads among urban residents. However, traditional delivery route optimization methods don't take the virus transmission risk into account. Here, we propose a novel living material delivery route approach considering the possible COVID-19 transmission during the delivery. A complex network-based virus transmission model is developed to simulate the possible COVID-19 infection between urban residents and the deliverymen. A bi-objective model considering the COVID-19 transmission risk and the total route length is proposed and solved by the hybrid meta-heuristics integrating the adaptive large neighborhood search and simulated annealing. The experiment was conducted in Wuhan, China to assess the performance of the proposed approach. The results demonstrate that 935 vehicles will totally travel 56,424.55 km to deliver necessary living materials to 3,154 neighborhoods, with total risk [Formula: see text]. The presented approach reduces the risk of COVID-19 transmission by 67.55% compared to traditional distance-based optimization methods. The presented approach can facilitate a well response to the COVID-19 in the transportation sector.

Customer Prioritization Integrated Supply Chain Optimization Model with Outsourcing Strategies

Pre-COVID-19, most of the supply chains functioned with more capacity than demand. However, COVID-19 changed traditional supply chains' dynamics, resulting in more demand than their production capacity. This article presents a multiobjective and multiperiod supply chain network design along with customer prioritization, keeping in view price discounts and outsourcing strategies to deal with the situation when demand exceeds the production capacity. Initially, a multiperiod, multiobjective supply chain network is designed that incorporates prices discounts, customer prioritization, and outsourcing strategies. The main objectives are profit and prioritization maximization and time minimization. The introduction of the prioritization objective function having customer ranking as a parameter and considering less capacity than demand and outsourcing differentiates this model from the literature. A four-valued neutrosophic multiobjective optimization method is introduced to solve the model developed. To validate the model, a case study of the supply chain of a surgical mask is presented as the real-life application of research. The research findings are useful for the managers to make price discounts and preferred customer prioritization decisions under uncertainty and imbalance between supply and demand. In future, the logic in the proposed model can be used to create web application for optimal decision-making in supply chains.

How optimal allocation of limited testing capacity changes epidemic dynamics

Insufficient testing capacity has been a critical bottleneck in the worldwide fight against COVID-19. Optimizing the deployment of limited testing resources has therefore emerged as a keystone problem in pandemic response planning. Here, we use a modified SEIR model to optimize testing strategies under a constraint of limited testing capacity. We define pre-symptomatic, asymptomatic, and symptomatic infected classes, and assume that positively tested individuals are immediately moved into quarantine. We further define two types of testing. Clinical testing focuses only on the symptomatic class. Non-clinical testing detects pre- and asymptomatic individuals from the general population, and a concentration parameter governs the degree to which such testing can be focused on high infection risk individuals. We then solve for the optimal mix of clinical and non-clinical testing as a function of both testing capacity and the concentration parameter. We find that purely clinical testing is optimal at very low testing capacities, supporting early guidance to ration tests for the sickest patients. Additionally, we find that a mix of clinical and non-clinical testing becomes optimal as testing capacity increases. At high but empirically observed testing capacities, a mix of clinical testing and non-clinical testing, even if extremely unfocused, becomes optimal. We further highlight the advantages of early implementation of testing programs, and of combining optimized testing with contact reduction interventions such as lockdowns, social distancing, and masking.

Operational research: A multidisciplinary approach for the management of infectious disease in a global context

Infectious diseases, both established and emerging, impose a significant burden globally. Successful management of infectious diseases requires considerable effort and a multidisciplinary approach to tackle the complex web of interconnected biological, public health and economic systems. Through a wide range of problem-solving techniques and computational methods, operational research can strengthen health systems and support decision-making at all levels of disease control. From improved understanding of disease biology, intervention planning and implementation, assessing economic feasibility of new strategies, identifying opportunities for cost reductions in routine processes, and informing health policy, this paper highlights areas of opportunity for operational research to contribute to effective and efficient infectious disease management and improved health outcomes.

A multi-stage stochastic programming approach to epidemic resource allocation with equity considerations

Existing compartmental models in epidemiology are limited in terms of optimizing the resource allocation to control an epidemic outbreak under disease growth uncertainty. In this study, we address this core limitation by presenting a multi-stage stochastic programming compartmental model, which integrates the uncertain disease progression and resource allocation to control an infectious disease outbreak. The proposed multi-stage stochastic program involves various disease growth scenarios and optimizes the distribution of treatment centers and resources while minimizing the total expected number of new infections and funerals. We define two new equity metrics, namely infection and capacity equity, and explicitly consider equity for allocating treatment funds and facilities over multiple time stages. We also study the multi-stage value of the stochastic solution (VSS), which demonstrates the superiority of the proposed stochastic programming model over its deterministic counterpart. We apply the proposed formulation to control the Ebola Virus Disease (EVD) in Guinea, Sierra Leone, and Liberia of West Africa to determine the optimal and fair resource-allocation strategies. Our model balances the proportion of infections over all regions, even without including the infection equity or prevalence equity constraints. Model results also show that allocating treatment resources proportional to population is sub-optimal, and enforcing such a resource allocation policy might adversely impact the total number of infections and deaths, and thus resulting in a high cost that we have to pay for the fairness. Our multi-stage stochastic epidemic-logistics model is practical and can be adapted to control other infectious diseases in meta-populations and dynamically evolving situations.

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.

Allocating epidemic response teams and vaccine deliveries by drone in generic network structures, according to expected prevented exposures

The tumultuous inception of an epidemic is usually accompanied by difficulty in determining how to respond best. In developing nations, this can be compounded by logistical challenges, such as vaccine shortages and poor road infrastructure. To provide guidance towards improved epidemic response, various resource allocation models, in conjunction with a network-based SEIRVD epidemic model, are proposed in this article. Further, the feasibility of using drones for vaccine delivery is evaluated, and assorted relevant parameters are discussed. For the sake of generality, these results are presented for multiple network structures, representing interconnected populations-upon which repeated epidemic simulations are performed. The resource allocation models formulated maximise expected prevented exposures on each day of a simulated epidemic, by allocating response teams and vaccine deliveries according to the solutions of two respective integer programming problems-thereby influencing the simulated epidemic through the SEIRVD model. These models, when compared with a range of alternative resource allocation strategies, were found to reduce both the number of cases per epidemic, and the number of vaccines required. Consequently, the recommendation is made that such models be used as decision support tools in epidemic response. In the absence thereof, prioritizing locations for vaccinations according to susceptible population, rather than total population or number of infections, is most effective for the majority of network types. In other results, fixed-wing drones are demonstrated to be a viable delivery method for vaccines in the context of an epidemic, if sufficient drones can be promptly procured; the detrimental effect of intervention delay was discovered to be significant. In addition, the importance of well-documented routine vaccination activities is highlighted, due to the benefits of increased pre-epidemic immunity rates, and targeted vaccination.

HIV supply chains in low- and middle-income countries: overview and research opportunities

Purpose

Despite HIV being reported as one of the major global health issues, availability and accessibility of HIV services and supplies remain limited, especially in low- and middle-income countries. The effective and efficient operation of HIV supply chains is critical to tackle this problem. The purpose of this paper is to give an introduction to HIV supply chains in low- and middle-income countries and identify research opportunities for the operations research/operations management (OR/OM) community.

Design/methodology/approach

First, the authors review a combination of the scientific and grey literature, including both qualitative and quantitative papers, to give an overview of HIV supply chain operations in low- and middle-income countries and the challenges that are faced by organizing such supply chains. The authors then classify and discuss the relevant OR/OM literature based on seven classification criteria: decision level, methodology, type of HIV service modeled, challenges, performance measures, real-life applicability and countries covered. Because research on HIV supply chains in low- and middle-income countries is limited in the OR/OM field, this part also includes papers focusing on HIV supply chain modeling in high-income countries.

Findings

The authors conclude this study by identifying several tendencies and gaps and by proposing future research directions for OR/OM research.

Originality/value

To the best of the authors’ knowledge, this paper is the first literature review addressing this specific topic from an OR/OM perspective.

How resource limitations and household economics may compromise efforts to safeguard children during outbreaks

Background

Epidemiological models have been employed with great success to explore the efficacy of alternative strategies at combating disease outbreaks. These models have often incorporated an understanding of age-based susceptibility and severity of outcome, considering how to limit the adverse outcomes or disease burden relative to an age structure. Such models frequently recommend the preferential treatment/vaccination of children or the elderly, demonstrating how prevention of serious disease within these etiological subgroups can provide both protection within the subgroup itself and indirect protection to the broader population. However, it is most frequently the case that these target populations are consumers, rather than providers, of household resources. In areas of the globe where continued health of household members relies on continued provision of resources, these models may fail to provide the most effective overall strategies for health outcomes in both target populations and overall. This is particularly important for tropical diseases impacting rural and low-income areas in which the disease may be endemic or newly emergent, particularly in the wake of natural disasters.

Methods

We propose a modified epidemiological model with targeted treatment in resource-limited populations. We evaluate the model over a broad parameter space.

Results

This model demonstrates how economic limitations may shift the optimal strategy. It may be advantageous to treat populations at lesser direct risk if they are responsible for providing secondary protection to higher-risk population(s) by producing household resources. Evaluation of this model over the parameter space reveals that, in some cases, targeting treatment towards consumers may result in greater numbers of consumer infections.

Conclusions

Our results demonstrate how household resource limitation can drastically affect the impact of targeted treatment strategies for limiting epidemics. Depending on the economic circumstances, it is possible that focusing treatment on consumers such as children can produce a counter-intuitive outcome in which more children contract the disease.

Optimization Models for HIV/AIDS Resource Allocation: A Systematic Review

OBJECTIVE

This study reviews optimization models for human immunodeficiency virus (HIV) and acquired immunodeficiency syndrome (AIDS) resource allocation.

METHODS

We searched 2 databases for peer-reviewed articles published from January 1985 through August 2019 that describe optimization models for resource allocation in HIV/AIDS. We included models that consider 2 or more competing HIV/AIDS interventions. We extracted data on selected characteristics and identified similarities and differences across models. We also assessed the quality of mathematical disease transmission models based on the best practices identified by a 2010 task force.

RESULTS

The final qualitative synthesis included 23 articles that used 14 unique optimization models. The articles shared several characteristics, including the use of dynamic transmission modeling to estimate health benefits and the inclusion of specific high-risk groups in the study population. The models explored similar HIV/AIDS interventions that span primary and secondary prevention and antiretroviral treatment. Most articles were focused on sub-Saharan African countries (57%) and the United States (39%). There was notable variation in the types of optimization objectives across the articles; the most common was minimizing HIV incidence or maximizing infections averted (87%). Articles that utilized mathematical modeling of HIV disease and transmission displayed variable quality.

CONCLUSIONS

This systematic review of the literature identified examples of optimization models that have been applied in different settings, many of which displayed similar features. There were similarities in objective functions across optimization models, but they did not align with global HIV/AIDS goals or targets. Future work should be applied in countries facing the largest declines in HIV/AIDS funding.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

Resource Allocation for Epidemic Control Across Multiple Sub-populations

The number of pathogenic threats to plant, animal and human health is increasing. Controlling the spread of such threats is costly and often resources are limited. A key challenge facing decision makers is how to allocate resources to control the different threats in order to achieve the least amount of damage from the collective impact. In this paper we consider the allocation of limited resources across n independent target populations to treat pathogens whose spread is modelled using the susceptible–infected–susceptible model. Using mathematical analysis of the systems dynamics, we show that for effective disease control, with a limited budget, treatment should be focused on a subset of populations, rather than attempting to treat all populations less intensively. The choice of populations to treat can be approximated by a knapsack-type problem. We show that the knapsack closely approximates the exact optimum and greatly outperforms a number of simpler strategies. A key advantage of the knapsack approximation is that it provides insight into the way in which the economic and epidemiological dynamics affect the optimal allocation of resources. In particular using the knapsack approximation to apportion control takes into account two important aspects of the dynamics: the indirect interaction between the populations due to the shared pool of limited resources and the dependence on the initial conditions.

From Theory to Practice: Implementation of a Resource Allocation Model in Health Departments

OBJECTIVE

To develop a resource allocation model to optimize health departments' Centers for Disease Control and Prevention (CDC)-funded HIV prevention budgets to prevent the most new cases of HIV infection and to evaluate the model's implementation in 4 health departments.

DESIGN, SETTINGS, AND PARTICIPANTS

We developed a linear programming model combined with a Bernoulli process model that allocated a fixed budget among HIV prevention interventions and risk subpopulations to maximize the number of new infections prevented. The model, which required epidemiologic, behavioral, budgetary, and programmatic data, was implemented in health departments in Philadelphia, Chicago, Alabama, and Nebraska.

MAIN OUTCOME MEASURES

The optimal allocation of funds, the site-specific cost per case of HIV infection prevented rankings by intervention, and the expected number of HIV cases prevented.

RESULTS

The model suggested allocating funds to HIV testing and continuum-of-care interventions in all 4 health departments. The most cost-effective intervention for all sites was HIV testing in nonclinical settings for men who have sex with men, and the least cost-effective interventions were behavioral interventions for HIV-negative persons. The pilot sites required 3 to 4 months of technical assistance to develop data inputs and generate and interpret the results. Although the sites found the model easy to use in providing quantitative evidence for allocating HIV prevention resources, they criticized the exclusion of structural interventions and the use of the model to allocate only CDC funds.

CONCLUSIONS

Resource allocation models have the potential to improve the allocation of limited HIV prevention resources and can be used as a decision-making guide for state and local health departments. Using such models may require substantial staff time and technical assistance. These model results emphasize the allocation of CDC funds toward testing and continuum-of-care interventions and populations at highest risk of HIV transmission.

Three-level global resource allocation model for hiv control: A hierarchical decision system approach

Funds from various global organizations, such as, The Global Fund, The World Bank, etc. are not directly distributed to the targeted risk groups. Especially in the so-called third-world-countries, the major part of the fund in HIV prevention programs comes from these global funding organizations. The allocations of these funds usually pass through several levels of decision making bodies that have their own specific parameters to control and specific objectives to achieve. However, these decisions are made mostly in a heuristic manner and this may lead to a non-optimal allocation of the scarce resources. In this paper, a hierarchical mathematical optimization model is proposed to solve such a problem. Combining existing epidemiological models with the kind of interventions being on practice, a 3-level hierarchical decision making model in optimally allocating such resources has been developed and analyzed. When the impact of antiretroviral therapy (ART) is included in the model, it has been shown that the objective function of the lower level decision making structure is a non-convex minimization problem in the allocation variables even if all the production functions for the intervention programs are assumed to be linear.

Deriving effective vaccine allocation strategies for pandemic influenza: Comparison of an agent-based simulation and a compartmental model

Individuals are prioritized based on their risk profiles when allocating limited vaccine stocks during an influenza pandemic. Computationally expensive but realistic agent-based simulations and fast but stylized compartmental models are typically used to derive effective vaccine allocation strategies. A detailed comparison of these two approaches, however, is often omitted. We derive age-specific vaccine allocation strategies to mitigate a pandemic influenza outbreak in Seattle by applying derivative-free optimization to an agent-based simulation and also to a compartmental model. We compare the strategies derived by these two approaches under various infection aggressiveness and vaccine coverage scenarios. We observe that both approaches primarily vaccinate school children, however they may allocate the remaining vaccines in different ways. The vaccine allocation strategies derived by using the agent-based simulation are associated with up to 70% decrease in total cost and 34% reduction in the number of infections compared to the strategies derived by using the compartmental model. Nevertheless, the latter approach may still be competitive for very low and/or very high infection aggressiveness. Our results provide insights about potential differences between the vaccine allocation strategies derived by using agent-based simulations and those derived by using compartmental models.

A Little Planning Goes a Long Way: Multilevel Allocation of HIV Prevention Resources

Background. HIV prevention funds are often allocated by decision makers at multiple levels. High-level decision makers may allocate funds to regions, and regional decision makers then allocate those funds to specific programs. Often, funds are allocated proportionally (e.g., in proportion to HIV incidence) rather than efficiently (i.e., to maximize HIV infections averted). The authors investigate the impact of efficient and proportional allocation methods at 2 different decision levels.

Methods. The authors developed an optimization model of resource allocation at 2 levels—an aggregate upper level and multiple local levels—and considered efficient allocation and allocation proportional to HIV incidence. Using data from 40 U.S. states, they compared 4 strategies for allocating HIV prevention funds.

Results. The greatest health benefit (HIV infections averted) occurred when efficient allocations were made at both levels. When funds were allocated proportionally at the higher level and efficiently at the lower level, the health benefit was about 5% less than when efficient allocations were made at both levels. When funds were allocated efficiently at the higher level and proportionally at the lower level, the health benefit was 15% less than when efficient allocations were made at both levels. The least health benefit (23% less than when efficient allocations were made at both levels) occurred with proportional allocation at both levels.

Conclusions. Efficient allocation only at the higher level cannot overcome poor allocations at lower levels. Moreover, efficient allocation at the lower level is likely to yield greater gains than efficient allocation at the higher level. Thus, upper-level decision makers, such as donor organizations, should develop incentives to promote efficient allocation by lower-level decision makers.

Creating impact with operations research in health: making room for practice in academia

Operations research (OR)-based analyses have the potential to improve decision making for many important, real-world health care problems. However, junior scholars often avoid working on practical applications in health because promotion and tenure processes tend to value theoretical studies more highly than applied studies. This paper discusses the author's experiences in using OR to inform and influence decisions in health and provides a blueprint for junior researchers who wish to find success by taking a similar path. This involves selecting good problems to study, forming productive collaborations with domain experts, developing appropriate models, identifying the most salient results from an analysis, and effectively disseminating findings to decision makers. The paper then suggests how journals, funding agencies, and senior academics can encourage such work by taking a broader and more informed view of the potential role and contributions of OR to solving health care problems. Making room in academia for the application of OR in health follows in the tradition begun by the founders of operations research: to work on important real-world problems where operations research can contribute to better decision making.

HIV epidemic control-a model for optimal allocation of prevention and treatment resources

With 33 million people living with human immunodeficiency virus (HIV) worldwide and 2.7 million new infections occurring annually, additional HIV prevention and treatment efforts are urgently needed. However, available resources for HIV control are limited and must be used efficiently to minimize the future spread of the epidemic. We develop a model to determine the appropriate resource allocation between expanded HIV prevention and treatment services. We create an epidemic model that incorporates multiple key populations with different transmission modes, as well as production functions that relate investment in prevention and treatment programs to changes in transmission and treatment rates. The goal is to allocate resources to minimize R 0, the reproductive rate of infection. We first develop a single-population model and determine the optimal resource allocation between HIV prevention and treatment. We extend the analysis to multiple independent populations, with resource allocation among interventions and populations. We then include the effects of HIV transmission between key populations. We apply our model to examine HIV epidemic control in two different settings, Uganda and Russia. As part of these applications, we develop a novel approach for estimating empirical HIV program production functions. Our study provides insights into the important question of resource allocation for a country's optimal response to its HIV epidemic and provides a practical approach for decision makers. Better decisions about allocating limited HIV resources can improve response to the epidemic and increase access to HIV prevention and treatment services for millions of people worldwide.

Incentives for Optimal Multi-level Allocation of HIV Prevention Resources

HIV/AIDS prevention funds are often allocated at multiple levels of decision-making. Optimal allocation of HIV prevention funds maximizes the number of HIV infections averted. However, decision makers often allocate using simple heuristics such as proportional allocation. We evaluate the impact of using incentives to encourage optimal allocation in a two-level decision-making process. We model an incentive based decision-making process consisting of an upper-level decision maker allocating funds to a single lower-level decision maker who then distributes funds to local programs. We assume that the lower-level utility function is linear in the amount of the budget received from the upper-level, the fraction of funds reserved for proportional allocation, and the number of infections averted. We assume that the upper level objective is to maximize the number of infections averted. We illustrate with an example using data from California, U.S.

Decision making for HIV prevention and treatment scale up: bridging the gap between theory and practice

BACKGROUND

Effectively controlling the HIV epidemic will require efficient use of limited resources. Despite ambitious global goals for HIV prevention and treatment scale up, few comprehensive practical tools exist to inform such decisions.

METHODS

We briefly summarize modeling approaches for resource allocation for epidemic control, and discuss the practical limitations of these models. We describe typical challenges of HIV resource allocation in practice and some of the tools used by decision makers. We identify the characteristics needed in a model that can effectively support planners in decision making about HIV prevention and treatment scale up.

RESULTS

An effective model to support HIV scale-up decisions will be flexible, with capability for parameter customization and incorporation of uncertainty. Such a model needs certain key technical features: it must capture epidemic effects; account for how intervention effectiveness depends on the target population and the level of scale up; capture benefit and cost differentials for packages of interventions versus single interventions, including both treatment and prevention interventions; incorporate key constraints on potential funding allocations; identify optimal or near-optimal solutions; and estimate the impact of HIV interventions on the health care system and the resulting resource needs. Additionally, an effective model needs a user-friendly design and structure, ease of calibration and validation, and accessibility to decision makers in all settings.

CONCLUSIONS

Resource allocation theory can make a significant contribution to decision making about HIV prevention and treatment scale up. What remains now is to develop models that can bridge the gap between theory and practice.

Cost-effective control of chronic viral diseases: finding the optimal level of screening and contact tracing

Chronic viral diseases such as human immunodeficiency virus (HIV) and hepatitis B virus (HBV) afflict millions of people worldwide. A key public health challenge in managing such diseases is identifying infected, asymptomatic individuals so that they can receive antiviral treatment. Such treatment can benefit both the treated individual (by improving quality and length of life) and the population as a whole (through reduced transmission). We develop a compartmental model of a chronic, treatable infectious disease and use it to evaluate the cost and effectiveness of different levels of screening and contact tracing. We show that: (1) the optimal strategy is to get infected individuals into treatment at the maximal rate until the incremental health benefits balance the incremental cost of controlling the disease; (2) as one reduces the disease prevalence by moving people into treatment (which decreases the chance that they will infect others), one should increase the level of contact tracing to compensate for the decreased effectiveness of screening; (3) as the disease becomes less prevalent, it is optimal to spend more per case identified; and (4) the relative mix of screening and contact tracing at any level of disease prevalence is such that the marginal efficiency of contact tracing (cost per infected person found) equals that of screening if possible (e.g., when capacity limitations are not binding). We also show how to determine the cost-effective equilibrium level of disease prevalence (among untreated individuals), and we develop an approximation of the path of the optimal prevalence over time. Using this, one can obtain a close approximation of the optimal solution without having to solve an optimal control problem. We apply our methods to an example of hepatitis B virus.

Optimal investment in HIV prevention programs: more is not always better

This paper develops a mathematical/economic framework to address the following question: Given a particular population, a specific HIV prevention program, and a fixed amount of funds that could be invested in the program, how much money should be invested? We consider the impact of investment in a prevention program on the HIV sufficient contact rate (defined via production functions that describe the change in the sufficient contact rate as a function of expenditure on a prevention program), and the impact of changes in the sufficient contact rate on the spread of HIV (via an epidemic model). In general, the cost per HIV infection averted is not constant as the level of investment changes, so the fact that some investment in a program is cost effective does not mean that more investment in the program is cost effective. Our framework provides a formal means for determining how the cost per infection averted changes with the level of expenditure. We can use this information as follows: When the program has decreasing marginal cost per infection averted (which occurs, for example, with a growing epidemic and a prevention program with increasing returns to scale), it is optimal either to spend nothing on the program or to spend the entire budget. When the program has increasing marginal cost per infection averted (which occurs, for example, with a shrinking epidemic and a prevention program with decreasing returns to scale), it may be optimal to spend some but not all of the budget. The amount that should be spent depends on both the rate of disease spread and the production function for the prevention program. We illustrate our ideas with two examples: that of a needle exchange program, and that of a methadone maintenance program.

Contact tracing to control infectious disease: when enough is enough

Contact tracing (also known as partner notification) is a primary means of controlling infectious diseases such as tuberculosis (TB), human immunodeficiency virus (HIV), and sexually transmitted diseases (STDs). However, little work has been done to determine the optimal level of investment in contact tracing. In this paper, we present a methodology for evaluating the appropriate level of investment in contact tracing. We develop and apply a simulation model of contact tracing and the spread of an infectious disease among a network of individuals in order to evaluate the cost and effectiveness of different levels of contact tracing. We show that contact tracing is likely to have diminishing returns to scale in investment: incremental investments in contact tracing yield diminishing reductions in disease prevalence. In conjunction with a cost-effectiveness threshold, we then determine the optimal amount that should be invested in contact tracing. We first assume that the only incremental disease control is contact tracing. We then extend the analysis to consider the optimal allocation of a budget between contact tracing and screening for exogenous infection, and between contact tracing and screening for endogenous infection. We discuss how a simulation model of this type, appropriately tailored, could be used as a policy tool for determining the appropriate level of investment in contact tracing for a specific disease in a specific population. We present an example application to contact tracing for chlamydia control.

A linear programming model for allocating HIV prevention funds with state agencies: a pilot study

Given the initiatives to improve resource allocation decisions for HIV prevention activities, a linear programming model was designed specifically for use by state and local decision-makers. A pilot study using information from the state of Florida was conducted and studied under a series of scenarios depicting the impact of common resource allocation constraints. Improvements over the past allocation strategy in the number of potential infections averted were observed in all scenarios with a maximal improvement of 73%. When allocating limited resources, policymakers must balance efficiency and equity. In this pilot study, the optimal allocation (i.e., most-efficient strategy) would not distribute resources in an equitable manner. Instead, only 12% of at-risk people would receive prevention funds. We find that less efficient strategies, where 58% fewer infections are averted, result in significantly more equitable allocations. This tool serves as a guide for allocating funds for prevention activities.

Efficient allocation of resources to prevent HIV infection among injection drug users: the Prevention Point Philadelphia (PPP) needle exchange program

The objective of this study is to determine the allocation of resources within a multi-site needle exchange program (NEP) that achieves the largest possible reduction in new HIV infections at minimum cost. We present a model that relates the number of injection drug user (IDU) clients and the number of syringes exchanged per client to both the costs of the NEP and the expected reduction in HIV infections per unit time. We show that cost-effective allocation within a multi-site NEP requires that sites be located where the density of IDUs is highest, and that the number of syringes exchanged per client be equal across sites. We apply these optimal allocation rules to a specific multi-site needle exchange program, Prevention Point Philadelphia (PPP). This NEP, we find, needs to add 2 or 3 new sites in neighborhoods with the highest density of IDU AIDS cases, and to increase its total IDU client base by about 28%, from approximately 6400 to 8200 IDU clients. The case-study NEP also needs to increase its hours of operation at two existing sites, where the number of needles distributed per client is currently sub-optimal, by 50%. At the optimal allocation, the estimated cost per case of HIV averted would be dollar 2800 (range dollar 2300-dollar 4200). Such a favorable cost-effectiveness ratio derives primarily from PPP's low marginal costs per distributed needle.

Improved allocation of HIV prevention resources: using information about prevention program production functions

To allocate HIV prevention resources effectively, it is important to have information about the effectiveness of alternative prevention programs as a function of expenditure. We refer to this relationship as the "production function" for a prevention program. Few studies of HIV prevention programs have reported this relationship. This paper demonstrates the value of such information. We present a simple model for allocating HIV prevention resources, and apply the model to an illustrative HIV prevention resource allocation problem. We show that, without sufficient information about prevention program production functions, suboptimal decisions may be made. We show that epidemiologic data, such as estimates of HIV prevalence or incidence, may not provide enough information to support optimal allocation of HIV prevention resources. Our results suggest that good allocations can be obtained based on fairly basic information about prevention program production functions: an estimate of fixed cost plus a single estimate of cost and resulting risk reduction. We find that knowledge of production functions is most important when fixed cost is high and/or when the budget is a significantly constraining factor. We suggest that, at the minimum, future data collection on prevention program effectiveness should include fixed and variable cost estimates for the intervention when implemented at a "typical" level, along with a detailed description of the intervention and detailed description of costs by category.

Resource allocation for control of infectious diseases in multiple independent populations: beyond cost-effectiveness analysis

Traditional cost-effectiveness analysis (CEA) assumes that program costs and benefits scale linearly with investment-an unrealistic assumption for epidemic control programs. This paper combines epidemic modeling with optimization techniques to determine the optimal allocation of a limited resource for epidemic control among multiple noninteracting populations. We show that the optimal resource allocation depends on many factors including the size of each population, the state of the epidemic in each population before resources are allocated (e.g. infection prevalence and incidence), the length of the time horizon, and prevention program characteristics. We establish conditions that characterize the optimal solution in certain cases.

Integer/linear mathematical programming models: a tool for allocating healthcare resources

In today's environment, the demand for efficient healthcare resource allocation is increasing. As new technologies become available, allocation decisions become more complex and tools to assist decision makers in determining efficient allocations of healthcare resources are encouraged. Mathematical programs have multiple properties that are desirable for healthcare decision makers such as the simultaneous consideration of multiple constraints and a built-in sensitivity analysis. These models have been well researched and are considered invaluable in other industries. Mathematical programming has also become increasingly visible in facilitating the allocation of healthcare resources in the health services research sector. However, the use of mathematical programming tools has been limited in economic evaluations of new technologies. Budget allocations, such as formulary, drug development, and pricing decisions may benefit greatly from the use of mathematical programs. As an increasing number of expensive new technologies become available and pressure grows to contain healthcare costs, these tools may help guide a more efficient allocation of resources for technologies under budgetary and other constraints.

Optimal allocation of resources across four interventions for type 2 diabetes

BACKGROUND

Several interventions can be applied to prevent complications of type 2 diabetes. This article examines the optimal allocation of resources across 4 interventions to treat patients newly diagnosed with type 2 diabetes. The interventions are intensive glycemic control, intensified hypertension control, cholesterol reduction, and smoking cessation.

METHODS

A linear programming model was designed to select sets of interventions to maximize quality-adjusted life years (QALYs), subject to varied budget and equity constraints.

RESULTS

For no additional cost, approximately 211,000 QALYs can be gained over the lifetimes of all persons newly diagnosed with diabetes by implementing interventions rather than standard care. With increased availability of funds, additional health benefits can be gained but with diminishing marginal returns. The impact of equity constraints is extensive compared to the solution with the same intervention costs and no equity constraint. Under the conditions modeled, intensified hypertension control and smoking cessation interventions were provided most often, and intensive glycemic control and cholesterol reduction interventions were provided less often.

CONCLUSIONS

A resource allocation model identifies trade-offs involved when imposing budget and equity constraints on care for individuals with newly diagnosed diabetes.

Optimal investment in a portfolio of HIV prevention programs

OBJECTIVES

In this article, the authors determine the optimal allocation of HIV prevention funds and investigate the impact of different allocation methods on health outcomes.

METHODS

The authors present a resource allocation model that can be used to determine the allocation of HIV prevention funds that maximizes quality-adjusted life years (or life years) gained or HIV infections averted in a population over a specified time horizon. They apply the model to determine the allocation of a limited budget among 3 types of HIV prevention programs in a population of injection drug users and nonusers: needle exchange programs, methadone maintenance treatment, and condom availability programs. For each prevention program, the authors estimate a production function that relates the amount invested to the associated change in risky behavior.

RESULTS

The authors determine the optimal allocation of funds for both objective functions for a high-prevalence population and a low-prevalence population. They also consider the allocation of funds under several common rules of thumb that are used to allocate HIV prevention resources. It is shown that simpler allocation methods (e.g., allocation based on HIV incidence or notions of equity among population groups) may lead to alloctions that do not yield the maximum health benefit.

CONCLUSIONS

The optimal allocation of HIV prevention funds in a population depends on HIV prevalence and incidence, the objective function, the production functions for the prevention programs, and other factors. Consideration of cost, equity, and social and political norms may be important when allocating HIV prevention funds. The model presented in this article can help decision makers determine the health consequences of different allocations of funds.

AIDS policy modeling for the 21st century: an overview of key issues

Decisions about HIV prevention and treatment programs are based on factors such as program costs and health benefits, social and ethical issues, and political considerations. AIDS policy models--that is, models that evaluate the monetary and non-monetary consequences of decisions about HIV/AIDS interventions--can play a role in helping policy makers make better decisions. This paper provides an overview of the key issues related to developing useful AIDS policy models. We highlight issues of importance for researchers in the field of AIDS policy modeling as well as for policy makers. These include geographic area, setting, target groups, interventions, affordability and effectiveness of interventions, type and time horizon of policy model, and type of economic analysis. This paper is not intended to be an exhaustive review of the AIDS policy modeling literature, although many papers from the literature are discussed as examples; rather, we aim to convey the composition, achievements, and challenges of AIDS policy modeling.