Optimal allocation of limited vaccine to control an infectious disease: Simple analytical conditions.
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ABSTRACT:
SUBMITTER: Rao IJ
PROVIDER: S-EPMC8076816 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description: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.
| S-EPMC9288241 | biostudies-literature
Project description:Initial supply of the coronavirus disease (COVID-19) vaccine may be limited, necessitating its effective use. Herein, an age-structured model of COVID-19 spread in South Korea is parameterized to understand the epidemiological characteristics of COVID-19. The model determines optimal vaccine allocation for minimizing infections, deaths, and years of life lost while accounting for population factors, such as country-specific age distribution and contact structure, and various levels of vaccine efficacy. A transmission-blocking vaccine should be prioritized in adults aged 20-49 years and those older than 50 years to minimize the cumulative incidence and mortality, respectively. A strategy to minimize years of life lost involves the vaccination of adults aged 40-69 years, reflecting the relatively high case-fatality rates and years of life lost in this age group. An incidence-minimizing vaccination strategy is highly sensitive to vaccine efficacy, and vaccines with lower efficacy should be administered to teenagers and adults aged 50-59 years. Consideration of age-specific contact rates and vaccine efficacy is critical to optimize vaccine allocation. New recommendations for COVID-19 vaccines under consideration by the Korean Centers for Disease Control and Prevention are mainly based on a mortality-minimizing allocation strategy.
| S-EPMC7914460 | biostudies-literature
Project description:The World Health Organization (WHO) recently established a global stockpile of oral cholera vaccine (OCV) to be preferentially used in epidemic response (reactive campaigns) with any vaccine remaining after 1 year allocated to endemic settings. Hence, the number of cholera cases or deaths prevented in an endemic setting represents the minimum utility of these doses, and the optimal risk-averse response to any reactive vaccination request (i.e. the minimax strategy) is one that allocates the remaining doses between the requested epidemic response and endemic use in order to ensure that at least this minimum utility is achieved. Using mathematical models, we find that the best minimax strategy is to allocate the majority of doses to reactive campaigns, unless the request came late in the targeted epidemic. As vaccine supplies dwindle, the case for reactive use of the remaining doses grows stronger. Our analysis provides a lower bound for the amount of OCV to keep in reserve when responding to any request. These results provide a strategic context for the fulfilment of requests to the stockpile, and define allocation strategies that minimize the number of OCV doses that are allocated to suboptimal situations.
| S-EPMC4614506 | biostudies-literature
Project description:Vaccination is an effective way to prevent an epidemic. It results in immunity for the vaccinated individuals, but it also reduces the infection pressure for unvaccinated people. Thus people may actually escape infection without being vaccinated: the so-called "herd effect." We analytically study the relation between the herd effect and the vaccination fraction for the seminal SIR compartmental model, which consists of a set of differential equations describing the time course of an epidemic. We prove that the herd effect is in general convex-concave in the vaccination fraction and give precise conditions on the epidemic for the convex part to arise. We derive the significant consequences of these structural insights for allocating a limited vaccine stockpile to multiple non-interacting populations. We identify for each population a unique vaccination fraction that is most efficient per dose of vaccine: our dose-optimal coverage. We characterize the solution of the vaccine allocation problem and we show the crucial importance of the dose-optimal coverage. A single dose of vaccine may be a drop in the ocean, but multiple doses together can save a population. To benefit from this, policy makers should select a subset of populations to which the vaccines are allocated. Focusing on a limited number of populations can make a significant difference, whereas allocating equally to all populations would be substantially less effective.
| S-EPMC7168135 | biostudies-literature
Project description:Emerging infectious diseases such as Ebola Virus Disease (EVD), Nipah Virus Encephalitis and Lassa fever pose significant epidemic threats. Responses to emerging infectious disease outbreaks frequently occur in resource-constrained regions and under high pressure to quickly contain the outbreak prior to potential spread. As seen in the 2020 EVD outbreaks in the Democratic Republic of Congo and the current COVID-19 pandemic, there is a continued need to evaluate and address the ethical challenges that arise in the high stakes environment of an emerging infectious disease outbreak response. The research presented here provides analysis of the ethical challenges with regard to allocation of limited resources, particularly experimental therapeutics, using the 2013-2016 EVD outbreak in West Africa as a case study. In-depth semi-structured interviews were conducted with senior healthcare personnel (n = 16) from international humanitarian aid organizations intimately engaged in the 2013-2016 EVD outbreak response in West Africa. Interviews were recorded in private setting, transcribed, and iteratively coded using grounded theory methodology. A majority of respondents indicated a clear propensity to adopt an ethical framework of guiding principles for international responses to emerging infectious disease outbreaks. Respondents agreed that prioritization of frontline workers' access to experimental therapeutics was warranted based on a principle of reciprocity. There was widespread acceptance of adaptive trial designs and greater trial transparency in providing access to experimental therapeutics. Many respondents also emphasized the importance of community engagement in limited resource allocation scheme design and culturally appropriate informed consent procedures. The study results inform a potential ethical framework of guiding principles based on the interview participants' insights to be adopted by international response organizations and their healthcare workers in the face of allocating limited resources such as experimental therapeutics in future emerging infectious disease outbreaks to ease the moral burden of individual healthcare providers.
| S-EPMC7853513 | biostudies-literature
Project description:BackgroundCyanobacteria and other phototrophic microorganisms allow to couple the light-driven assimilation of atmospheric [Formula: see text] directly to the synthesis of carbon-based products, and are therefore attractive platforms for microbial cell factories. While most current engineering efforts are performed using small-scale laboratory cultivation, the economic viability of phototrophic cultivation also crucially depends on photobioreactor design and culture parameters, such as the maximal areal and volumetric productivities. Based on recent insights into the cyanobacterial cell physiology and the resulting computational models of cyanobacterial growth, the aim of this study is to investigate the limits of cyanobacterial productivity in continuous culture with light as the limiting nutrient.ResultsWe integrate a coarse-grained model of cyanobacterial growth into a light-limited chemostat and its heterogeneous light gradient induced by self-shading of cells. We show that phototrophic growth in the light-limited chemostat can be described using the concept of an average light intensity. Different from previous models based on phenomenological growth equations, our model provides a mechanistic link between intracellular protein allocation, population growth and the resulting reactor productivity. Our computational framework thereby provides a novel approach to investigate and predict the maximal productivity of phototrophic cultivation, and identifies optimal proteome allocation strategies for developing maximally productive strains.ConclusionsOur results have implications for efficient phototrophic cultivation and the design of maximally productive phototrophic cell factories. The model predicts that the use of dense cultures in well-mixed photobioreactors with short light-paths acts as an effective light dilution mechanism and alleviates the detrimental effects of photoinhibition even under very high light intensities. We recover the well-known trade-offs between a reduced light-harvesting apparatus and increased population density. Our results are discussed in the context of recent experimental efforts to increase the yield of phototrophic cultivation.
| S-EPMC6785936 | biostudies-literature
Project description:BackgroundThe world is currently confronting the first influenza pandemic of the 21(st) century. Influenza vaccination is an effective preventive measure, but the unique epidemiological features of swine-origin influenza A (H1N1) (pH1N1) introduce uncertainty as to the best strategy for prioritization of vaccine allocation. We sought to determine optimal prioritization of vaccine distribution among different age and risk groups within the Canadian population, to minimize influenza-attributable morbidity and mortality.Methodology/principal findingsWe developed a deterministic, age-structured compartmental model of influenza transmission, with key parameter values estimated from data collected during the initial phase of the epidemic in Ontario, Canada. We examined the effect of different vaccination strategies on attack rates, hospitalizations, intensive care unit admissions, and mortality. In all scenarios, prioritization of high-risk individuals (those with underlying chronic conditions and pregnant women), regardless of age, markedly decreased the frequency of severe outcomes. When individuals with underlying medical conditions were not prioritized and an age group-based approach was used, preferential vaccination of age groups at increased risk of severe outcomes following infection generally resulted in decreased mortality compared to targeting vaccine to age groups with higher transmission, at a cost of higher population-level attack rates. All simulations were sensitive to the timing of the epidemic peak in relation to vaccine availability, with vaccination having the greatest impact when it was implemented well in advance of the epidemic peak.Conclusions/significanceOur model simulations suggest that vaccine should be allocated to high-risk groups, regardless of age, followed by age groups at increased risk of severe outcomes. Vaccination may significantly reduce influenza-attributable morbidity and mortality, but the benefits are dependent on epidemic dynamics, time for program roll-out, and vaccine uptake.
| S-EPMC2865540 | biostudies-literature
Project description:With new cases of avian influenza H5N1 (H5N1AV) arising frequently, the threat of a new influenza pandemic remains a challenge for public health. Several vaccines have been developed specifically targeting H5N1AV, but their production is limited and only a few million doses are readily available. Because there is an important time lag between the emergence of new pandemic strain and the development and distribution of a vaccine, shortage of vaccine is very likely at the beginning of a pandemic. We coupled a mathematical model with a genetic algorithm to optimally and dynamically distribute vaccine in a network of cities, connected by the airline transportation network. By minimizing the illness attack rate (i.e., the percentage of people in the population who become infected and ill), we focus on optimizing vaccine allocation in a network of 16 cities in Southeast Asia when only a few million doses are available. In our base case, we assume the vaccine is well-matched and vaccination occurs 5 to 10 days after the beginning of the epidemic. The effectiveness of all the vaccination strategies drops off as the timing is delayed or the vaccine is less well-matched. Under the best assumptions, optimal vaccination strategies substantially reduced the illness attack rate, with a maximal reduction in the attack rate of 85%. Furthermore, our results suggest that cooperative strategies where the resources are optimally distributed among the cities perform much better than the strategies where the vaccine is equally distributed among the network, yielding an illness attack rate 17% lower. We show that it is possible to significantly mitigate a more global epidemic with limited quantities of vaccine, provided that the vaccination campaign is extremely fast and it occurs within the first weeks of transmission.
| S-EPMC3605056 | biostudies-literature
Project description:ObjectiveThe objective of this study was to implement a model-based approach to identify the optimal allocation of a coronavirus disease 2019 (COVID-19) vaccine in the province of Alberta, Canada.MethodsWe developed an epidemiologic model to evaluate allocation strategies defined by age and risk target groups, coverage, effectiveness and cost of vaccine. The model simulated hypothetical immunisation scenarios within a dynamic context, capturing concurrent public health strategies and population behavioural changes.ResultsIn a scenario with 80% vaccine effectiveness, 40% population coverage and prioritisation of those over the age of 60 years at high risk of poor outcomes, active cases are reduced by 17% and net monetary benefit increased by $263 million dollars, relative to no vaccine. Concurrent implementation of policies such as school closure and senior contact reductions have similar impacts on incremental net monetary benefit ($352 vs $292 million, respectively) when there is no prioritisation given to any age or risk group. When older age groups are given priority, the relative benefit of school closures is much larger ($214 vs $118 million). Results demonstrate that the rank ordering of different prioritisation options varies by prioritisation criteria, vaccine effectiveness and coverage, and concurrently implemented policies.ConclusionsOur results have three implications: (i) optimal vaccine allocation will depend on the public health policies in place at the time of allocation and the impact of those policies on population behaviour; (ii) outcomes of vaccine allocation policies can be greatly supported with interventions targeting contact reduction in critical sub-populations; and (iii) identification of the optimal strategy depends on which outcomes are prioritised.
| S-EPMC8209775 | biostudies-literature
Project description:For the control of COVID-19, vaccination programmes provide a long-term solution. The amount of available vaccines is often limited, and thus it is crucial to determine the allocation strategy. While mathematical modelling approaches have been used to find an optimal distribution of vaccines, there is an excessively large number of possible allocation schemes to be simulated. Here, we propose an algorithm to find a near-optimal allocation scheme given an intervention objective such as minimization of new infections, hospitalizations, or deaths, where multiple vaccines are available. The proposed principle for allocating vaccines is to target subgroups with the largest reduction in the outcome of interest. We use an approximation method to reconstruct the age-specific transmission intensity (the next generation matrix), and express the expected impact of vaccinating each subgroup in terms of the observed incidence of infection and force of infection. The proposed approach is firstly evaluated with a simulated epidemic and then applied to the epidemiological data on COVID-19 in the Netherlands. Our results reveal how the optimal allocation depends on the objective of infection control. In the case of COVID-19, if we wish to minimize deaths, the optimal allocation strategy is not efficient for minimizing other outcomes, such as infections. In simulated epidemics, an allocation strategy optimized for an outcome outperforms other strategies such as the allocation from young to old, from old to young, and at random. Our simulations clarify that the current policy in the Netherlands (i.e., allocation from old to young) was concordant with the allocation scheme that minimizes deaths. The proposed method provides an optimal allocation scheme, given routine surveillance data that reflect ongoing transmissions. This approach to allocation is useful for providing plausible simulation scenarios for complex models, which give a more robust basis to determine intervention strategies.
| S-EPMC8699630 | biostudies-literature