The most efficient critical vaccination coverage and its equivalence with maximizing the herd effect

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.

Optimizing two-dose vaccine resource allocation to combat a pandemic in the context of limited supply: The case of COVID-19

The adequate vaccination is a promising solution to mitigate the enormous socio-economic costs of the ongoing COVID-19 pandemic and allow us to return to normal pre-pandemic activity patterns. However, the vaccine supply shortage will be inevitable during the early stage of the vaccine rollout. Public health authorities face a crucial challenge in allocating scarce vaccines to maximize the benefits of vaccination. In this paper, we study a multi-period two-dose vaccine allocation problem when the vaccine supply is highly limited. To address this problem, we constructed a novel age-structured compartmental model to capture COVID-19 transmission and formulated as a nonlinear programming (NLP) model to minimize the total number of deaths in the population. In the NLP model, we explicitly take into account the two-dose vaccination procedure and several important epidemiologic features of COVID-19, such as pre-symptomatic and asymptomatic transmission, as well as group heterogeneity in susceptibility, symptom rates, severity, etc. We validated the applicability of the proposed model using a real case of the 2021 COVID-19 vaccination campaign in the Midlands of England. We conducted comparative studies to demonstrate the superiority of our method. Our numerical results show that prioritizing the allocation of vaccine resources to older age groups is a robust strategy to prevent more subsequent deaths. In addition, we show that releasing more vaccine doses for first-dose recipients could lead to a greater vaccination benefit than holding back second doses. We also find that it is necessary to maintain appropriate non-pharmaceutical interventions (NPIs) during the vaccination rollout, especially in low-resource settings. Furthermore, our analysis indicates that starting vaccination as soon as possible is able to markedly alleviate the epidemic impact when the vaccine resources are limited but are currently available. Our model provides an effective tool to assist policymakers in developing adaptive COVID-19 likewise vaccination strategies for better preparedness against future pandemic threats.

Optimal vaccination at high reproductive numbers: sharp transitions and counterintuitive allocations

Optimization of vaccine allocations among different segments of a heterogeneous population is important for enhancing the effectiveness of vaccination campaigns in reducing the burden of epidemics. Intuitively, it would seem that allocations designed to minimize infections should prioritize those with the highest risk of being infected and infecting others. This prescription is well supported by vaccination theory, e.g. when the vaccination campaign aims to reach herd immunity. In this work, we show, however, that for vaccines providing partial protection (leaky vaccines) and for sufficiently high values of the basic reproduction number, intuition is overturned: the optimal allocation minimizing the number of infections prioritizes the vaccination of those who are least likely to be infected. The work combines numerical investigations, asymptotic analysis for a general model, and complete mathematical analysis in a two-group model. The results point to important considerations in managing vaccination campaigns for infections with high transmissibility.

Time-dependent force of infection and effective reproduction ratio in an age-structure dengue transmission model in Bandung City, Indonesia

Dengue virus infection is a leading health problem in many endemic countries, including Indonesia, characterized by high morbidity and wide spread. It is known that the risk factors that influence the transmission intensity vary among different age groups, which can have implications for dengue control strategies. A time-dependent four - age structure model of dengue transmission was constructed in this study. A vaccination scenario as control strategy was also applied to one of the age groups. Daily incidence data of dengue cases from Santo Borromeus Hospital, Bandung, Indonesia, from 2014 to 2016 was used to estimate the infection rate. We used two indicators to identify the changes in dengue transmission intensity for this period in each age group: the annual force of infection (FoI) and the effective reproduction ratio based on a time-dependent transmission rate. The results showed that the yearly FoI of children (age 0-4 years) increased significantly from 2014 to 2015, at 10.08%. Overall, the highest FoI before and after vaccination occurred in youngsters (age 5-14 years), with a FoI of about 6% per year. In addition, based on the daily effective reproduction ratio, it was found that vaccination of youngsters could reduce the number of dengue cases in Bandung city faster than vaccination of children.

An epidemiology-based model for the operational allocation of COVID-19 vaccines: A case study of Thailand

This paper addresses a framework for the operational allocation and administration of COVID-19 vaccines in Thailand, based on both COVID-19 transmission dynamics and other vital operational restrictions that might affect the effectiveness of vaccination strategies in the early stage of vaccine rollout. In this framework, the SIQRV model is first developed and later combined with the COVID-19 Vaccine Allocation Problem (CVAP) to determine the optimal allocation/administration strategies that minimize total weighted strain on the whole healthcare system. According to Thailand's second pandemic wave data (17^th January 2021, to 15^th February 2021), we find that the epicenter-based strategy is surprisingly the worst allocation strategy, due largely to the negligence of provincial demographics, vaccine efficacy, and overall transmission dynamics that lead to higher number of infectious individuals. We also find that early vaccination seems to significantly contribute to the reduction in the number of infectious individuals, whose effects tend to increase with more vaccine supply. With these insights, healthcare policy-makers should therefore focus not only on the procurement of COVID-19 vaccines at strategic levels but also on the allocation and administration of such vaccines at operational levels for the best of their limited vaccine supply.

The role of childrens’ vaccination for COVID-19—Pareto-optimal allocations of vaccines

COVID-19 vaccines have been approved for children of age five and older in many countries. However, there is an ongoing debate as to whether children should be vaccinated and at what priority. In this work, we use mathematical modeling and optimization to study how vaccine allocations to different age groups effect epidemic outcomes. In particular, we consider the effect of extending vaccination campaigns to include the vaccination of children. When vaccine availability is limited, we consider Pareto-optimal allocations with respect to competing measures of the number of infections and mortality and systematically study the trade-offs among them. In the scenarios considered, when some weight is given to the number of infections, we find that it is optimal to allocate vaccines to adolescents in the age group 10-19, even when they are assumed to be less susceptible than adults. We further find that age group 0-9 is included in the optimal allocation for sufficiently high values of the basic reproduction number.

The management of a vaccination campaign requires constant evaluation, and, as conditions change, redesign of the campaign for the future. One example of a change that leads to a decision point is the extension of vaccine eligibility to broader segments of the population. Indeed, one of the questions public health experts and policymakers confront is whether children of age 5 and older should be vaccinated against COVID-19 and at what priority. In this work, we use mathematical and computational methods to study this question in a systematic, quantitative way, by considering optimal outcomes, under different criteria for optimality, that can be achieved with and without vaccination of children, under conditions of limited vaccine availability. To explore tradeoffs among different goals, such as reducing the number of infections and reducing mortality, we use the the idea of Pareto optimization. Our results show that, under a broad range of conditions, optimal vaccine allocations include vaccination of age group 10–19, while the population-level benefits of vaccination of age group 0–9 depend on the reproductive number and vaccine availability.

Data-driven prediction and origin identification of epidemics in population networks

Effective intervention strategies for epidemics rely on the identification of their origin and on the robustness of the predictions made by network disease models. We introduce a Bayesian uncertainty quantification framework to infer model parameters for a disease spreading on a network of communities from limited, noisy observations; the state-of-the-art computational framework compensates for the model complexity by exploiting massively parallel computing architectures. Using noisy, synthetic data, we show the potential of the approach to perform robust model fitting and additionally demonstrate that we can effectively identify the disease origin via Bayesian model selection. As disease-related data are increasingly available, the proposed framework has broad practical relevance for the prediction and management of epidemics.

Optimised prophylactic vaccination in metapopulations

A highly effective method for controlling the spread of an infectious disease is vaccination. However, there are many situations where vaccines are in limited supply. The ability to determine, under this constraint, a vaccination strategy which minimises the number of people that become infected over the course of a potential epidemic is essential. Two questions naturally arise: when is it best to allocate vaccines, and to whom should they be allocated? We address these questions in the context of metapopulation models of disease spread. We discover that in practice it is generally optimal to distribute all vaccines prophylactically, rather than withholding until infection is introduced. For small metapopulations, we provide a method for determining the optimal prophylactic allocation. As the optimal strategy becomes computationally intensive to obtain when the population size increases, we detail an approximation method to determine an approximately optimal vaccination scheme. We find that our approximate strategy is consistently at least as good as three strategies reported in the literature across a wide range of parameter values.

Dose-Optimal Vaccine Allocation over Multiple Populations

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.