Dose-Optimal Vaccine Allocation over Multiple Populations

To give or not to give? Pandemic vaccine donation policy

OBJECTIVES

The purpose of this work is to characterize scenarios under which it may be in a donor country's own public health interests to donate vaccine doses to another country before its own population has been fully vaccinated. In these scenarios, vaccinating other countries can delay the evolution of new variants of the virus, decrease total deaths, and, in some cases, decrease deaths in the donor countries.

STUDY DESIGN

We simulate the effects of different vaccine donation policies using an epidemiological model employing COVID-19 transmission parameters.

METHODS

We use the epidemiological model of Holleran et al. that incorporates virus mutation to simulate epidemic progression and estimate numbers of deaths arising from several vaccine allocation policies (donor-first, non-donor-first, and vaccine sharing) across a number of scenarios. We analyze the results in light of herd immunity limits derived in Holleran et al.

RESULTS

We identify realistic scenarios under which a donor country prefers to donate vaccines before distributing them locally in order to minimize local deaths during a pandemic. We demonstrate that a non-donor-first vaccination policy can delay, sometimes dramatically, the emergence of more-contagious variants. Even more surprising, donating all vaccines is sometimes better for the donor country than a sharing policy in which half of the vaccines are donated, and half are retained because of the impact donation can have on delaying the emergence of a more contagious virus. Non-donor-first vaccine allocation is optimal in scenarios in which the local health impact of the vaccine is limited or when delaying the emergence of a variant is especially valuable.

CONCLUSION

In all cases, we find that vaccine distribution is not a zero-sum game between donor and non-donor countries, illustrating the general moral reasons to donate vaccines. In some cases, donor nations can also realize local health benefits from donating vaccines. The insights yielded by this framework can be used to guide equitable vaccine distribution in future pandemics.

Fair-split distribution of multi-dose vaccines with prioritized age groups and dynamic demand: The case study of COVID-19

The emergence of the SARS-CoV-2 virus and new viral variations with higher transmission and mortality rates have highlighted the urgency to accelerate vaccination to mitigate the morbidity and mortality of the COVID-19 pandemic. For this purpose, this paper formulates a new multi-vaccine, multi-depot location-inventory-routing problem for vaccine distribution. The proposed model addresses a wide variety of vaccination concerns: prioritizing age groups, fair distribution, multi-dose injection, dynamic demand, etc. To solve large-size instances of the model, we employ a Benders decomposition algorithm with a number of acceleration techniques. To monitor the dynamic demand of vaccines, we propose a new adjusted susceptible-infectious-recovered (SIR) epidemiological model, where infected individuals are tested and quarantined. The solution to the optimal control problem dynamically allocates the vaccine demand to reach the endemic equilibrium point. Finally, to illustrate the applicability and performance of the proposed model and solution approach, the paper reports extensive numerical experiments on a real case study of the vaccination campaign in France. The computational results show that the proposed Benders decomposition algorithm is 12 times faster, and its solutions are, on average, 16% better in terms of quality than the Gurobi solver under a limited CPU time. In terms of vaccination strategies, our results suggest that delaying the recommended time interval between doses of injection by a factor of 1.5 reduces the unmet demand up to 50%. Furthermore, we observed that the mortality is a convex function of fairness and an appropriate level of fairness should be adapted through the vaccination.

Optimality of Maximal-Effort Vaccination

It is widely acknowledged that vaccinating at maximal effort in the face of an ongoing epidemic is the best strategy to minimise infections and deaths from the disease. Despite this, no one has proved that this is guaranteed to be true if the disease follows multi-group SIR (Susceptible-Infected-Recovered) dynamics. This paper provides a novel proof of this principle for the existing SIR framework, showing that the total number of deaths or infections from an epidemic is decreasing in vaccination effort. Furthermore, it presents a novel model for vaccination which assumes that vaccines assigned to a subgroup are distributed randomly to the unvaccinated population of that subgroup. It suggests, using COVID-19 data, that this more accurately captures vaccination dynamics than the model commonly found in the literature. However, as the novel model provides a strictly larger set of possible vaccination policies, the results presented in this paper hold for both models.

Optimal vaccine allocation for the control of sexually transmitted infections

The burden of sexually transmitted infections (STIs) poses a challenge due to its large negative impact on sexual and reproductive health worldwide. Besides simple prevention measures and available treatment efforts, prophylactic vaccination is a powerful tool for controlling some viral STIs and their associated diseases. Here, we investigate how prophylactic vaccines are best distributed to prevent and control STIs. We consider sex-specific differences in susceptibility to infection, as well as disease severity outcomes. Different vaccination strategies are compared assuming distinct budget constraints that mimic a scarce vaccine stockpile. Vaccination strategies are obtained as solutions to an optimal control problem subject to a two-sex Kermack-McKendrick-type model, where the control variables are the daily vaccination rates for females and males. One important aspect of our approach relies on conceptualizing a limited but specific vaccine stockpile via an isoperimetric constraint. We solve the optimal control problem via Pontryagin's Maximum Principle and obtain a numerical approximation for the solution using a modified version of the forward-backward sweep method that handles the isoperimetric budget constraint in our formulation. The results suggest that for a limited vaccine supply ([Formula: see text]-[Formula: see text] vaccination coverage), one-sex vaccination, prioritizing females, appears to be more beneficial than the inclusion of both sexes into the vaccination program. Whereas, if the vaccine supply is relatively large (enough to reach at least [Formula: see text] coverage), vaccinating both sexes, with a slightly higher rate for females, is optimal and provides an effective and faster approach to reducing the prevalence of the infection.

Comparative performance of between-population vaccine allocation strategies with applications for emerging pandemics

Vaccine allocation decisions during emerging pandemics have proven to be challenging due to competing ethical, practical, and political considerations. Complicating decision making, policy makers need to consider vaccine allocation strategies that balance needs both within and between populations. When vaccine stockpiles are limited, doses should be allocated in locations to maximize their impact. Using a susceptible-exposed-infectious-recovered (SEIR) model we examine optimal vaccine allocation decisions across two populations considering the impact of characteristics of the population (e.g., size, underlying immunity, heterogeneous risk structure, interaction), vaccine (e.g., vaccine efficacy), pathogen (e.g., transmissibility), and delivery (e.g., varying speed and timing of rollout). Across a wide range of characteristics considered, we find that vaccine allocation proportional to population size (i.e., pro-rata allocation) performs either better or comparably to nonproportional allocation strategies in minimizing the cumulative number of infections. These results may argue in favor of sharing of vaccines between locations in the context of an epidemic caused by an emerging pathogen, where many epidemiologic characteristics may not be known.

Optimal spatial evaluation of a pro rata vaccine distribution rule for COVID-19

The COVID-19 Vaccines Global Access (COVAX) is a World Health Organization (WHO) initiative that aims for an equitable access of COVID-19 vaccines. Despite potential heterogeneous infection levels across a country, countries receiving allotments of vaccines may follow WHO's allocation guidelines and distribute vaccines based on a jurisdictions' relative population size. Utilizing economic-epidemiological modeling, we benchmark the performance of this pro rata allocation rule by comparing it to an optimal one that minimizes the economic damages and expenditures over time, including a penalty representing the social costs of deviating from the pro rata strategy. The pro rata rule performs better when the duration of naturally- and vaccine-acquired immunity is short, when there is population mixing, when the supply of vaccine is high, and when there is minimal heterogeneity in demographics. Despite behavioral and epidemiological uncertainty diminishing the performance of the optimal allocation, it generally outperforms the pro rata vaccine distribution rule.

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.

Optimal vaccination: various (counter) intuitive examples

In previous articles, we formalized the problem of optimal allocation strategies for a (perfect) vaccine in an infinite-dimensional metapopulation model. The aim of the current paper is to illustrate this theoretical framework with multiple examples where one can derive the analytic expression of the optimal strategies. We discuss in particular the following points: whether or not it is possible to vaccinate optimally when the vaccine doses are given one at a time (greedy vaccination strategies); the effect of assortativity (that is, the tendency to have more contacts with similar individuals) on the shape of optimal vaccination strategies; the particular case where everybody has the same number of neighbors.

Emergency order allocation of e-medical supplies due to the disruptive events of the healthcare crisis

The availability of electronic (e-medical) homecare essentials, such as thermometers, oximeters, and oxygen concentrators during the peaks of the pandemic coronavirus disease (COVID-19), has been witnessed as critical in saving the lives of people across the world. This paper presents a supply order allocation strategy of e-medical homecare essentials (HCEs) in a multi-supplier environment by a distributor while ensuring sufficient and timely availability for emergency consumption during pandemic peaks. The results, based on the actual demand data of HCEs obtained from a regional HCE distributor during the pandemic peak of the second wave in India, i.e. April-May 2021, suggest that a minimum (maximum) average of 94% (98%) availability of e-medical HCEs respectively at pharmacies could be achieved during the peak demand period using the proposed emergency order allocation algorithm in this study. Conclusively, the analysis of this study could generate insightful implications for emergency operations decisions in the HCEs supply-distribution channel.

Bi-objective optimization of a stochastic resilient vaccine distribution network in the context of the COVID-19 pandemic

This paper develops an approach to optimize a vaccine distribution network design through a mixed-integer nonlinear programming model with two objectives: minimizing the total expected number of deaths among the population and minimizing the total distribution cost of the vaccination campaign. Additionally, we assume that a set of input parameters (e.g., death rate, social contacts, vaccine supply, etc.) is uncertain, and the distribution network is exposed to disruptions. We then investigate the resilience of the distribution network through a scenario-based robust-stochastic optimization approach. The proposed model is linearized and finally validated through a real case study of the COVID-19 vaccination campaign in France. We show that the current vaccination strategies are not optimal, and vaccination prioritization among the population and the equity of vaccine distribution depend on other factors than those conceived by health policymakers. Furthermore, we demonstrate that a vaccination strategy mixing the population prioritization and the quarantine restrictions leads to an 8.5% decrease in the total number of deaths.

Managing two-dose COVID-19 vaccine rollouts with limited supply: Operations strategies for distributing time-sensitive resources

Distributing scarce resources such as COVID-19 vaccines is often a highly time-sensitive and mission-critical operation. Our research was prompted by a significant obstacle that the United States and other nations encountered during the early months of the COVID-19 vaccination campaign: Most COVID-19 vaccines require two doses given 3 or 4 weeks apart. Given the severely limited supply and mounting pressure on many countries to reduce hospitalizations and mortality, how to effectively roll out two-dose vaccines was a critical policy decision. In this paper, we first model and analyze inventory dynamics of the rollout process under three rollout strategies: (1) holding back second doses, (2) releasing second doses, and (3) stretching the lead time between doses. Then we develop an SEIR (susceptible, exposed, infectious, recovered) model that incorporates COVID-19 asymptomatic and symptomatic infections to evaluate these strategies in terms of infections, hospitalizations, and mortality. Among our findings, we show releasing second doses reduces infections but creates uneven vaccination patterns. In addition, to ensure second doses are given on time without holding back inventory, strictly less than half of the supply can be allocated to first-dose appointments. Stretching the between-dose lead time flattens the infection curve and reduces both hospitalizations and mortality compared with the strategy of releasing second doses. We also consider an alternative single-dose vaccine with lower efficacy and show that the vaccine can be more effective than its two-dose counterparts in reducing infections and mortality. We conduct extensive sensitivity analyses related to age composition, risk-based prioritization, supply disruptions, and disease transmissibility. Our paper provides important implications for policymakers to develop effective vaccine rollout strategies in developed and developing countries alike. More broadly, our paper sheds light on how to develop effective operations strategies for distributing time-sensitive resources in times of crisis.

A decision analytic approach for social distancing policies during early stages of COVID-19 pandemic

The COVID-19 pandemic has become a crucial public health problem in the world that disrupted the lives of millions in many countries including the United States. In this study, we present a decision analytic approach which is an efficient tool to assess the effectiveness of early social distancing measures in communities with different population characteristics. First, we empirically estimate the reproduction numbers for two different states. Then, we develop an age-structured compartmental simulation model for the disease spread to demonstrate the variation in the observed outbreak. Finally, we analyze the computational results and show that early trigger social distancing strategies result in smaller death tolls; however, there are relatively larger second waves. Conversely, late trigger social distancing strategies result in higher initial death tolls but relatively smaller second waves. This study shows that decision analytic tools can help policy makers simulate different social distancing scenarios at the early stages of a global outbreak. Policy makers should expect multiple waves of cases as a result of the social distancing policies implemented when there are no vaccines available for mass immunization and appropriate antiviral treatments.

How can age-based vaccine allocation strategies be optimized? A multi-objective optimization framework

Human life is deeply influenced by infectious diseases. A vaccine, when available, is one of the most effective ways of controlling the spread of an epidemic. However, vaccine shortage and uncertain vaccine effectiveness in the early stage of vaccine production make vaccine allocation a critical issue. To tackle this issue, we propose a multi-objective framework to optimize the vaccine allocation strategy among different age groups during an epidemic under vaccine shortage in this study. Minimizing total disease onsets and total severe cases are the two objectives of this vaccine allocation optimization problem, and the multistage feature of vaccine allocation are considered in the framework. An improved Strength Pareto Evolutionary Algorithm (SPEA2) is used to solve the optimization problem. To evaluate the two objectives under different strategies, a deterministic age-stratified extended SEIR model is developed. In the proposed framework, different combinations of vaccine effectiveness and vaccine production capacity are investigated, and it is identified that for COVID-19 the optimal strategy is highly related to vaccine-related parameters. When the vaccine effectiveness is low, allocating most of vaccines to 0-19 age group or 65+ age group is a better choice under a low production capacity, while allocating most of vaccines to 20-49 age group or 50-64 age group is a better choice under a relatively high production capacity. When the vaccine effectiveness is high, a better strategy is to allocate vaccines to 65+ age group under a low production capacity, while to allocate vaccines to 20-49 age group under a relatively high production capacity.

Comparative performance of between-population vaccine allocation strategies with applications for emerging pandemics

Vaccine allocation decisions during emerging pandemics have proven to be challenging due to competing ethical, practical, and political considerations. Complicating decision making, policy makers need to consider vaccine allocation strategies that balance needs both within and between populations. Due to limited vaccine stockpiles, vaccine doses should be allocated in locations where their impact will be maximized. Using a susceptible-exposed-infectious-recovered (SEIR) model we examine optimal vaccine allocation decisions across two populations considering the impact of population size, underlying immunity, continuous vaccine roll-out, heterogeneous population risk structure, and differences in disease transmissibility. We find that in the context of an emerging pathogen where many epidemiologic characteristics might not be known, equal vaccine allocation between populations performs optimally in most scenarios. In the specific case considering heterogeneous population risk structure, first targeting individuals at higher risk of transmission or death due to infection leads to equal resource allocation across populations.

Bi-objective optimization for a multi-period COVID-19 vaccination planning problem

This work investigates a new multi-period vaccination planning problem that simultaneously optimizes the total travel distance of vaccination recipients (service level) and the operational cost. An optimal plan determines, for each period, which vaccination sites to open, how many vaccination stations to launch at each site, how to assign recipients from different locations to opened sites, and the replenishment quantity of each site. We formulate this new problem as a bi-objective mixed-integer linear program (MILP). We first propose a weighted-sum and an ϵ -constraint methods, which rely on solving many single-objective MILPs and thus lose efficiency for practical-sized instances. To this end, we further develop a tailored genetic algorithm where an improved assignment strategy and a new dynamic programming method are designed to obtain good feasible solutions. Results from a case study indicate that our methods reduce the operational cost and the total travel distance by up to 9.3% and 36.6%, respectively. Managerial implications suggest enlarging the service capacity of vaccination sites can help improve the performance of the vaccination program. The enhanced performance of our heuristic is due to the newly proposed assignment strategy and dynamic programming method. Our findings demonstrate that vaccination programs during pandemics can significantly benefit from formal methods, drastically improving service levels and decreasing operational costs.

Dynamical intervention planning against COVID-19-like epidemics

COVID-19 has got us to face a new situation where, for the lack of ready-to-use vaccines, it is necessary to support vaccination with complex non-pharmaceutical strategies. In this paper, we provide a novel Mixed Integer Nonlinear Programming formulation for fine-grained optimal intervention planning (i.e., at the level of the single day) against newborn epidemics like COVID-19, where a modified SIR model accounting for heterogeneous population classes, social distancing and several types of vaccines (each with its efficacy and delayed effects), allows us to plan an optimal mixed strategy (both pharmaceutical and non-pharmaceutical) that takes into account both the vaccine availability in limited batches at selected time instants and the need for second doses while keeping hospitalizations and intensive care occupancy below a threshold and requiring that new infections die out at the end of the planning horizon. In order to show the effectiveness of the proposed formulation, we analyze a case study for Italy with realistic parameters.

Mitigation themes in supply chain research during the COVID-19 pandemic: a systematic literature review

Purpose

The purpose of this paper is to understand the themes and direction of supply chain mitigation and resilience research during the COVID-19 pandemic by conducting a systematic literature review (SLR) of supply chain mitigation literature since pandemic.

Design/methodology/approach

This study uses the Web of Science (WoS) Database to analyze the contribution in supply chain mitigation literature by authors, themes in supply chain mitigation and the citing articles. An investigation based on bibliometric approach for the SLR represents the bibliographic data of over 530 publications between the years 2020–2021. Additionally, the article also develops graphical visualizations of the bibliographic data analyzed using the R-program Bibliometrix to ascertain the top sources, authors, keywords and conceptual themes.

Findings

Most strategies in the existing literature focused on reactive approaches to supply chain disruption and current mitigation literature has not evolved in parallel to the changing macro environment leaving a wide gap in considering vaccines as a supply chain mitigation strategy. Hence, this study identifies the potential need to focus on building proactive supply chain mitigation strategies preferably by studying the role of vaccines in mitigating supply chains.

Practical implications

This article helps the reader to understand the scientific research in terms of contributions in supply chain mitigation research since pandemic. Though, the time frame considered limits the connection the findings to previous work on supply chain disruptions and mitigation, it offers an understanding of the various mitigation themes evolved in light of mitigating the supply chain disruptions as one caused by the current pandemic. Further, this research helps us understand how businesses can help reduce the social consequences by preventing the disruptions and helping life normalize during this ongoing COVID-19 pandemic.

Originality/value

This is the first of its kind contribution offering a SLR of supply chain mitigation strategies during the COVID-19 pandemic identifying the focal themes in current literature and establishing the need for future venues of research studying the role of vaccines in supply chain mitigation strategies.

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.

Vaccine and inclusion

In majoritarian democracies, popular policies may not be inclusive, and inclusive policies may not be popular. This dilemma raises the crucial question of when it is possible to design a policy that is both inclusive and popular. We address this question in the context of vaccine allocation in a polarized economy facing a pandemic. In such an economy, individuals are organized around distinct networks and groups and have in-group preferences. We provide a complete characterization of the set of inclusive and popular vaccine allocations. The findings imply that the number of vaccine doses necessary to generate an inclusive and popular vaccine allocation is greater than the one necessary to obtain an allocation that is only popular. The analysis further reveals that it is always possible to design the decision-making rule of the economy to implement an inclusive and popular vaccine allocation. Under such a rule, the composition of any group endowed with the veto power should necessarily reflect the diversity of the society.

Dynamic resource allocation for controlling pathogen spread on a large metapopulation network

To control the spread of an infectious disease over a large network, the optimal allocation by a social planner of a limited resource is a fundamental and difficult problem. We address this problem for a livestock disease that propagates on an animal trade network according to an epidemiological–demographic model based on animal demographics and trade data. We assume that the resource is dynamically allocated following a certain score, up to the limit of resource availability. We adapt a greedy approach to the metapopulation framework, obtaining new scores that minimize approximations of two different objective functions, for two control measures: vaccination and treatment. Through intensive simulations, we compare the greedy scores with several heuristics. Although topology-based scores can limit the spread of the disease, information on herd health status seems crucial to eradicating the disease. In particular, greedy scores are among the most effective in reducing disease prevalence, even though they do not always perform the best. However, some scores may be preferred in real life because they are easier to calculate or because they use a smaller amount of resources. The developed approach could be adapted to other epidemiological models or to other control measures in the metapopulation setting.

A fuzzy decision framework of lean-agile-green (LAG) practices for sustainable vaccine supply chain

Purpose

The already-strained vaccine supply chain (VSC) of the expanded program for immunization (EPI) require a more robust and structured distribution network for pandemic/outbreak vaccination due to huge volume demand and time constraint. In this paper, a lean-agile-green (LAG) practices approach is proposed to improve the operational, economic and environmental efficiency of the VSC.

Design/methodology/approach

A fuzzy decision framework of importance performance analysis (IPA)–analytical hierarchy process (AHP)–technique for order for preference by similarity in ideal solution (TOPSIS) has been presented in this paper to prioritize the LAG practices on the basis of the influence on performance indicators. Sensitivity analysis is carried out to check the robustness of the presented model.

Findings

The derived result indicates that sustainable packaging, coordination among supply chain stakeholders and cold chain technology improvement are among the top practices affecting most of the performance parameters of VSC. The sensitivity analysis reveals that the priority of practices is highly dependent on the weightage of performance indicators.

Practical implications

This study's finding will help policymakers reframe strategies for sustainable VSC (SVSC) by including new management practices that can handle regular immunization programs as well as emergency mass vaccination.

Originality/value

To the best of the authors' knowledge, this is the first study that proposes the LAG framework for SVSC. The IPA–Fuzzy AHP (FAHP)–Fuzyy TOPSIS (FTOPSIS) is also a novel combination in decision-making.

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.

Model-informed COVID-19 vaccine prioritization strategies by age and serostatus

Limited initial supply of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine raises the question of how to prioritize available doses. We used a mathematical model to compare five age-stratified prioritization strategies. A highly effective transmission-blocking vaccine prioritized to adults ages 20 to 49 years minimized cumulative incidence, but mortality and years of life lost were minimized in most scenarios when the vaccine was prioritized to adults greater than 60 years old. Use of individual-level serological tests to redirect doses to seronegative individuals improved the marginal impact of each dose while potentially reducing existing inequities in COVID-19 impact. Although maximum impact prioritization strategies were broadly consistent across countries, transmission rates, vaccination rollout speeds, and estimates of naturally acquired immunity, this framework can be used to compare impacts of prioritization strategies across contexts.

Model-informed COVID-19 vaccine prioritization strategies by age and serostatus

Limited initial supply of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine raises the question of how to prioritize available doses. We used a mathematical model to compare five age-stratified prioritization strategies. A highly effective transmission-blocking vaccine prioritized to adults ages 20 to 49 years minimized cumulative incidence, but mortality and years of life lost were minimized in most scenarios when the vaccine was prioritized to adults greater than 60 years old. Use of individual-level serological tests to redirect doses to seronegative individuals improved the marginal impact of each dose while potentially reducing existing inequities in COVID-19 impact. Although maximum impact prioritization strategies were broadly consistent across countries, transmission rates, vaccination rollout speeds, and estimates of naturally acquired immunity, this framework can be used to compare impacts of prioritization strategies across contexts.

Complexity analysis of cold chain transportation in a vaccine supply chain considering activity inspection and time-delay

The development of COVID-19 vaccine is highly concerned by all countries in the world. So far, many kinds of COVID-19 vaccines have entered phase III clinical trial. However, it is difficult to deliver COVID-19 vaccines efficiently and safely to the areas affected by the epidemic. This paper focuses on vaccine transportation in a supply chain model composed of one distributor and one retailer (clinic or hospital), in which the distributor procures COVID-19 vaccines from the manufacturer and then resells them to the retailer. Distributor detects the activity level of the vaccines, and retailer is responsible for transportation of the vaccines. Firstly, we establish a difference equations model with time-delay. Secondly, we investigate the impact of time-delay on the stability of vaccine supply chain. In addition, we explore the influence of decision adjustment speed of the distributor (or retailer) on the stability of vaccine supply chain. Finally, we verify the theoretical results by a two-dimensional bifurcation diagram, the largest Lyapunov exponent, entropy, and domain of attraction. The results show that when the decision delay-time or the adjustment speed of decision variables exceeds a certain threshold, it brings a negative impact on the stability of vaccine supply chain system. The stability domain of the system shrinks as customers' sensitivity to cold chain transportation decreases and by contrast expends as customers' sensitivity to vaccine prices decreases. When the vaccine supply chain is in a state of chaos, the effect of external control over the system is superior to that of internal control over the system.

Infectious or Recovered? Optimizing the Infectious Disease Detection Process for Epidemic Control and Prevention Based on Social Media

Detecting the period of a disease is of great importance to building information management capacity in disease control and prevention. This paper aims to optimize the disease surveillance process by further identifying the infectious or recovered period of flu cases through social media. Specifically, this paper explores the potential of using public sentiment to detect flu periods at word level. At text level, we constructed a deep learning method to classify the flu period and improve the classification result with sentiment polarity. Three important findings are revealed. Firstly, bloggers in different periods express significantly different sentiments. Blogger sentiments in the recovered period are more positive than in the infectious period when measured by the interclass distance. Secondly, the optimized disease detection process can substantially improve the classification accuracy of flu periods from 0.876 to 0.926. Thirdly, our experimental results confirm that sentiment classification plays a crucial role in accuracy improvement. Precise identification of disease periods enhances the channels for the disease surveillance processes. Therefore, a disease outbreak can be predicted credibly when a larger population is monitored. The research method proposed in our work also provides decision making reference for proactive and effective epidemic control and prevention in real time.

Optimal vaccine allocation during the mumps outbreak in two SIR centres

The aim of this work is to investigate the optimal vaccine sharing between two susceptible, infected, removed (SIR) centres in the presence of migration fluxes of susceptibles and infected individuals during the mumps outbreak. Optimality of the vaccine allocation means the minimization of the total number of lost working days during the whole period of epidemic outbreak $[0,t_f]$, which can be described by the functional $Q=\int _0^{t_f}I(t)\,{\textrm{d}}t$, where $I(t)$ stands for the number of infectives at time $t$. We explain the behaviour of the optimal allocation, which depends on the model parameters and the amount of vaccine available $V$.

A theoretical single-parameter model for urbanisation to study infectious disease spread and interventions

The world is continuously urbanising, resulting in clusters of densely populated urban areas and more sparsely populated rural areas. We propose a method for generating spatial fields with controllable levels of clustering of the population. We build a synthetic country, and use this method to generate versions of the country with different clustering levels. Combined with a metapopulation model for infectious disease spread, this allows us to in silico explore how urbanisation affects infectious disease spread. In a baseline scenario with no interventions, the underlying population clustering seems to have little effect on the final size and timing of the epidemic. Under within-country restrictions on non-commuting travel, the final size decreases with increased population clustering. The effect of travel restrictions on reducing the final size is larger with higher clustering. The reduction is larger in the more rural areas. Within-country travel restrictions delay the epidemic, and the delay is largest for lower clustering levels. We implemented three different vaccination strategies-uniform vaccination (in space), preferentially vaccinating urban locations and preferentially vaccinating rural locations. The urban and uniform vaccination strategies were most effective in reducing the final size, while the rural vaccination strategy was clearly inferior. Visual inspection of some European countries shows that many countries already have high population clustering. In the future, they will likely become even more clustered. Hence, according to our model, within-country travel restrictions are likely to be less and less effective in delaying epidemics, while they will be more effective in decreasing final sizes. In addition, to minimise final sizes, it is important not to neglect urban locations when distributing vaccines. To our knowledge, this is the first study to systematically investigate the effect of urbanisation on infectious disease spread and in particular, to examine effectiveness of prevention measures as a function of urbanisation.