The COVID-19 pandemic began over two years ago, yet schools, businesses, and other organizations are still struggling to keep the risk of disease outbreak low while returning to (near) normal functionality. Observations from these past years suggest that this goal can be achieved through the right balance of mitigation strategies, which may include some combination of mask use, vaccinations, viral testing, and contact tracing. The choice of mitigation measures will be uniquely based on the needs and available resources of each organization. This article presents practical guidance for creating these policies based on an analytical model of disease spread that captures the combined effects of each of these interventions. The resulting guidance is tested through simulation across a wide range of parameters and used to discuss the spread of disease on college campuses.
India is one of the worst affected countries by the Covid-19 pandemic at present. We studied publicly available data of the Covid-19 patients in India and analyzed possible impacts of quarantine and social distancing within the stochastic framework of the SEQIR model to illustrate the controlling strategy of the pandemic. Our simulation results clearly show that proper quarantine and social distancing should be maintained from an early time just at the start of the pandemic and should be continued till its end to effectively control the pandemic. This calls for a more socially disciplined life…
Several analytical models have been used in this work to describe the evolution of death cases arising from coronavirus (COVID-19). The Death or `D' model is a simplified version of the SIR (susceptible-infected-recovered) model, which assumes no recovery over time, and allows for the transmission-dynamics equations to be solved analytically. The D-model can be extended to describe various focuses of infection, which may account for the original pandemic (D1), the lockdown (D2) and other effects (Dn). The evolution of the COVID-19 pandemic in several countries (China, Spain, Italy, France, UK,…
The COVID-19 pandemic is the profoundest health crisis of the 21rst century. The SARS-CoV-2 virus arrived in Brazil around March, 2020 and its social and economical backlashes are catastrophic. In this paper, it is investigated how Model Predictive Control (MPC) could be used to plan appropriate social distancing policies to mitigate the pandemic effects in Bahia and Santa Catarina, two states of different regions, culture, and population demography in Brazil. In addition, the parameters of Susceptible-Infected-Recovered-Deceased (SIRD) models for these two states are identified using an optim…
We propose two simple probability models to compute the probability of an influenza pandemic. Under a random walk model the probability that all pandemics between times 0 and 300 occur by time 150 is 1/2. Under a Poisson model with mean inter arrival time of 30 years the probability that no pandemic occurs during at least 60 years is 14%. These probabilities are much higher than generally perceived. So yes the next influenza pandemic will happen but maybe much later than generally thought.
The goal of this work is to study the optimal controls for the COVID-19 epidemic in Brazil. We consider an age-structured SEIRQ model with quarantine compartment, where the controls are the quarantine entrance parameters. We then compare the optimal controls for different quarantine lengths and distribution of the total control cost by assessing their respective reductions in deaths in comparison to the same period without quarantine. The best strategy provides a calendar of when to relax the isolation measures for each age group. Finally, we analyse how a delay in the beginning of the quarant…
We analytically study the SEIR (Susceptible Exposed Infectious Removed) epidemic model. The aim is to provide simple analytical expressions for the peak and asymptotic values and their characteristic times of the populations affected by the COVID-19 pandemic.
During a pandemic, there are conflicting demands arising from public health and economic cost. Lockdowns are a common way of containing infections, but they adversely affect the economy. We study the question of how to minimise the economic damage of a lockdown while still containing infections. Our analysis is based on the SIR model, which we analyse using a clock set by the virus. This use of the "virus time" permits a clean mathematical formulation of our problem. We optimise the economic cost for a fixed health cost and arrive at a strategy for navigating the pandemic. This involves adjust…
We provide a probabilistic SIRD model for the COVID-19 pandemic in Italy, where we allow the infection, recovery and death rates to be random. In particular, the underlying random factor is driven by a fractional Brownian motion. Our model is simple and needs only some few parameters to be calibrated.
In this study, we present a new epidemiological model, with contamination from confirmed and unreported. We also compute equilibria and study their stability without intervention strategies. Optimal control theory has proven to be a successful tool in understanding ways to curtail the spread of infectious diseases by devising the optimal disease intervention strategies. We investigate the impact of distancing, case finding, and case holding controls while at the same time, we minimize the number of infected and dead individuals. The method consists of minimizing the cost functional related to …
Universidad de Sevilla（塞维利亚大学）；Universidad Loyola Andalucía（安达卢西亚洛约拉大学）
This document analyzes the role of data-driven methodologies in Covid-19 pandemic. We provide a SWOT analysis and a roadmap that goes from the access to data sources to the final decision-making step. We aim to review the available methodologies while anticipating the difficulties and challenges in the development of data-driven strategies to combat the Covid-19 pandemic. A 3M-analysis is presented: Monitoring, Modelling and Making decisions. The focus is on the potential of well-known datadriven schemes to address different challenges raised by the pandemic: i) monitoring and forecasting the …
In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while minimizing the costs incurred by the introduction of societal control measures (such as closing schools, social distancing, lockdowns, etc.), under the constraint that the infected fraction of the population does never exceed a certain maximum corresponding to public health system capacity. Optimality is derived and verified by variational and numerical methods for a…
COVID-19--a viral infectious disease--has quickly emerged as a global pandemic infecting millions of people with a significant number of deaths across the globe. The symptoms of this disease vary widely. Depending on the symptoms an infected person is broadly classified into two categories namely, asymptomatic and symptomatic. Asymptomatic individuals display mild or no symptoms but continue to transmit the infection to otherwise healthy individuals. This particular aspect of asymptomatic infection poses a major obstacle in managing and controlling the transmission of the infectious disease. I…
Several non-pharmaceutical interventions have been proposed to control the spread of the COVID-19 pandemic. On the large scale, these empirical solutions, often associated with extended and complete lockdowns, attempt to minimize the costs associated with mortality, economic losses and social factors, while being subject to constraints such as finite hospital capacity. Here we pose the question of how to mitigate pandemic costs subject to constraints by adopting the language of optimal control theory. This allows us to determine top-down policies for the nature and dynamics of social contact r…
After the first lockdown in response to the COVID-19 outbreak, many countries faced difficulties in balancing infection control with economics. Due to limited prior knowledge, economists began researching this issue using cost-benefit analysis and found that infection control processes significantly affect economic efficiency. A UK study used economic parameters to numerically demonstrate an optimal balance in the process, including keeping the infected population stationary. However, universally applicable knowledge, which is indispensable for the guiding principles of infection control, has …
A model-based signal processing framework is proposed for pandemic trend forecasting and control, by using non-pharmaceutical interventions (NPI) at regional and country levels worldwide. The control objective is to prescribe quantifiable NPI strategies at different levels of stringency, which balance between human factors (such as new cases and death rates) and cost of intervention per region/country. Due to infrastructural disparities and differences in priorities of regions and countries, strategists are given the flexibility to weight between different NPIs and to select the desired balanc…
Purpose: In this study we propose to identify significant economic, political, and social factors that helped contribute to the incidence and mortality of SARS-CoV-2 around the world during the first seven months of the COVID-19 pandemic. Methods: Retrospective analyses were conducted using data acquired by the World Health Organization regarding the number of new cases and deaths from 76 countries from January through July 2020. Hierarchical cluster and principal component analyses were used to categorize different countries based on their ability to control the outbreak based on number of ca…
The present article studies the extension of two deterministic models for describing the novel coronavirus pandemic crisis, the SIR model and the SEIR model. The models were studied and compared to real data in order to support the validity of each description and extract important information regarding the pandemic, such as the basic reproductive number R0, which might provide useful information concerning the rate of increase of the pandemic predicted by each model. We next proceed to making predictions and comparing more complex models derived from the SEIR model with the SIRD model, in ord…
The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so an…
This work constructs, analyzes, and simulates a new compartmental SEIR-type model for the dynamics and potential control of the current COVID-19 pandemic. The novelty in this work is two-fold. First, the population is divided according to its compliance with disease control directives (lockdown, shelter-in-place, masks/face coverings, physical distancing, etc.) into those who fully comply and those who follow the directives partially, or are necessarily mobile (such as medical staff). This split, indirectly, reflects on the quality and consistency of these measures. This allows the assessment …
In this paper, we introduce a new control-theoretic paradigm for mitigating the spread of a virus. To this end, our discrete-time controller, aims to reduce the number of new daily deaths, and consequently, the cumulative number of deaths. In contrast to much of the existing literature, we do not rely on a potentially complex virus transmission model whose equations must be customized to the "particulars" of the pandemic at hand. For new viruses such as Covid-19, the epidemiology driving the modelling process may not be well known and model estimation with limited data may be unreliable. With …
University of Houston（休斯顿大学）；Houston Methodist Research Institute（休斯顿卫理公会研究所）；Weill Cornell Medical College（威尔康奈尔医学院）；The University of Texas M.D. Anderson Cancer Center（德克萨斯大学MD安德森癌症中心）；Weill Cornell Medicine（威尔康奈尔医学院）
The COVID-19 pandemic has affected countries across the world, demanding drastic public health policies to mitigate the spread of infection, leading to economic crisis as a collateral damage. In this work, we investigated the impact of human mobility (described via international commercial flights) on COVID-19 infection dynamics at the global scale. For this, we developed a graph neural network-based framework referred to as Dynamic Connectivity GraphSAGE (DCSAGE), which operates over spatiotemporal graphs and is well-suited for dynamically changing adjacency information. To obtain insights on…
During decades, mathematical models have been used to predict the behavior of physical and biologic systems, and to define strategies aiming the minimization of the effects regarding different types of diseases. In the present days, the development of mathematical models to simulate the dynamic behavior of novel coronavirus disease (COVID-19) is considered an important theme due to the quantity of infected people worldwide. In this work, the aim is to determine an optimal control strategy for vaccine administration in COVID-19 pandemic treatment considering real data from China. For this purpo…
Covid-19 is one of the most dreaded pandemics/epidemics in the world threatening the human population. The dynamics of this pandemic is quite complicated and prediction of pandemic states often fails. In this work, we study and correlate the SIR epidemiological model with the ongoing pandemic and found that pandemic dynamics and states are quite sensitively dependent on model parameters. The analysis of the exact parametric solution of the deterministic SIR model shows that the fixed points ($g^*$) depend on the SIR parameters, where, if $g^*\langle\fracγ{βx_0}$ then $g^*$ is stable and the pa…
A second wave pandemic constitutes an imminent threat to society, with a potentially immense toll in terms of human lives and a devastating economic impact. We employ the epidemic renormalisation group approach to pandemics, together with the first wave data for COVID-19, to efficiently simulate the dynamics of disease transmission and spreading across different European countries. The framework allows us to model, not only inter and extra European border control effects, but also the impact of social distancing for each country. We perform statistical analyses averaging on different level of …
Modeling and analysis of the large scale Covid-19 pandemic data can yield inferences about it's dynamics and characteristics of disease propagation. These inferences can then be correlated with contextual factors like population density, effects of strategic interventions, heterogeneous disease propagation etc, and such set of validated inferences can serve as precedents for designing of subsequent mitigation strategies. In this work, we present the analysis of Covid-19 pandemic data in Indian context using growth functions fitting procedure and harmonic analysis method. Our results of growth …
Some of the key questions of interest during the COVID-19 pandemic (and all outbreaks) include: where did the disease start, how is it spreading, who is at risk, and how to control the spread. There are a large number of complex factors driving the spread of pandemics, and, as a result, multiple modeling techniques play an increasingly important role in shaping public policy and decision making. As different countries and regions go through phases of the pandemic, the questions and data availability also changes. Especially of interest is aligning model development and data collection to suppo…
This paper presents the assessment of time-dependent national-level restrictions and control actions and their effects in fighting the COVID-19 pandemic. By analysing the transmission dynamics during the first wave of COVID-19 in the country, the effectiveness of the various levels of control actions taken to flatten the curve can be better quantified and understood. This in turn can help the relevant authorities to better plan for and control the subsequent waves of the pandemic. To achieve this, a deterministic population model for the pandemic is firstly developed to take into consideration…
The traditional long-term solutions for epidemic control involve eradication or population immunity. Here, we analytically derive the existence of a third viable solution: a stable equilibrium at low case numbers, where test-trace-and-isolate policies partially compensate for local spreading events, and only moderate restrictions remain necessary. In this equilibrium, daily cases stabilize around ten new infections per million people or less. However, stability is endangered if restrictions are relaxed or case numbers grow too high. The latter destabilization marks a tipping point beyond which…
Understanding the dynamics of the COVID-19 pandemic is crucial for improved control and social distancing strategies. To that effect, we have employed the susceptible-exposed-infectious-recovered model, refined by contact tracing and hospitalization data from Indian provinces Kerala, Delhi, Maharashtra, and West Bengal, as well as from overall India. We have performed a sensitivity analysis to identify the most crucial input parameters, and we have calibrated the model to describe the data as best as possible. Short-term predictions reveal an increasing and worrying trend of COVID-19 cases for…
With the invention of the COVID-19 vaccine, shipping and distributing are crucial in controlling the pandemic. In this paper, we build a mean-field variational problem in a spatial domain, which controls the propagation of pandemic by the optimal transportation strategy of vaccine distribution. Here we integrate the vaccine distribution into the mean-field SIR model designed in our previous paper arXiv:2006.01249. Numerical examples demonstrate that the proposed model provides practical strategies in vaccine distribution on a spatial domain.
COVID-19 is now the largest pandemic crisis of this century, with over 16 million registered cases worldwide. African countries have now begun registering an increasing number of cases, yet, not many models developed focus in specific African countries. In our study we use a simple SEIR model to evaluate and predict future scenarios regarding the pandemic crisis in Mozambique. We compare the effect of different policies on the infection curve and estimate epidemiological parameters such as the current infection reproduction number Rt and the growth rate g. We have found a low value for Rt, ran…
We consider a global (location independent) model of pandemic growth which generalizes the SIR model to accommodate important features of the COVID-19 pandemic, notably the implementation of pandemic reduction measures. This "SHIR" model is applied to COVID-19 data, and shows promise as a simple, tractable formalism with few parameters that can be used to model pandemic case numbers. As an example we show that the average time dependence of new COVID-19 cases per day from 15 Central and Western European countries is in good agreement with the analytic, parameter-free prediction of the model
Background: The pandemic of influenza A (H1N1) is a serious on-going global public crisis. Understanding its spreading dynamics is of fundamental importance for both public health and scientific researches. Recent studies have focused mainly on evaluation and prediction of on-going spreading, which strongly depends on detailed information about the structure of social contacts, human traveling patterns and biological activity of virus, etc. Methodology/Principal Findings: In this work we analyzed the distributions of confirmed cases of influenza A (H1N1) in different levels and find the Zipf's…
The ongoing COVID-19 pandemic has progressed with varying degrees of intensity in individual countries, suggesting it is important to analyse factors that vary between them. We study measures of `population-weighted density', which capture density as perceived by a randomly chosen individual. These measures of population density can significantly explain variation in the initial rate of spread of COVID-19 between countries within Europe. However, such measures do not explain differences on a global scale, particularly when considering countries in East Asia, or looking later into the epidemics…
The COVID-19 pandemic has posed a policy making crisis where efforts to slow down or end the pandemic conflict with economic priorities. This paper provides mathematical analysis of optimal disease control policies with idealized compartmental models for disease propagation and simplistic models of social and economic costs. Two locally optimal control strategies are found and categorized as `suppression' and `mitigation' strategies. We analyze how these strategies change when we incorporate vaccination into the model and find a new optimal `delay-mitigation' strategy.
There is a continuing debate on relative benefits of various mitigation and suppression strategies aimed to control the spread of COVID-19. Here we report the results of agent-based modelling using a fine-grained computational simulation of the ongoing COVID-19 pandemic in Australia. This model is calibrated to match key characteristics of COVID-19 transmission. An important calibration outcome is the age-dependent fraction of symptomatic cases, with this fraction for children found to be one-fifth of such fraction for adults. We apply the model to compare several intervention strategies, incl…
The development and authorization of COVID-19 vaccines has provided the clearest path forward to eliminate community spread hence end the ongoing SARS-CoV-2 pandemic. However, the limited pace at which the vaccine can be administered motivates the question, to what extent must we continue to adhere to social intervention measures such as mask wearing and social distancing? To address this question, we develop a mathematical model of COVID-19 spread incorporating both vaccine dynamics and socio-epidemiological parameters. We use this model to study two important measures of disease control and …
Besides maintaining health precautions, vaccination has been the only prevention from SARS-CoV-2, though no clinically proved 100% effective vaccine has been developed till date. At this stage, to withhold the debris of this pandemic, experts need to know the impact of the vaccine efficacy rate's threshold and how long this pandemic may extent with vaccines that have different efficacy rates. In this article, a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing pandemic. We simulated a five compartment mathematical model to ana…
We consider here an extended SIR model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care unit (ICU) capacity. Our model enables a tractable quantitative analysis of the optimal policy for the control of the epidemic dynamics using both lockdown and detection intervention levers. With parametric specification based on literature on COVID-19, we investigate the sensitivities of various quantities on the optimal strategies, taking into account the su…
Controlling the spread of COVID-19 - even after a licensed vaccine is available - requires the effective use of non-pharmaceutical interventions: physical distancing, limits on group sizes, mask wearing, etc. To date, such interventions have neither been uniformly nor systematically implemented in most countries. For example, even when under strict stay-at-home orders, numerous jurisdictions granted exceptions and/or were in close proximity to locations with entirely different regulations in place. Here, we investigate the impact of such geographic inconsistencies in epidemic control policies …
The rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies, balancing public health considerations with the economic costs of social distancing measures. We introduce a modified epidemic model that we name the controlled-SIR model, in which the disease reproduction rate evolves dynamically in response to political and societal reactions. An analytic solution is presented. The model reproduces official COVID-19 cases counts of a large number of regions and countries that surpassed the first peak of the outbrea…
University of Cambridge（剑桥大学）；UNC-Chapel Hill（北卡罗来纳大学教堂山分校）；UNC Gilling School of Global Public Health（北卡罗来纳大学吉林斯全球公共卫生学院）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；University of Toronto（多伦多大学）；Canadian Institute for Advanced Research（加拿大高等研究院）；California State University Fullerton（加州州立大学富勒顿分校）；Oberlin College（欧柏林学院）
We present a new mathematical model to explicitly capture the effects that the three restriction measures: the lockdown date and duration, social distancing and masks, and, schools and border closing, have in controlling the spread of COVID-19 infections $i(r, t)$. Before restrictions were introduced, the random spread of infections as described by the SEIR model grew exponentially. The addition of control measures introduces a mixing of order and disorder in the system's evolution which fall under a different mathematical class of models that can eventually lead to critical phenomena. A gener…
The investigation focuses on an on-off protocol for controlling the COVID-19 widespread. The protocol establishes a working period of 4 days for all the citizens, followed by 8 days of lock-down. We further propose splitting people into smaller groups that undergo the on-off protocol, but shifted in time. This procedure is expected to regularize the overall economic activity. Our results show that either the on-of protocol and the splitting into groups reduces the amount of infected people. However, the latter seems to be better for economic reasons. Our simulations further show that the start…
We demonstrate that the epidemic renormalisation group approach to pandemics provides an effective and simple way to investigate the dynamics of disease transmission and spreading across different regions of the world. The framework also allows for reliable projections on the impact of travel limitations and social distancing measures on global epidemic spread. We test and calibrate it on reported cases while unveiling the mechanism that governs the delay in the relative peaks of newly infected cases among different regions of the globe. We discover that social distancing measures are more eff…
A mathematical model for the COVID-19 pandemic spread, which integrates age-structured Susceptible-Exposed-Infected-Recovered-Deceased dynamics with real mobile phone data accounting for the population mobility, is presented. The dynamical model adjustment is performed via Approximate Bayesian Computation. Optimal lockdown and exit strategies are determined based on nonlinear model predictive control, constrained to public-health and socio-economic factors. Through an extensive computational validation of the methodology, it is shown that it is possible to compute robust exit strategies with r…
This work examines the use of reinforcement learning (RL) to optimize cyclic lockdowns, which is one of the methods available for control of the COVID-19 pandemic. The problem is structured as an optimal control system for tracking a reference value, corresponding to the maximum usage level of a critical resource, such as ICU beds. However, instead of using conventional optimal control methods, RL is used to find optimal control policies. A framework was developed to calculate optimal cyclic lockdown timings using an RL-based on-off controller. The RL-based controller is implemented as an RL a…
Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health. In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic. We start revisiting the basic properties of simple Kermack-McKendrick type models. Then, we discuss extensions of such models and important epidemiological quantities applied to investigate the role of heterogeneity in disease transmission e.g. mixing functions and superspreading events, …
The current global health emergency triggered by the pandemic COVID-19 is one of the greatest challenges mankind face in this generation. Computational simulations have played an important role to predict the development of the current pandemic. Such simulations enable early indications on the future projections of the pandemic and is useful to estimate the efficiency of control action in the battle against the SARS-CoV-2 virus. The SEIR model is a well-known method used in computational simulations of infectious viral diseases and it has been widely used to model other epidemics such as Ebola…
We consider the $SEIRS$ epidemiology model with such features of the COVID-19 outbreak as: abundance of unidentified infected individuals, limited time of immunity and a possibility of vaccination. Within a compartmental realization of this model, we found the disease-free and the endemic stationary states. They exist in their respective restricted regions of the le via linear stability analysis. The expression for the basic reproductive number is obtained as well. The positions and heights of a first peak for the fractions of infected individuals are obtained numerically and are fitted to sim…
The ongoing COVID-19 pandemic is challenging every part of society. From a scientific point of view the first major task is to predict the dynamics of the pandemic, allowing governments to allocate proper resources and measures to fight it, as well as gauging the success of these measures by comparison with the predictions in hindsight. The vast majority of pandemic models are based on extensive models with large numbers of fit parameters, leading to individual descriptions for every hot spot on the world. This makes predictions and comparisons cumbersome, if not impossible. We here propose a …
This survey analyses the role of data-driven methodologies for pandemic modelling and control. We provide a roadmap from the access to epidemiological data sources to the control of epidemic phenomena. We review the available methodologies and discuss the challenges in the development of data-driven strategies to combat the spreading of infectious diseases. Our aim is to bring together several different disciplines required to provide a holistic approach to epidemic analysis, such as data science, epidemiology, and systems-and-control theory. A 3M-analysis is presented, whose three pillars are…
Given multiple new COVID-19 variants are continuously emerging, non-pharmaceutical interventions are still primary control strategies to curb the further spread of coronavirus. However, implementing strict interventions over extended periods of time is inevitably hurting the economy. With an aim to solve this multi-objective decision-making problem, we investigate the underlying associations between policies, mobility patterns, and virus transmission. We further evaluate the relative performance of existing COVID-19 control measures and explore potential optimal strategies that can strike the …
In this paper, we propose a machine learning technics and SIR models (deterministic and stochastic cases) with numerical approximations to predict the number of cases infected with the COVID-19, for both in few days and the following three weeks. Like in [1] and based on the public data from [2], we estimate parameters and make predictions to help on how to find concrete actions to control the situation. Under optimistic estimation, the pandemic in some countries will end soon, while for most of the countries in the world, the hit of anti-pandemic will be no later than the beginning of May.
We develop a simple 3-dimensional iterative map model to forecast the global spread of the coronavirus disease. Our model contains at most two fitting parameters, which we determine from the data supplied by the world health organisation for the total number of cases and new cases each day. We find that our model provides a surprisingly good fit to the currently-available data, which exhibits a cross-over from exponential to power-law growth, as lock-down measures begin to take effect. Before these measures, our model predicts exponential growth from day 30 to 69, starting from the date on whi…
Since early 2020, the world has been dealing with a raging pandemic outbreak: COVID-19. A year later, vaccines have become accessible, but in limited quantities, so that governments needed to devise a strategy to decide which part of the population to prioritize when assigning the available doses, and how to manage the interval between doses for multi-dose vaccines. In this paper, we present an optimization framework to address the dynamic double-dose vaccine allocation problem whereby the available vaccine doses must be administered to different age-groups to minimize specific societal object…
