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Representation of the Metapopulation Model Adopted The model includes 3,100 airports in 220 countries worldwide. The map portrays the locations of urban airports worldwide; geographical data are obtained from open sources on the Internet and mapped with ArcGIS software ( A schematic illustration represents the patch or metapopulation model adopted, in which the total population is divided into subpopulations each corresponding to the urban area surrounding each airport. Filled circles inside each subpopulation represent individuals, and the colors correspond to a specific stage of the disease. Homogeneous mixing for the infection dynamics is assumed inside each urban area, and different urban areas; subpopulations are coupled by means of air travel, according to the International Air Transport Association traffic fluxes. doi:10.1371/journal.pmed.0040013.g001
Source publication
Background
The highly pathogenic H5N1 avian influenza virus, which is now widespread in Southeast Asia and which diffused recently in some areas of the Balkans region and Western Europe, has raised a public alert toward the potential occurrence of a new severe influenza pandemic. Here we study the worldwide spread of a pandemic and its possible con...
Contexts in source publication
Context 1
... contains the worldwide list of airport pairs connected by direct flights and the number of available seats on any given connection. The resulting worldwide air- transportation network is therefore a weighted graph comprising V ¼ 3,100 vertices denoting airports in 220 different countries (see Figure 1), and E ¼ 17,182 weighted edges whose weight w jl represents the passenger flow between the airports j and l. This dataset accounts for 99% of worldwide traffic and has been complemented by the population N j of each large metropolitan area served by the corresponding airport as obtained from different sources. ...
Context 2
... a basic modeling strategy we used a metapopulation approach [15][16][17] in which individuals are allowed to travel from one city to another by means of the airline trans- portation network, and to change compartments because of the infection dynamics in each city (see Figure 1), similarly to the models elsewhere [18][19][20][21][22][23] and the stochastic general- izations in other studies [13,14,24]. Specifically, two studies [19,22] address the computational analysis of influenza pandemics. ...
Context 3
... avian influenza pathogen H5N1 has proven its ability to pass directly from birds to humans, causing a severe disease with high mortality [1]. This has raised a public alert toward the potential occurrence of a new severe influenza pandemic caused by a novel human virus strain originating from the avian H5N1 influenza virus, through adaptive mutations or recombinations with human influenza viruses. In this eventuality, the timescale necessary for the worldwide production and deployment of adequate vaccine supplies could exceed six to eight months [2]. In addition, in the case of diseases in which the infected individuals are infectious before the appearance of the first clinical signs [3], nonmedical interventions such as travel-related measures might not be as efficient [4] as they proved to be during the spread of SARS [5]. In this context, antiviral (AV) drugs represent one of the crucial resources to reduce morbidity and mortality of a pandemic in the absence of a vaccine [6–9]. For this reason, several recent studies provided evidence that the use of AV drugs is an effective strategy for the local containment of the emerging pandemic strain at the source [7,10]. The real issue in assessing the impact of a pandemic is, however, in its global character, and in the effects resulting from the complex interplay of epidemic spread occurring in different countries. The study of the global scale of a pandemic must examine three major factors in modeling studies: (i) In learning from the lessons of the 1918 pandemic and the ongoing debate on its origins, scenario evaluations must investigate the possibility of a pandemic starting anywhere in the world and not only in underdeveloped countries. (ii) Determining the likelihood of the global spread of a pandemic must include consideration of the effects of human travel. Even if local intervention were to mitigate and eradicate an epidemic locally, it is possible that during the course of containment, which generally lasts for weeks, air traffic might trigger a global event affecting multiple countries. The air traffic would also alter the evolution of the local epidemics with the entry of new, infectious individuals from elsewhere, a nonlocal effect not specifically considered in previous studies [7,10], or implemented as assumed boundary conditions [11,12]. (iii) AV stockpiling is mainly a function of a country’s wealth and level of preparedness to deal with a future pandemic; consequently, stockpiles are very low or absent in a majority of countries. It is, therefore, relevant to study effective strategies that optimize the use of the available supplies of AV drugs in the case of a worldwide spread. In this article, we examine stochastic computational modeling of the temporal and worldwide geographical spread of an emerging pandemic [13,14]. The epidemic model includes census data for all 3,100 urban areas studied and airline traffic flow between those regions, all of which accounts for 99% of airline traffic worldwide. Such detailed information allows for the study of a pandemic originating anywhere in the world. We first investigate the pandemic evolution on a global scale in the absence of containment strategies, studying the effect of different initial conditions and virus infectiousness, quantified by the basic reproductive number R 0 . This preliminary analysis allows us to outline a set of baseline cases to contrast with different intervention scenarios. We first analyse the effect of travel restrictions on the overall evolution of the pandemic, and then consider the best-case scenario in which each hit country can rely on massive AV stockpiles. We also investigate the effect of traveling patterns on the occurrence of a global outbreak affecting a large number of countries worldwide even if an effective mitigation of the epidemic is achieved in the hit populations. Finally, with the aim of designing realistic scenarios concerning AV stockpiles, we take into consideration that the amount of available supplies is finite and concentrated in a limited number of countries. We therefore contrast uncooperative intervention strategies, in which prepared countries use their stockpiles only within their own borders, against increasingly cooperative strategies in which progressively larger fractions of the stockpiles of prepared countries are shared with unprepared countries worldwide. The International Air Transport Association (IATA) (http:// www.iata.org) database contains the worldwide list of airport pairs connected by direct flights and the number of available seats on any given connection. The resulting worldwide air- transportation network is therefore a weighted graph comprising V 1⁄4 3,100 vertices denoting airports in 220 different countries (see Figure 1), and E 1⁄4 17,182 weighted edges whose weight w jl represents the passenger flow between the airports j and l . This dataset accounts for 99% of worldwide traffic and has been complemented by the population N j of each large metropolitan area served by the corresponding airport as obtained from different sources. The network that was obtained is highly heterogeneous both in its connectivity pattern and traffic capacities [13,14]. As a basic modeling strategy we used a metapopulation approach [15–17] in which individuals are allowed to travel from one city to another by means of the airline transportation network, and to change compartments because of the infection dynamics in each city (see Figure 1), similarly to the models elsewhere [18–23] and the stochastic general- izations in other studies [13,14,24]. Specifically, two studies [19,22] address the computational analysis of influenza pandemics. These approaches were limited, however, by a small dataset of 50 cities available at that time and a simplified compartmental model. Moreover, the methods [19,22] do not take into account stochastic effects and AV distribution, or other containment measures. In this study, we are in a position to take advantage of the recent increase in computer power and scale up the modeling approach to utilize the IATA dataset to its fullest extent, as well as taking the stochastic nature of the dynamics into account. We used the standard compartmentalization in which individuals can exist only in one of the discrete states such as susceptible (S), latent (L), infected (I), permanently recovered (R), etc. In the case of AV administration we used up to seven different compartments (see below). In each city j the population is N j , and t . By X definition j 1⁄2 m ð t Þ is the it number follows of that individuals N j 1⁄4 P m in X j 1⁄2 m the ð t Þ state . The (m) dynamics at time of individuals based on travels between cities is described by the stochastic transport operator X j ( X ) representing the net balance of individuals in a given state X [ m ] that entered and left each city j . This operator is a function of the traffic flows with the neighboring cities w jl per unit time and of the city population N j . In particular, the number of passengers in each category traveling from a city j to a city l is an integer random variable, in that each of the potential travelers has a probability p jl 1⁄4 w jl D t / N j to go from j to l in the time interval D t . In each city j the numbers of passengers traveling on each connection j ! l at time t define a set of stochastic variables that follow a multinomial distribution [13,14] . The calculation can be extended to include transit traffic (e.g., up to one connection flight). The infection evolution inside each urban area is described by compartmental schemes [6,7], in which the dynamics of the individuals among the different compartments depend on the specific etiology of the disease and the containment interventions considered. We used the two compartmental schemes reported in Figure 2. In the baseline scenario with no intervention, a susceptible individual (S) in contact with a symptomatic (I t , I nt ) or asymptomatic (I a ) infectious individual becomes infected with rate b or r b b , respectively, and enters the latent class (L). When the latency period ends, the individual becomes infectious, i.e. able to transmit the infection, developing symptoms (I t , I nt ) with probability 1 p a , while becoming asymptomatic (I a ) with probability p a . Among the symptomatic individuals, we distinguished between those who are allowed to travel (I t ) —with probability p t — and those who are not allowed (I nt )— with probability 1 p t — depending on the severity of the disease. After the infectious period, all infectious individuals enter the recovered class (R). e À 1 and l À 1 represent the mean latency period and the average duration of infection, respectively. We assumed that the latency period coincides with the incubation period with mean length of e À 1 1⁄4 1.9 d, followed by the infectious phase of average duration l À 1 1⁄4 3 d [6–8]. Both the incubation and infectious periods are distributed exponen- tially around these averages. We assumed the probability of being asymptomatic given that infection has occurred to be p a 33% [6,7]. The relative infectiousness of asymptomatic individuals is r b 1⁄4 50%. If the individual develops symptoms during the infectious period, he/she is then restricted from traveling (I nt ) with probability 1 À p t 1⁄4 50% [6,7]. Whenever AV stockpiles are available, a certain fraction per day p AV of symptomatic infected individuals will enter the AV treatment, the efficacy of which is modeled through a reduction of both the infectiousness and the period during which the individual is contagious [6,7]. Moreover, individuals under AV treatment are not allowed to travel. Note that asymptomatic individuals do not look for health-care ...
Context 4
... vaccine supplies could exceed six to eight months [2]. In addition, in the case of diseases in which the infected individuals are infectious before the appearance of the first clinical signs [3], nonmedical interventions such as travel-related measures might not be as efficient [4] as they proved to be during the spread of SARS [5]. In this context, antiviral (AV) drugs represent one of the crucial resources to reduce morbidity and mortality of a pandemic in the absence of a vaccine [6–9]. For this reason, several recent studies provided evidence that the use of AV drugs is an effective strategy for the local containment of the emerging pandemic strain at the source [7,10]. The real issue in assessing the impact of a pandemic is, however, in its global character, and in the effects resulting from the complex interplay of epidemic spread occurring in different countries. The study of the global scale of a pandemic must examine three major factors in modeling studies: (i) In learning from the lessons of the 1918 pandemic and the ongoing debate on its origins, scenario evaluations must investigate the possibility of a pandemic starting anywhere in the world and not only in underdeveloped countries. (ii) Determining the likelihood of the global spread of a pandemic must include consideration of the effects of human travel. Even if local intervention were to mitigate and eradicate an epidemic locally, it is possible that during the course of containment, which generally lasts for weeks, air traffic might trigger a global event affecting multiple countries. The air traffic would also alter the evolution of the local epidemics with the entry of new, infectious individuals from elsewhere, a nonlocal effect not specifically considered in previous studies [7,10], or implemented as assumed boundary conditions [11,12]. (iii) AV stockpiling is mainly a function of a country’s wealth and level of preparedness to deal with a future pandemic; consequently, stockpiles are very low or absent in a majority of countries. It is, therefore, relevant to study effective strategies that optimize the use of the available supplies of AV drugs in the case of a worldwide spread. In this article, we examine stochastic computational modeling of the temporal and worldwide geographical spread of an emerging pandemic [13,14]. The epidemic model includes census data for all 3,100 urban areas studied and airline traffic flow between those regions, all of which accounts for 99% of airline traffic worldwide. Such detailed information allows for the study of a pandemic originating anywhere in the world. We first investigate the pandemic evolution on a global scale in the absence of containment strategies, studying the effect of different initial conditions and virus infectiousness, quantified by the basic reproductive number R 0 . This preliminary analysis allows us to outline a set of baseline cases to contrast with different intervention scenarios. We first analyse the effect of travel restrictions on the overall evolution of the pandemic, and then consider the best-case scenario in which each hit country can rely on massive AV stockpiles. We also investigate the effect of traveling patterns on the occurrence of a global outbreak affecting a large number of countries worldwide even if an effective mitigation of the epidemic is achieved in the hit populations. Finally, with the aim of designing realistic scenarios concerning AV stockpiles, we take into consideration that the amount of available supplies is finite and concentrated in a limited number of countries. We therefore contrast uncooperative intervention strategies, in which prepared countries use their stockpiles only within their own borders, against increasingly cooperative strategies in which progressively larger fractions of the stockpiles of prepared countries are shared with unprepared countries worldwide. The International Air Transport Association (IATA) (http:// www.iata.org) database contains the worldwide list of airport pairs connected by direct flights and the number of available seats on any given connection. The resulting worldwide air- transportation network is therefore a weighted graph comprising V 1⁄4 3,100 vertices denoting airports in 220 different countries (see Figure 1), and E 1⁄4 17,182 weighted edges whose weight w jl represents the passenger flow between the airports j and l . This dataset accounts for 99% of worldwide traffic and has been complemented by the population N j of each large metropolitan area served by the corresponding airport as obtained from different sources. The network that was obtained is highly heterogeneous both in its connectivity pattern and traffic capacities [13,14]. As a basic modeling strategy we used a metapopulation approach [15–17] in which individuals are allowed to travel from one city to another by means of the airline transportation network, and to change compartments because of the infection dynamics in each city (see Figure 1), similarly to the models elsewhere [18–23] and the stochastic general- izations in other studies [13,14,24]. Specifically, two studies [19,22] address the computational analysis of influenza pandemics. These approaches were limited, however, by a small dataset of 50 cities available at that time and a simplified compartmental model. Moreover, the methods [19,22] do not take into account stochastic effects and AV distribution, or other containment measures. In this study, we are in a position to take advantage of the recent increase in computer power and scale up the modeling approach to utilize the IATA dataset to its fullest extent, as well as taking the stochastic nature of the dynamics into account. We used the standard compartmentalization in which individuals can exist only in one of the discrete states such as susceptible (S), latent (L), infected (I), permanently recovered (R), etc. In the case of AV administration we used up to seven different compartments (see below). In each city j the population is N j , and t . By X definition j 1⁄2 m ð t Þ is the it number follows of that individuals N j 1⁄4 P m in X j 1⁄2 m the ð t Þ state . The (m) dynamics at time of individuals based on travels between cities is described by the stochastic transport operator X j ( X ) representing the net balance of individuals in a given state X [ m ] that entered and left each city j . This operator is a function of the traffic flows with the neighboring cities w jl per unit time and of the city population N j . In particular, the number of passengers in each category traveling from a city j to a city l is an integer random variable, in that each of the potential travelers has a probability p jl 1⁄4 w jl D t / N j to go from j to l in the time interval D t . In each city j the numbers of passengers traveling on each connection j ! l at time t define a set of stochastic variables that follow a multinomial distribution [13,14] . The calculation can be extended to include transit traffic (e.g., up to one connection flight). The infection evolution inside each urban area is described by compartmental schemes [6,7], in which the dynamics of the individuals among the different compartments depend on the specific etiology of the disease and the containment interventions considered. We used the two compartmental schemes reported in Figure 2. In the baseline scenario with no intervention, a susceptible individual (S) in contact with a symptomatic (I t , I nt ) or asymptomatic (I a ) infectious individual becomes infected with rate b or r b b , respectively, and enters the latent class (L). When the latency period ends, the individual becomes infectious, i.e. able to transmit the infection, developing symptoms (I t , I nt ) with probability 1 p a , while becoming asymptomatic (I a ) with probability p a . Among the symptomatic individuals, we distinguished between those who are allowed to travel (I t ) —with probability p t — and those who are not allowed (I nt )— with probability 1 p t — depending on the severity of the disease. After the infectious period, all infectious individuals enter the recovered class (R). e À 1 and l À 1 represent the mean latency period and the average duration of infection, respectively. We assumed that the latency period coincides with the incubation period with mean length of e À 1 1⁄4 1.9 d, followed by the infectious phase of average duration l À 1 1⁄4 3 d [6–8]. Both the incubation and infectious periods are distributed exponen- tially around these averages. We assumed the probability of being asymptomatic given that infection has occurred to be p a 33% [6,7]. The relative infectiousness of asymptomatic individuals is r b 1⁄4 50%. If the individual develops symptoms during the infectious period, he/she is then restricted from traveling (I nt ) with probability 1 À p t 1⁄4 50% [6,7]. Whenever AV stockpiles are available, a certain fraction per day p AV of symptomatic infected individuals will enter the AV treatment, the efficacy of which is modeled through a reduction of both the infectiousness and the period during which the individual is contagious [6,7]. Moreover, individuals under AV treatment are not allowed to travel. Note that asymptomatic individuals do not look for health-care assistance and therefore cannot receive any treatment. The rate p AV takes into account the probability per unit time of detecting a symptomatic infected individual and the efficiency of AV distribution in the infected area. We assumed that ill individuals under treatment might naturally recover, thus modeling a possible excessive use of AV courses. The infectiousness of an ill individual under treatment is reduced by a factor AVE I 1⁄4 0.62 which represents the efficacy of the AV drugs [7]; in this case the transmission parameter is thus given by b (1 À AVE I ). Moreover, the average infectious period for a treated ill individual is reduced by one day. The combination of p AV , AVE I , and the reduction ...
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Citations
... Complexity science has shown that networks of social interactions are heterogeneous, resulting in deeply connected hubs and modular structures [47][48][49][50][51][52][53]. This structural heterogeneity interacts with social effects like inequalities and segregation, impacting on network processes such as the spreading of epidemics, information and opinions [14,54,55]; the success of products, ideas, and people [56][57][58]; and urban dynamics [59][60][61][62][63][64][65][66][67][68]. The human-AI feedback loop affects these network processes differently than before the advent of AI. ...
Human-AI coevolution, defined as a process in which humans and AI algorithms continuously influence each other, increasingly characterises our society, but is understudied in artificial intelligence and complexity science literature. Recommender systems and assistants play a prominent role in human-AI coevolution, as they permeate many facets of daily life and influence human choices on online platforms. The interaction between users and AI results in a potentially endless feedback loop, wherein users' choices generate data to train AI models, which, in turn, shape subsequent user preferences. This human-AI feedback loop has peculiar characteristics compared to traditional human-machine interaction and gives rise to complex and often "unintended" social outcomes. This paper introduces Coevolution AI as the cornerstone for a new field of study at the intersection between AI and complexity science focused on the theoretical, empirical, and mathematical investigation of the human-AI feedback loop. In doing so, we: (i) outline the pros and cons of existing methodologies and highlight shortcomings and potential ways for capturing feedback loop mechanisms; (ii) propose a reflection at the intersection between complexity science, AI and society; (iii) provide real-world examples for different human-AI ecosystems; and (iv) illustrate challenges to the creation of such a field of study, conceptualising them at increasing levels of abstraction, i.e., technical, epistemological, legal and socio-political.
... If a different value is used for a particular simulation, it will be noted in the caption of the corresponding figure. The values of β, γ, ν and τ are based on those given [54] and CDC [1] corresponding to seasonal influenza. All the others are estimated. ...
The basic reproduction, or reproductive number, is a useful index that indicates whether or not there will be an epidemic. However, it is also very important to determine whether an epidemic will eventually decrease and disappear or persist as an endemic. Different infectious diseases have different behaviors and mathematical models used to simulated them should capture the most important processes; however, the models also involve simplifications. Influenza epidemics are usually short-lived and can be modeled with ordinary differential equations without considering demographics. Delays such as the infection time can change the behavior of the solutions. The same is true if there is permanent or temporary immunity, or complete or partial immunity. Vaccination, isolation and the use of antivirals can also change the outcome. In this paper, we introduce several new models and use them to find the effects of all the above factors paying special attention to whether the model can represent an infectious process that eventually disappears. We determine the equilibrium solutions and establish the stability of the disease-free equilibrium using various methods. We also show that many models of influenza or other epidemics with a short duration do not have solutions with a disappearing epidemic. The main objective of the paper is to introduce different ways of modeling immunity in epidemic models. Several scenarios with different immunities are studied since a person may not be re-infected because he/she has total or partial immunity or because there were no close contacts. We show that some relatively small changes, such as in the vaccination rate, can significantly change the dynamics; for example, the existence and number of the disease-free equilibria. We also illustrate that while introducing delays makes the models more realistic, the dynamics have the same qualitative behavior.
... Even further, should the contact be established and should one of the individuals be infectious, the infection of the second individual is not a certainty, but rather an event that occurs with some probability. Computational epidiomiologists have implemented these stochastic contagions in all the modeling efforts and at different scales, from agent-based [6][7][8][9][10][11][12] to population-based [13][14][15][16][17] . In the case of agent-based models stochastic contagion events can be traced one by one, even though for practical purposes in computation sometimes they may be aggregated. ...
... Exact binomial method. Simulations of the radioactive decay process with rates given by Eq.(12), using the binomial method [Eq.(15)]. In a the time discretization is Δt = 1, whereas in b is Δt = 0.5. ...
Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, numerical approximations are of extended use to deal with epidemic, ecological and biological models, since unbiased methods like the Gillespie algorithm can become unpractical due to high CPU time usage required. However, the use of approximations has been debated and there is no clear consensus about whether unbiased methods or biased approach is the best option. In this work, we derive scaling relations for the errors in approximations based on binomial extractions. This finding allows us to build rules to compute the optimal values of both the discretization time and number of realizations needed to compute averages with the biased method with a target precision and minimum CPU-time usage. Furthermore, we also present another rule to discern whether the unbiased method or biased approach is more efficient. Ultimately, we will show that the choice of the method should depend on the desired precision for the estimation of averages.
... 1 Though WHO shifted its recommendations over the course of the COVID-19 pandemic to support some travel measures under certain conditions, its initial recommendation reflected its guidance during most of the other seven declared public health emergency of international concerns (PHEICs). 2 WHO has long held the view that the limited public health benefits of such measures are outweighed by their social and economic costs (indeed, at the start of COVID-19, existing research on past outbreaks suggested that some travel measures may delay outbreak spread but alone have not stopped spread [3][4][5][6] ). The large-scale and prolonged use of travel measures during COVID-19 has prompted study of their effectiveness in achieving public health objectives. ...
Introduction
Assessment of the use of travel measures during COVID-19 has focused on their effectiveness in achieving public health objectives. However, the prolonged use of highly varied and frequently changing measures by governments, and their unintended consequences caused, has been controversial. This has led to a call for coordinated decision-making focused on risk-based approaches, which requires better understanding of the broader impacts of international travel measures (ITMs) on individuals and societies.
Methods
Our scoping review investigates the literature on the economic impact of COVID-19 ITMs. We searched health, social science and COVID-19-specific databases for empirical studies preprinted or published between 1 January 2020 and 31 October 2023. Evidence was charted using a narrative approach and included jurisdiction of study, ITMs studied, study design, outcome categories, and main findings.
Results
Twenty-six studies met the inclusion criteria and were included for data extraction. Twelve of them focused on the international travel restrictions implemented in early 2020. Limited attention was given to measures such as entry/exit screening and vaccination requirements. Eight studies focused on high-income countries, 6 on low-income and middle-income countries and 10 studies were comparative although did not select countries by income. Economic outcomes assessed included financial markets (n=13), economic growth (n=4), economic activities (n=1), performance of industries central to international travel (n=9), household-level economic status (n=3) and consumer behaviour (n=1). Empirical methods employed included linear regression (n=17), mathematical modelling (n=3) and mixed strategies (n=6).
Conclusion
Existing studies have begun to provide evidence of the wide-ranging economic impacts resulting from ITMs. However, the small body of research combined with difficulties in isolating the effects of such measures and limitations in available data mean that it is challenging to draw general and robust conclusions. Future research using rigorous empirical methods and high-quality data is needed on this topic.
... More broadly, our study demonstrates that stockpile design is a spatially-structured problem. A significant body of work recognizes that epidemic dynamics of many infectious diseases are heavily shaped by several aspects of human behavior, including animal-human contact (Plowright et al. 2017;Dudas et al. 2018;Gurley et al. 2017), multiscale mobility (Balcan et al. 2009;Colizza et al. 2007), social contact networks (Bansal, Grenfell, and Meyers 2007), patient-clinician interactions (Cooper, Medley, and Scott 1999;Ueno and Masuda 2008), and several facets of epidemic response. Our study establishes a parsimonious and generalizable framework for simulating these dynamics on real landscapes, parameterized with multiple sources of real-world data, without the opacity, complexity, and computational cost frequently associated with agent-based approaches (Ajelli et al. 2010;Tracy, Cerdá, and Keyes 2018). ...
Multinational epidemics of emerging infectious diseases are increasingly common, due to anthropogenic pressure on ecosystems and the growing connectivity of human populations. Early and efficient vaccination can contain outbreaks and prevent mass mortality, but optimal vaccine stockpiling strategies are dependent on pathogen characteristics, reservoir ecology, and epidemic dynamics. Here, we model major regional outbreaks of Nipah virus and Middle East respiratory syndrome, and use these to develop a generalized framework for estimating vaccine stockpile needs based on spillover geography, spatially-heterogeneous healthcare capacity and spatially-distributed human mobility networks. Because outbreak sizes were highly skewed, we found that most outbreaks were readily contained (median stockpile estimate for MERS-CoV: 2,089 doses; Nipah: 1,882 doses), but the maximum estimated stockpile need in a highly unlikely large outbreak scenario was 2-3 orders of magnitude higher (MERS-CoV: ~87,000 doses; Nipah ~1.1 million doses). Sensitivity analysis revealed that stockpile needs were more dependent on basic epidemiological parameters (i.e., death and recovery rate) and healthcare availability than any uncertainty related to vaccine efficacy or deployment strategy. Our results highlight the value of descriptive epidemiology for real-world modeling applications, and suggest that stockpile allocation should consider ecological, epidemiological, and social dimensions of risk.
... 22 On the difference between 'specific predictions' (that is, prediction of details) and 'qualitative predictions' (that is, predictions of the principle), see Moroni (2015). 23 See also Nguyen- Van-Tam and Hampson (2003), Cooper et al. (2006), Colizza et al. (2007) and Saunders-Hastings and Krewski (2016). Interestingly, issues such as Scholars therefore knew that a certain kind of pandemic was due to happen; they just did not know exactly when it would do so (Kliger, 2021). ...
... The analogy in our case is quite intuitive where a congested road segment can "infect" its adjacent road due to traffic queues extending and overflowing to the next junctions. Collizza et al. [56] associated the epidemic spreading with the traffic flow based on the metapopulation model. Wu et al. [57], on the other hand, described traffic congestion spread with the SIR epidemic model and conducted simulation studies. ...
The continuous urbanisation and increase in vehicle ownership have increasingly exacerbated traffic congestion problems. In this paper, we advocate the use of epidemic theory to model the spreading of traffic congestion in urban cities. Specifically, we use the Susceptible-Infected-Recovered (SIR) model but propose to explicitly consider the road network structure in the model to understand the contagion process of road congestion. This departs from the classical SIR model where homogeneous mixing based on the law of mass action is assumed. For this purpose, we adopt the N-intertwined modeling framework for the SIR model based on continuous-time Markov chain analysis. In our evaluation, we used two real-world traffic datasets collected in California and Los Angeles. We compare our results against both classical and average-degree-based SIR models. Our results show better agreement between the model and actual congestion conditions and shed light on how congestion propagates across a road network. We see the potential application of insights gained from this work on the development of traffic congestion mitigation strategies.
... P, A cannot. Antivirals treat severe forms of seasonal influenza, but most importantly represent the first line of defense against an emerging pandemic, as they mitigate morbidity and mortality at the population level 5,6 . For this reason, neuraminidase inhibitorsthe most common influenza antivirals-are stockpiled for pandemic preparedness 4 . ...
COVID-19 highlighted modeling as a cornerstone of pandemic response. But it also revealed that current models may not fully exploit the high-resolution data on disease progression, epidemic surveillance and host behavior, now available. Take the epidemic threshold, which quantifies the spreading risk throughout epidemic emergence, mitigation, and control. Its use requires oversimplifying either disease or host contact dynamics. We introduce the epidemic graph diagrams to overcome this by computing the epidemic threshold directly from arbitrarily complex data on contacts, disease and interventions. A grammar of diagram operations allows to decompose, compare, simplify models with computational efficiency, extracting theoretical understanding. We use the diagrams to explain the emergence of resistant influenza variants in the 2007–2008 season, and demonstrate that neglecting non-infectious prodromic stages of sexually transmitted infections biases the predicted epidemic risk, compromising control. The diagrams are general, and improve our capacity to respond to present and future public health challenges.
... Recent studies focused on improving the effectiveness [16][17][18] and equity [19][20][21][22][23] of the domestic distribution of vaccines, but have been incapable of modeling the national interests of sovereign countries and scaling up to global vaccine distribution [11,24]. To address this gap, several early attempts employed highly simplified models with hypothetical parameters; however, they usually overlooked the structure of global mobility [20] and lacked evidence supported by real-world data [14,15,25,26]. Although they provide important theoretical results for various hypothetical scenarios, such studies cannot adequately reflect the complexity of real-world pandemics, limiting their capability of promoting global vaccine sharing with practical incentives. ...
Background
Despite consensus that vaccines play an important role in combatting the global spread of infectious diseases, vaccine inequity is still a prevalent issue due to a deep-seated mentality of self-priority. We aimed to evaluate the existence and possible outcomes of a more equitable global vaccine distribution and explore a concrete incentive mechanism that promotes vaccine equity.
Methods
We designed a metapopulation epidemiological model that simultaneously considers global vaccine distribution and human mobility, which we then calibrated by the number of infections and real-world vaccination records during the coronavirus disease 2019 (COVID-19) pandemic from March 2020 to July 2021. We explored the possibility of the enlightened self-interest incentive mechanism, which comprises improving one’s own epidemic outcomes by sharing vaccines with other countries, by evaluating the number of infections and deaths under various vaccine sharing strategies using the proposed model. To understand how these strategies affect the national interests, we distinguished imported from local cases for further cost-benefit analyses that rationalise the enlightened self-interest incentive mechanism behind vaccine sharing.
Results
The proposed model accurately reproduces the real-world cumulative infections for both global and regional epidemics (R²>0.990), which can support the following evaluations of different vaccine sharing strategies: High-income countries can reduce 16.7 (95% confidence interval (CI) = 8.4-24.9, P < 0.001) million infection cases and 82.0 (95% CI = 76.6-87.4, P < 0.001) thousand deaths on average by more actively sharing vaccines in an enlightened self-interest manner, where the reduced internationally imported cases outweigh the threat from increased local infections. Such vaccine sharing strategies can also reduce 4.3 (95% CI = 1.2-7.5, P < 0.01) million infections and 7.0 (95% CI = 5.7-8.3, P < 0.001) thousand deaths in middle- and low-income countries, effectively benefiting the whole global population. Lastly, the more equitable vaccine distribution could help largely reduce the global mobility reduction needed for pandemic control.
Conclusions
The incentive mechanism of enlightened self-interest we explored here could motivate vaccine equity by realigning the national interest to more equitable vaccine distributions. The positive results could promote multilateral collaborations in global vaccine redistribution and reconcile conflicted national interests, which could in turn benefit the global population.
... Over the past few decades, researchers have extensively relied on mobility data obtained from census records, surveys, transportation statistics, commuting data, and international air traffic data. Such datasets have widely contributed to a better understanding of human mobility patterns and their impact on the epidemic spread [4][5][6][7][8][9], but can be limited in their resolution or scale. More recently, this gap has been filled by the use of mobile phone data [10,11], primarily based on phone records, but no such data has been available in the United States. ...
Background
Human mobility is expected to be a critical factor in the geographic diffusion of infectious diseases, and this assumption led to the implementation of social distancing policies during the early fight against the COVID-19 emergency in the United States. Yet, because of substantial data gaps in the past, what still eludes our understanding are the following questions: 1) How does mobility contribute to the spread of infection within the United States at local, regional, and national scales? 2) How do seasonality and shifts in behavior affect mobility over time? 3) At what geographic level is mobility homogeneous across the United States? Addressing these questions is critical to developing accurate transmission models, predicting the spatial propagation of disease across scales, and understanding the optimal geographical and temporal scale for the implementation of control policies.
Methods
We address this problem using high-resolution human mobility data measured via mobile app usage. We compute the daily coupling network between US counties, and we integrate our mobility data into a spatially explicit transmission model to reproduce the national invasion of the first wave of SARS-CoV-2 in the US.
Findings
Temporally, we observe that intercounty connectivity is largely seasonal and was unperturbed by mobility restrictions during the early phase of the COVID-19 pandemic. Spatially, we identify 104 geographic clusters of US counties that are highly connected by mobility within the cluster and more sparsely connected to counties outside the cluster. These clusters are stable across time and highly overlap with US state boundaries. Together, these results suggest that intercounty connectivity in the US is relatively static across time and is homogeneous at the sub-state level. We also find that while having access to county-level, daily mobility data best captures the spatial invasion of disease, static mobility data aggregated to the scale of our mobility data-based clusters also performs well in capturing spatial diffusion of infection.
Interpretation
Our work demonstrates that intercounty mobility was negligibly affected outside the lockdown period of Spring 2020, explaining the broad spatial distribution of COVID-19 outbreaks in the US during the early phase of the pandemic. Such geographically dispersed outbreaks place a significant strain on national public health resources and necessitate complex metapopulation modeling approaches for predicting disease dynamics and control design. We thus inform the design of such metapopulation models to balance high disease predictability with low data requirements.
