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Journal articles on the topic 'Metapopulation; Epidemics'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Dearlove, Bethany, and Daniel J. Wilson. "Coalescent inference for infectious disease: meta-analysis of hepatitis C." Philosophical Transactions of the Royal Society B: Biological Sciences 368, no. 1614 (March 19, 2013): 20120314. http://dx.doi.org/10.1098/rstb.2012.0314.

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Genetic analysis of pathogen genomes is a powerful approach to investigating the population dynamics and epidemic history of infectious diseases. However, the theoretical underpinnings of the most widely used, coalescent methods have been questioned, casting doubt on their interpretation. The aim of this study is to develop robust population genetic inference for compartmental models in epidemiology. Using a general approach based on the theory of metapopulations, we derive coalescent models under susceptible–infectious (SI), susceptible–infectious–susceptible (SIS) and susceptible–infectious–recovered (SIR) dynamics. We show that exponential and logistic growth models are equivalent to SI and SIS models, respectively, when co-infection is negligible. Implementing SI, SIS and SIR models in BEAST, we conduct a meta-analysis of hepatitis C epidemics, and show that we can directly estimate the basic reproductive number ( R 0 ) and prevalence under SIR dynamics. We find that differences in genetic diversity between epidemics can be explained by differences in underlying epidemiology (age of the epidemic and local population density) and viral subtype. Model comparison reveals SIR dynamics in three globally restricted epidemics, but most are better fit by the simpler SI dynamics. In summary, metapopulation models provide a general and practical framework for integrating epidemiology and population genetics for the purposes of joint inference.

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2

Lloyd, Alun L., and Vincent A. A. Jansen. "Spatiotemporal dynamics of epidemics: synchrony in metapopulation models." Mathematical Biosciences 188, no. 1-2 (March 2004): 1–16. http://dx.doi.org/10.1016/j.mbs.2003.09.003.

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3

Watts, D. J., R. Muhamad, D. C. Medina, and P. S. Dodds. "Multiscale, resurgent epidemics in a hierarchical metapopulation model." Proceedings of the National Academy of Sciences 102, no. 32 (July 29, 2005): 11157–62. http://dx.doi.org/10.1073/pnas.0501226102.

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4

Wang, Jian-Bo, and Xiang Li. "Uncovering Spatial Invasion on Metapopulation Networks with SIR Epidemics." IEEE Transactions on Network Science and Engineering 6, no. 4 (October 1, 2019): 788–800. http://dx.doi.org/10.1109/tnse.2018.2873609.

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5

Ball, Frank, Tom Britton, Thomas House, Valerie Isham, Denis Mollison, Lorenzo Pellis, and Gianpaolo Scalia Tomba. "Seven challenges for metapopulation models of epidemics, including households models." Epidemics 10 (March 2015): 63–67. http://dx.doi.org/10.1016/j.epidem.2014.08.001.

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6

Nagatani, Takashi, Genki Ichinose, and Kei-ichi Tainaka. "Epidemics of random walkers in metapopulation model for complete, cycle, and star graphs." Journal of Theoretical Biology 450 (August 2018): 66–75. http://dx.doi.org/10.1016/j.jtbi.2018.04.029.

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7

Wiratsudakul, Anuwat, Parinya Suparit, and Charin Modchang. "Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches." PeerJ 6 (March 22, 2018): e4526. http://dx.doi.org/10.7717/peerj.4526.

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BackgroundThe Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics.Survey MethodologyIn this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms “dynamics,” “mathematical model,” “modeling,” and “vector-borne” together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were “compartmental,” “spatial,” “metapopulation,” “network,” “individual-based,” “agent-based” AND “Zika.” All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases.ResultsWe found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks.DiscussionMathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.

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Li, Zhengyan, Huichun Li, Xue Zhang, and Chengli Zhao. "Estimation of Human Mobility Patterns for Forecasting the Early Spread of Disease." Healthcare 9, no. 9 (September 16, 2021): 1224. http://dx.doi.org/10.3390/healthcare9091224.

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Human mobility data are indispensable in modeling large-scale epidemics, especially in predicting the spatial spread of diseases and in evaluating spatial heterogeneity intervention strategies. However, statistical data that can accurately describe large-scale population migration are often difficult to obtain. We propose an algorithm model based on the network science approach, which estimates the travel flow data in mainland China by transforming location big data and airline operation data into network structure information. In addition, we established a simplified deterministic SEIR (Susceptible-Exposed-Infectious-Recovered)-metapopulation model to verify the effectiveness of the estimated travel flow data in the study of predicting epidemic spread. The results show that individual travel distance in mainland China is mainly within 100 km. There is far more travel between prefectures within the same province than across provinces. The epidemic spatial spread model incorporating estimated travel data accurately predicts the spread of COVID-19 in mainland China. The results suggest that there are far more travelers than usual during the Spring Festival in mainland China, and the number of travelers from Wuhan mainly determines the number of confirmed cases of COVID-19 in each prefecture.

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9

Wu, Charles, Catherine Wu, and Kun Chan Wu. "Response to the Coronavirus Disease-2019 Pandemic: Lessons Learned from the Taiwan Model." Asian Social Science 16, no. 10 (September 24, 2020): 16. http://dx.doi.org/10.5539/ass.v16n10p16.

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The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), or coronavirus disease-2019 (COVID-19), emerged in December 2019 in Wuhan, China and has since then spurred a global pandemic (Lai et al., 2020). Taiwan and China, separated only by 130 km across the Taiwan Strait, have frequent cross-strait interactions with each other; millions of people travel to and from between the two countries (Wang & Lin, 2020). Considering these facts, Lauren Gardner, an associate professor at the Johns Hopkins University, even predicted that Taiwan will have the second highest number of COVID-19 cases among the world using a metapopulation model (Gardner et al., 2020). However, with a population of 23.7 million people, Taiwan leads one of the least COVID-19 cases worldwide. With the help of technology, swift reactions, advanced deployment of resources, and complete transparency, the Taiwan model has made its success. By analyzing the actions taken and how they functioned in Taiwan in preventing a nationwide epidemic, other countries may benefit in understanding how to design better models for the prevention of future epidemics and pandemics.

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10

Lieberthal, Brandon, and Allison M. Gardner. "Connectivity, reproduction number, and mobility interact to determine communities’ epidemiological superspreader potential in a metapopulation network." PLOS Computational Biology 17, no. 3 (March 18, 2021): e1008674. http://dx.doi.org/10.1371/journal.pcbi.1008674.

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Disease epidemic outbreaks on human metapopulation networks are often driven by a small number of superspreader nodes, which are primarily responsible for spreading the disease throughout the network. Superspreader nodes typically are characterized either by their locations within the network, by their degree of connectivity and centrality, or by their habitat suitability for the disease, described by their reproduction number (R). Here we introduce a model that considers simultaneously the effects of network properties and R on superspreaders, as opposed to previous research which considered each factor separately. This type of model is applicable to diseases for which habitat suitability varies by climate or land cover, and for direct transmitted diseases for which population density and mitigation practices influences R. We present analytical models that quantify the superspreader capacity of a population node by two measures: probability-dependent superspreader capacity, the expected number of neighboring nodes to which the node in consideration will randomly spread the disease per epidemic generation, and time-dependent superspreader capacity, the rate at which the node spreads the disease to each of its neighbors. We validate our analytical models with a Monte Carlo analysis of repeated stochastic Susceptible-Infected-Recovered (SIR) simulations on randomly generated human population networks, and we use a random forest statistical model to relate superspreader risk to connectivity, R, centrality, clustering, and diffusion. We demonstrate that either degree of connectivity or R above a certain threshold are sufficient conditions for a node to have a moderate superspreader risk factor, but both are necessary for a node to have a high-risk factor. The statistical model presented in this article can be used to predict the location of superspreader events in future epidemics, and to predict the effectiveness of mitigation strategies that seek to reduce the value of R, alter host movements, or both.

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Laine, Anna-Liisa, Jeremy J. Burdon, Adnane Nemri, and Peter H. Thrall. "Host ecotype generates evolutionary and epidemiological divergence across a pathogen metapopulation." Proceedings of the Royal Society B: Biological Sciences 281, no. 1787 (July 22, 2014): 20140522. http://dx.doi.org/10.1098/rspb.2014.0522.

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The extent and speed at which pathogens adapt to host resistance varies considerably. This presents a challenge for predicting when—and where—pathogen evolution may occur. While gene flow and spatially heterogeneous environments are recognized to be critical for the evolutionary potential of pathogen populations, we lack an understanding of how the two jointly shape coevolutionary trajectories between hosts and pathogens. The rust pathogen Melampsora lini infects two ecotypes of its host plant Linum marginale that occur in close proximity yet in distinct populations and habitats. In this study, we found that within-population epidemics were different between the two habitats. We then tested for pathogen local adaptation at host population and ecotype level in a reciprocal inoculation study. Even after controlling for the effect of spatial structure on infection outcome, we found strong evidence of pathogen adaptation at the host ecotype level. Moreover, sequence analysis of two pathogen infectivity loci revealed strong genetic differentiation by host ecotype but not by distance. Hence, environmental variation can be a key determinant of pathogen population genetic structure and coevolutionary dynamics and can generate strong asymmetry in infection risks through space.

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12

Citron, Daniel T., Carlos A. Guerra, Andrew J. Dolgert, Sean L. Wu, John M. Henry, Héctor M. Sánchez C., and David L. Smith. "Comparing metapopulation dynamics of infectious diseases under different models of human movement." Proceedings of the National Academy of Sciences 118, no. 18 (April 29, 2021): e2007488118. http://dx.doi.org/10.1073/pnas.2007488118.

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Newly available datasets present exciting opportunities to investigate how human population movement contributes to the spread of infectious diseases across large geographical distances. It is now possible to construct realistic models of infectious disease dynamics for the purposes of understanding global-scale epidemics. Nevertheless, a remaining unanswered question is how best to leverage the new data to parameterize models of movement, and whether one’s choice of movement model impacts modeled disease outcomes. We adapt three well-studied models of infectious disease dynamics, the susceptible–infected–recovered model, the susceptible–infected–susceptible model, and the Ross–Macdonald model, to incorporate either of two candidate movement models. We describe the effect that the choice of movement model has on each disease model’s results, finding that in all cases, there are parameter regimes where choosing one movement model instead of another has a profound impact on epidemiological outcomes. We further demonstrate the importance of choosing an appropriate movement model using the applied case of malaria transmission and importation on Bioko Island, Equatorial Guinea, finding that one model produces intelligible predictions of R0, whereas the other produces nonsensical results.

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13

Azman, Andrew S., and Justin Lessler. "Reactive vaccination in the presence of disease hotspots." Proceedings of the Royal Society B: Biological Sciences 282, no. 1798 (January 7, 2015): 20141341. http://dx.doi.org/10.1098/rspb.2014.1341.

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Reactive vaccination has recently been adopted as an outbreak response tool for cholera and other infectious diseases. Owing to the global shortage of oral cholera vaccine, health officials must quickly decide who and where to distribute limited vaccine. Targeted vaccination in transmission hotspots (i.e. areas with high transmission efficiency) may be a potential approach to efficiently allocate vaccine, however its effectiveness will likely be context-dependent. We compared strategies for allocating vaccine across multiple areas with heterogeneous transmission efficiency. We constructed metapopulation models of a cholera-like disease and compared simulated epidemics where: vaccine is targeted at areas of high or low transmission efficiency, where vaccine is distributed across the population, and where no vaccine is used. We find that connectivity between populations, transmission efficiency, vaccination timing and the amount of vaccine available all shape the performance of different allocation strategies. In highly connected settings (e.g. cities) when vaccinating early in the epidemic, targeting limited vaccine at transmission hotspots is often optimal. Once vaccination is delayed, targeting the hotspot is rarely optimal, and strategies that either spread vaccine between areas or those targeted at non-hotspots will avert more cases. Although hotspots may be an intuitive outbreak control target, we show that, in many situations, the hotspot-epidemic proceeds so fast that hotspot-targeted reactive vaccination will prevent relatively few cases, and vaccination shared across areas where transmission can be sustained is often best.

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Débarre, Florence, Sebastian Bonhoeffer, and Roland R. Regoes. "The effect of population structure on the emergence of drug resistance during influenza pandemics." Journal of The Royal Society Interface 4, no. 16 (July 3, 2007): 893–906. http://dx.doi.org/10.1098/rsif.2007.1126.

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The spread of H5N1 avian influenza and the recent high numbers of confirmed human cases have raised international concern about the possibility of a new pandemic. Therefore, antiviral drugs are now being stockpiled to be used as a first line of defence. The large-scale use of antivirals will however exert a strong selection pressure on the virus, and may lead to the emergence of drug-resistant strains. A few mathematical models have been developed to assess the emergence of drug resistance during influenza pandemics. These models, however, neglected the spatial structure of large populations and the stochasticity of epidemic and demographic processes. To assess the impact of population structure and stochasticity, we modify and extend a previous model of influenza epidemics into a metapopulation model which takes into account the division of large populations into smaller units, and develop deterministic and stochastic versions of the model. We find that the dynamics in a fragmented population is less explosive, and, as a result, prophylaxis will prevent more infections and lead to fewer resistant cases in both the deterministic and stochastic model. While in the deterministic model the final level of resistance during treatment is not affected by fragmentation, in the stochastic model it is. Our results enable us to qualitatively extrapolate the prediction of deterministic, homogeneous-mixing models to more realistic scenarios.

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Komarova, Natalia L., Luis M. Schang, and Dominik Wodarz. "Patterns of the COVID-19 pandemic spread around the world: exponential versus power laws." Journal of The Royal Society Interface 17, no. 170 (September 2020): 20200518. http://dx.doi.org/10.1098/rsif.2020.0518.

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We have analysed the COVID-19 epidemic data of more than 174 countries (excluding China) in the period between 22 January and 28 March 2020. We found that some countries (such as the USA, the UK and Canada) follow an exponential epidemic growth, while others (like Italy and several other European countries) show a power law like growth. Regardless of the best fitting law, many countries can be shown to follow a common trajectory that is similar to Italy (the epicentre at the time of analysis), but with varying degrees of delay. We found that countries with ‘younger’ epidemics, i.e. countries where the epidemic started more recently, tend to exhibit more exponential like behaviour, while countries that were closer behind Italy tend to follow a power law growth. We hypothesize that there is a universal growth pattern of this infection that starts off as exponential and subsequently becomes more power law like. Although it cannot be excluded that this growth pattern is a consequence of social distancing measures, an alternative explanation is that it is an intrinsic epidemic growth law, dictated by a spatially distributed community structure, where the growth in individual highly mixed communities is exponential but the longer term, local geographical spread (in the absence of global mixing) results in a power law. This is supported by computer simulations of a metapopulation model that gives rise to predictions about the growth dynamics that are consistent with correlations found in the epidemiological data. Therefore, seeing a deviation from straight exponential growth may be a natural progression of the epidemic in each country. On the practical side, this indicates that (i) even in the absence of strict social distancing interventions, exponential growth is not an accurate predictor of longer term infection spread, and (ii) a deviation from exponential spread and a reduction of estimated doubling times do not necessarily indicate successful interventions, which are instead indicated by a transition to a reduced power or by a deviation from power law behaviour.

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Haccou, Patsy, and Maria Conceição Serra. "Establishment versus population growth in spatio-temporally varying environments." Proceedings of the Royal Society B: Biological Sciences 288, no. 1942 (January 6, 2021): 20202009. http://dx.doi.org/10.1098/rspb.2020.2009.

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We consider situations where repeated invasion attempts occur from a source population into a receptor population over extended periods of time. The receptor population contains two locations that provide different expected offspring numbers to invaders. There is demographic stochasticity in offspring numbers. In addition, temporal variation causes local invader fitnesses to vary. We show that effects of environmental autocorrelation on establishment success depend on spatial covariance of the receptor subpopulations. In situations with a low spatial covariance this effect is positive, whereas high spatial covariance and/or high migration probabilities between the subpopulations causes the effect to be negative. This result reconciles seemingly contradictory results from the literature concerning effects of temporal variation on population dynamics with demographic stochasticity. We study an example in the context of genetic introgression, where invasions of cultivar plant genes occur through pollen flow from a source population into wild-type receptor populations, but our results have implications in a wider range of contexts, such as the spread of exotic species, metapopulation dynamics and epidemics.

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Getz, Wayne M., Richard Salter, and Whitney Mgbara. "Adequacy of SEIR models when epidemics have spatial structure: Ebola in Sierra Leone." Philosophical Transactions of the Royal Society B: Biological Sciences 374, no. 1775 (May 6, 2019): 20180282. http://dx.doi.org/10.1098/rstb.2018.0282.

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Dynamic SEIR (Susceptible, Exposed, Infectious, Removed) compartmental models provide a tool for predicting the size and duration of both unfettered and managed outbreaks—the latter in the context of interventions such as case detection, patient isolation, vaccination and treatment. The reliability of this tool depends on the validity of key assumptions that include homogeneity of individuals and spatio-temporal homogeneity. Although the SEIR compartmental framework can easily be extended to include demographic (e.g. age) and additional disease (e.g. healthcare workers) classes, dependence of transmission rates on time, and metapopulation structure, fitting such extended models is hampered by both a proliferation of free parameters and insufficient or inappropriate data. This raises the question of how effective a tool the basic SEIR framework may actually be. We go some way here to answering this question in the context of the 2014–2015 outbreak of Ebola in West Africa by comparing fits of an SEIR time-dependent transmission model to both country- and district-level weekly incidence data. Our novel approach in estimating the effective-size-of-the-populations-at-risk ( N eff ) and initial number of exposed individuals ( E 0 ) at both district and country levels, as well as the transmission function parameters, including a time-to-halving-the-force-of-infection ( t f/2 ) parameter, provides new insights into this Ebola outbreak. It reveals that the estimate R 0 ≈ 1.7 from country-level data appears to seriously underestimate R 0 ≈ 3.3 − 4.3 obtained from more spatially homogeneous district-level data. Country-level data also overestimate t f/2 ≈ 22 weeks, compared with 8–10 weeks from district-level data. Additionally, estimates for the duration of individual infectiousness is around two weeks from spatially inhomogeneous country-level data compared with 2.4–4.5 weeks from spatially more homogeneous district-level data, which estimates are rather high compared with most values reported in the literature. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’. This issue is linked with the subsequent theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’.

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Rowthorn, Robert E., Ramanan Laxminarayan, and Christopher A. Gilligan. "Optimal control of epidemics in metapopulations." Journal of The Royal Society Interface 6, no. 41 (March 3, 2009): 1135–44. http://dx.doi.org/10.1098/rsif.2008.0402.

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Little is known about how best to deploy scarce resources for disease control when epidemics occur in different but interconnected regions. We use a combination of optimal control methods and epidemiological theory for metapopulations to address this problem. We consider what strategy should be used if the objective is to minimize the discounted number of infected individuals during the course of an epidemic. We show, for a system with two interconnected regions and an epidemic in which infected individuals recover and can be reinfected, that equalizing infection in the two regions is the worst possible strategy in minimizing the total level of infection. Treatment should instead be preferentially directed at the region with the lower level of infection, treating the other subpopulation only when there is resource left over. The same strategy holds with preferential treatments of regions with lower levels of infection when quarantine is introduced.

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Stone, Chris M., Samantha R. Schwab, Dina M. Fonseca, and Nina H. Fefferman. "Human movement, cooperation and the effectiveness of coordinated vector control strategies." Journal of The Royal Society Interface 14, no. 133 (August 2017): 20170336. http://dx.doi.org/10.1098/rsif.2017.0336.

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Vector-borne disease transmission is often typified by highly focal transmission and influenced by movement of hosts and vectors across different scales. The ecological and environmental conditions (including those created by humans through vector control programmes) that result in metapopulation dynamics remain poorly understood. The development of control strategies that would most effectively limit outbreaks given such dynamics is particularly urgent given the recent epidemics of dengue, chikungunya and Zika viruses. We developed a stochastic, spatial model of vector-borne disease transmission, allowing for movement of hosts between patches. Our model is applicable to arbovirus transmission by Aedes aegypti in urban settings and was parametrized to capture Zika virus transmission in particular. Using simulations, we investigated the extent to which two aspects of vector control strategies are affected by human commuting patterns: the extent of coordination and cooperation between neighbouring communities. We find that transmission intensity is highest at intermediate levels of host movement. The extent to which coordination of control activities among neighbouring patches decreases the prevalence of infection is affected by both how frequently humans commute and the proportion of neighbouring patches that commits to vector surveillance and control activities. At high levels of host movement, patches that do not contribute to vector control may act as sources of infection in the landscape, yet have comparable levels of prevalence as patches that do cooperate. This result suggests that real cooperation among neighbours will be critical to the development of effective pro-active strategies for vector-borne disease control in today's commuter-linked communities.

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Metcalf, C. J. E., C. V. Munayco, G. Chowell, B. T. Grenfell, and O. N. Bjørnstad. "Rubella metapopulation dynamics and importance of spatial coupling to the risk of congenital rubella syndrome in Peru." Journal of The Royal Society Interface 8, no. 56 (July 21, 2010): 369–76. http://dx.doi.org/10.1098/rsif.2010.0320.

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Rubella is generally a mild childhood disease, but infection during early pregnancy may cause spontaneous abortion or congenital rubella syndrome (CRS), which may entail a variety of birth defects. Consequently, understanding the age-structured dynamics of this infection has considerable public health value. Vaccination short of the threshold for local elimination of transmission will increase the average age of infection. Accordingly, the classic concern for this infection is the potential for vaccination to increase incidence in individuals of childbearing age. A neglected aspect of rubella dynamics is how age incidence patterns may be moulded by the spatial dynamics inherent to epidemic metapopulations. Here, we use a uniquely detailed dataset from Peru to explore the implications of this for the burden of CRS. Our results show that the risk of CRS may be particularly severe in small remote regions, a prediction at odds with expectations in the endemic situation, and with implications for the outcome of vaccination. This outcome results directly from the metapopulation context: specifically, extinction–re-colonization dynamics are crucial because they allow for significant leakage of susceptible individuals into the older age classes during inter-epidemic periods with the potential to increase CRS risk by as much as fivefold.

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Han, Dun, Qi Shao, and Dandan Li. "Exploring the Epidemic Spreading in a Multilayer Metapopulation Network by considering Individuals’ Periodic Travelling." Complexity 2020 (April 21, 2020): 1–9. http://dx.doi.org/10.1155/2020/6782018.

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The convenience of transportation brings the diversity of individuals’ travelling modes; in this paper, we present an improved epidemic diffusion model in a multilayer metapopulation network. Firstly, we construct the metapopulation network with different travelling ways, and then, the epidemic spreading threshold is calculated by means of the mean-field method. Taking the periodicity of individuals’ travelling into account, we further explore the epidemic diffusion model with individuals’ periodic travelling and deduce the epidemic spreading threshold using the Perron–Frobenius theorem. Our results show that if all individuals in each area decide to move, the epidemic threshold can be effectively raised while each individual chooses an unbiased region to arrive. In addition, with the increase of individuals’ mobility rate or regional heterogeneous infection coefficient, the fluctuation range of the density of infected becomes larger, while the fluctuation period is almost unchanged. However, the change of individuals’ periodic motion could cause the change of the fluctuation period of infected density. We try to provide a new perspective for the research of metapopulation.

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Calvetti, Daniela, Alexander P. Hoover, Johnie Rose, and Erkki Somersalo. "Modeling Epidemic Spread among a Commuting Population Using Transport Schemes." Mathematics 9, no. 16 (August 5, 2021): 1861. http://dx.doi.org/10.3390/math9161861.

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Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamics in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in the Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two.

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Duncan, Alison B., Andrew Gonzalez, and Oliver Kaltz. "Stochastic environmental fluctuations drive epidemiology in experimental host–parasite metapopulations." Proceedings of the Royal Society B: Biological Sciences 280, no. 1769 (October 22, 2013): 20131747. http://dx.doi.org/10.1098/rspb.2013.1747.

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Environmental fluctuations are important for parasite spread and persistence. However, the effects of the spatial and temporal structure of environmental fluctuations on host–parasite dynamics are not well understood. Temporal fluctuations can be random but positively autocorrelated, such that the environment is similar to the recent past (red noise), or random and uncorrelated with the past (white noise). We imposed red or white temporal temperature fluctuations on experimental metapopulations of Paramecium caudatum , experiencing an epidemic of the bacterial parasite Holospora undulata . Metapopulations (two subpopulations linked by migration) experienced fluctuations between stressful (5°C) and permissive (23°C) conditions following red or white temporal sequences. Spatial variation in temperature fluctuations was implemented by exposing subpopulations to the same (synchronous temperatures) or different (asynchronous temperatures) temporal sequences. Red noise, compared with white noise, enhanced parasite persistence. Despite this, red noise coupled with asynchronous temperatures allowed infected host populations to maintain sizes equivalent to uninfected populations. It is likely that this occurs because subpopulations in permissive conditions rescue declining subpopulations in stressful conditions. We show how patterns of temporal and spatial environmental fluctuations can impact parasite spread and host population abundance. We conclude that accurate prediction of parasite epidemics may require realistic models of environmental noise.

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Wang, Yi, and Zhen Jin. "Epidemic Threshold for Metapopulation Networks with Demographical Dynamics." Advanced Materials Research 268-270 (July 2011): 2097–100. http://dx.doi.org/10.4028/www.scientific.net/amr.268-270.2097.

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In this paper, we investigate the dynamics of an epidemic model with birth anddeath and reaction-di usion processes in heterogeneous metapopulation networks. By mean- eld analysis, we obtain the conditions that the disease will outbreak on networks for somespeci c cases. This reminds us both the structure of the networks and population demographyplay an important role on the spread of infectious disease.

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Zhu, Xuzhen, Yuxin Liu, Shengfeng Wang, Ruijie Wang, Xiaolong Chen, and Wei Wang. "Allocating resources for epidemic spreading on metapopulation networks." Applied Mathematics and Computation 411 (December 2021): 126531. http://dx.doi.org/10.1016/j.amc.2021.126531.

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26

Ndeffo Mbah, Martial L., and Christopher A. Gilligan. "Resource Allocation for Epidemic Control in Metapopulations." PLoS ONE 6, no. 9 (September 13, 2011): e24577. http://dx.doi.org/10.1371/journal.pone.0024577.

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Caudron, Q., A. S. Mahmud, C. J. E. Metcalf, M. Gottfreðsson, C. Viboud, A. D. Cliff, and B. T. Grenfell. "Predictability in a highly stochastic system: final size of measles epidemics in small populations." Journal of The Royal Society Interface 12, no. 102 (January 2015): 20141125. http://dx.doi.org/10.1098/rsif.2014.1125.

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A standard assumption in the modelling of epidemic dynamics is that the population of interest is well mixed, and that no clusters of metapopulations exist. The well-known and oft-used SIR model, arguably the most important compartmental model in theoretical epidemiology, assumes that the disease being modelled is strongly immunizing, directly transmitted and has a well-defined period of infection, in addition to these population mixing assumptions. Childhood infections, such as measles, are prime examples of diseases that fit the SIR-like mechanism. These infections have been well studied for many systems with large, well-mixed populations with endemic infection. Here, we consider a setting where populations are small and isolated. The dynamics of infection are driven by stochastic extinction–recolonization events, producing large, sudden and short-lived epidemics before rapidly dying out from a lack of susceptible hosts. Using a TSIR model, we fit prevaccination measles incidence and demographic data in Bornholm, the Faroe Islands and four districts of Iceland, between 1901 and 1965. The datasets for each of these countries suffer from different levels of data heterogeneity and sparsity. We explore the potential for prediction of this model: given historical incidence data and up-to-date demographic information, and knowing that a new epidemic has just begun, can we predict how large it will be? We show that, despite a lack of significant seasonality in the incidence of measles cases, and potentially severe heterogeneity at the population level, we are able to estimate the size of upcoming epidemics, conditioned on the first time step, to within reasonable confidence. Our results have potential implications for possible control measures for the early stages of new epidemics in small populations.

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Liu, Maoxing, Jie Zhang, Zhengguang Li, and Yongzheng Sun. "Modeling epidemic in metapopulation networks with heterogeneous diffusion rates." Mathematical Biosciences and Engineering 16, no. 6 (2019): 7085–97. http://dx.doi.org/10.3934/mbe.2019355.

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29

Bolzoni, Luca, Rossella Della Marca, Maria Groppi, and Alessandra Gragnani. "Dynamics of a metapopulation epidemic model with localized culling." Discrete & Continuous Dynamical Systems - B 25, no. 6 (2020): 2307–30. http://dx.doi.org/10.3934/dcdsb.2020036.

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30

IGGIDR, ABDERRAHMAN, GAUTHIER SALLET, and BERGE TSANOU. "Global Stability Analysis of a Metapopulation SIS Epidemic Model." Mathematical Population Studies 19, no. 3 (July 2012): 115–29. http://dx.doi.org/10.1080/08898480.2012.693844.

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31

Wang, Jianrong, Maoxing Liu, and Youwen Li. "Analysis of epidemic models with demographics in metapopulation networks." Physica A: Statistical Mechanics and its Applications 392, no. 7 (April 2013): 1621–30. http://dx.doi.org/10.1016/j.physa.2012.12.007.

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32

Gong, Yong-Wang, Yu-Rong Song, and Guo-Ping Jiang. "Time-varying human mobility patterns with metapopulation epidemic dynamics." Physica A: Statistical Mechanics and its Applications 392, no. 19 (October 2013): 4242–51. http://dx.doi.org/10.1016/j.physa.2013.05.028.

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33

Gong, Yong-Wang, Yu-Rong Song, and Guo-Ping Jiang. "Epidemic spreading in metapopulation networks with heterogeneous infection rates." Physica A: Statistical Mechanics and its Applications 416 (December 2014): 208–18. http://dx.doi.org/10.1016/j.physa.2014.08.056.

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34

Apolloni, Andrea, Chiara Poletto, José J. Ramasco, Pablo Jensen, and Vittoria Colizza. "Metapopulation epidemic models with heterogeneous mixing and travel behaviour." Theoretical Biology and Medical Modelling 11, no. 1 (2014): 3. http://dx.doi.org/10.1186/1742-4682-11-3.

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35

Gong, Yongwang, and Michael Small. "Epidemic spreading on metapopulation networks including migration and demographics." Chaos: An Interdisciplinary Journal of Nonlinear Science 28, no. 8 (August 2018): 083102. http://dx.doi.org/10.1063/1.5021167.

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36

Shao, Qi, and Dun Han. "Epidemic spreading in metapopulation networks with heterogeneous mobility rates." Applied Mathematics and Computation 412 (January 2022): 126559. http://dx.doi.org/10.1016/j.amc.2021.126559.

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37

Doungmo Goufo, Emile Franc, Suares Clovis Oukouomi Noutchie, and Stella Mugisha. "A Fractional SEIR Epidemic Model for Spatial and Temporal Spread of Measles in Metapopulations." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/781028.

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Measles is a higher contagious disease that can spread in a community population depending on the number of people (children) susceptible or infected and also depending on their movement in the community. In this paper we present a fractional SEIR metapopulation system modeling the spread of measles. We restrict ourselves to the dynamics between four distinct cities (patches). We prove that the fractional metapopulation model is well posed (nonnegative solutions) and we provide the condition for the stability of the disease-free equilibrium. Numerical simulations show that infection will be proportional to the size of population in each city, but the disease will die out. This is an expected result since it is well known for measles (Bartlett (1957)) that, in communities which generate insufficient new hosts, the disease will die out.

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Wang, Jian-Bo, Lang Cao, and Xiang Li. "On Estimating Spatial Epidemic Parameters of a Simplified Metapopulation Model." IFAC Proceedings Volumes 46, no. 13 (2013): 383–88. http://dx.doi.org/10.3182/20130708-3-cn-2036.00047.

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39

Wang, Bing, Yuexing Han, and Gouhei Tanaka. "Interplay between epidemic spread and information propagation on metapopulation networks." Journal of Theoretical Biology 420 (May 2017): 18–25. http://dx.doi.org/10.1016/j.jtbi.2017.02.020.

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Gong, Yongwang, and Michael Small. "Modelling the effect of heterogeneous vaccination on metapopulation epidemic dynamics." Physics Letters A 383, no. 35 (December 2019): 125996. http://dx.doi.org/10.1016/j.physleta.2019.125996.

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41

Desalegn, Petros Kelkile, Samuel Mwalili, and John Mango. "Stability Analysis of a Deterministic Epidemic Model in Metapopulation Setting." Advances in Pure Mathematics 08, no. 03 (2018): 219–31. http://dx.doi.org/10.4236/apm.2018.83011.

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42

Huang, Wei, and Shengyong Chen. "Epidemic metapopulation model with traffic routing in scale-free networks." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 12 (December 7, 2011): P12004. http://dx.doi.org/10.1088/1742-5468/2011/12/p12004.

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43

Masuda, Naoki. "Effects of diffusion rates on epidemic spreads in metapopulation networks." New Journal of Physics 12, no. 9 (September 6, 2010): 093009. http://dx.doi.org/10.1088/1367-2630/12/9/093009.

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44

Vespignani, A. "Reaction-diffusion processes and epidemic metapopulation models in complex networks." European Physical Journal B 64, no. 3-4 (August 2008): 349–53. http://dx.doi.org/10.1140/epjb/e2008-00302-y.

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45

PATANARAPEELERT, KLOT. "INVESTIGATING THE ROLE OF WITHIN- AND BETWEEN-PATCH MOVEMENT IN A DYNAMIC MODEL OF DISEASE SPREAD." Journal of Biological Systems 28, no. 04 (October 12, 2020): 815–37. http://dx.doi.org/10.1142/s0218339020500187.

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The impact of human mobility on the spreading of disease in a metapopulation is emphasized on interconnecting between patches, whereas the current volume of movement within the local population is usually neglected. Here, the role of internal commuters is taken into account by two means, a local transmission rate and the volume of internal commuters. Dynamic model of human mobility in the metapopulation with gravity coupling is presented. In conjunction with the disease spreading, the impact on invasion threshold and epidemic final size are analyzed. For two-patch model, we show that under fixing parameters in gravity model, the existence of invasion threshold depends on the difference of local transmission rates and the proportion of internal commuters between two patches. For a fully connected network with an identical transmission rate, the difference in patch final sizes is driven by patch distribution of internal commuters. By neglecting the effect of spatial variation in a simple core–satellite model, we show that the heterogeneity of internal commuters and gravity coupling induce a complex pattern of threshold, which depend mostly on the exponent in gravity model, and are responsible for the differences among local epidemic sizes.

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Krause, Andrew L., Lawrence Kurowski, Kamran Yawar, and Robert A. Van Gorder. "Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies." Journal of Theoretical Biology 449 (July 2018): 35–52. http://dx.doi.org/10.1016/j.jtbi.2018.04.023.

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47

Qian, Rongrong, and Yuan Qi. "Analysis for hidden-geometry phenomenon of epidemic spreading in metapopulation networks." International Journal of Automation and Logistics 2, no. 3 (2016): 234. http://dx.doi.org/10.1504/ijal.2016.078493.

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48

Bjørnstad, Ottar N., and Bryan T. Grenfell. "Hazards, spatial transmission and timing of outbreaks in epidemic metapopulations." Environmental and Ecological Statistics 15, no. 3 (December 6, 2007): 265–77. http://dx.doi.org/10.1007/s10651-007-0059-3.

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49

Li, Lingbo, Ying Fan, An Zeng, and Zengru Di. "Understanding the Anticontagion Process and Reopening of China during COVID-19 via Coevolution Network of Epidemic and Awareness." Complexity 2021 (May 11, 2021): 1–11. http://dx.doi.org/10.1155/2021/6623427.

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The novel coronavirus (COVID-19) pandemic is intensifying all over the world, but some countries, including China, have developed extensive and successful experience in controlling this pandemic. In this context, some questions arise naturally: What can countries caught up in the epidemic learn from China’s experience? In regions where the outbreak is under control, what would lead to a resurgence of the epidemic? To address these issues, we investigate China’s experience in anticontagion interventions and reopening process, focusing on the coevolution of epidemic and awareness during COVID-19 outbreak. Through an empirical analysis based on large-scale data and simulation based on a metapopulation and multilayer network model, we ascertain the impact of human movements and awareness diffusion on the epidemic, elucidate the inherent patterns and effective interventions of different epidemic prevention methods, and highlight the crunch time of each measure. The results are also employed to analyze COVID-19 evolution in other countries so as to find unified rules in complex situations around the world and provide advice on anticontagion and reopening policies. Our findings explain some key mechanisms of epidemic prevention and may help the epidemic analysis and decision-making in various countries suffering from COVID-19.

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Nagatani, Takashi, Genki Ichinose, and Kei-ichi Tainaka. "Epidemic spreading of random walkers in metapopulation model on an alternating graph." Physica A: Statistical Mechanics and its Applications 520 (April 2019): 350–60. http://dx.doi.org/10.1016/j.physa.2019.01.033.

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