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

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          Abstract

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

          Author summary

          We study the interplay between urbanisation and infectious disease spread. As part of the worldwide urbanisation process, people are continuously moving to urban areas, and the cities are growing in size. This causes clusters of areas with high population density and clusters of areas with low population density, which is what we call population clustering. By simulating infectious disease spread in a synthetic country where we vary this population clustering, we explore the consequences of urbanisation on infectious disease spread. Our qualitative results have direct implications for infectious disease control guidelines and policies. We find that implementing internal travel restrictions have greater impact on the final number ill in the most urbanised countries than in the less urbanised countries. The effect is largest in the more rural parts of the country. According to our model, travel restrictions are more effective in delaying the epidemic in the less urbanised countries than in the more urbanised countries. We investigate vaccination strategies, where locations are targeted depending on how urban or rural they are. We find that it is important to vaccinate the urban locations—if the most urban locations are not covered by the vaccine, the final number ill will be a lot larger.

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          Most cited references42

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          A universal model for mobility and migration patterns.

          Introduced in its contemporary form in 1946 (ref. 1), but with roots that go back to the eighteenth century, the gravity law is the prevailing framework with which to predict population movement, cargo shipping volume and inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of the phenomena affected by mobility and transport processes.
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            Urbanization, malaria transmission and disease burden in Africa.

            Many attempts have been made to quantify Africa's malaria burden but none has addressed how urbanization will affect disease transmission and outcome, and therefore mortality and morbidity estimates. In 2003, 39% of Africa's 850 million people lived in urban settings; by 2030, 54% of Africans are expected to do so. We present the results of a series of entomological, parasitological and behavioural meta-analyses of studies that have investigated the effect of urbanization on malaria in Africa. We describe the effect of urbanization on both the impact of malaria transmission and the concomitant improvements in access to preventative and curative measures. Using these data, we have recalculated estimates of populations at risk of malaria and the resulting mortality. We find there were 1,068,505 malaria deaths in Africa in 2000 - a modest 6.7% reduction over previous iterations. The public-health implications of these findings and revised estimates are discussed.
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              Urbanisation and infectious diseases in a globalised world

              Summary The world is becoming urban. The UN predicts that the world's urban population will almost double from 3·3 billion in 2007 to 6·3 billion in 2050. Most of this increase will be in developing countries. Exponential urban growth is having a profound effect on global health. Because of international travel and migration, cities are becoming important hubs for the transmission of infectious diseases, as shown by recent pandemics. Physicians in urban environments in developing and developed countries need to be aware of the changes in infectious diseases associated with urbanisation. Furthermore, health should be a major consideration in town planning to ensure urbanisation works to reduce the burden of infectious diseases in the future.
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                Author and article information

                Contributors
                Role: ConceptualizationRole: Formal analysisRole: MethodologyRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: ConceptualizationRole: MethodologyRole: SupervisionRole: Writing – review & editing
                Role: ConceptualizationRole: MethodologyRole: SupervisionRole: Writing – review & editing
                Role: ConceptualizationRole: MethodologyRole: SupervisionRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, CA USA )
                1553-734X
                1553-7358
                March 2019
                7 March 2019
                : 15
                : 3
                : e1006879
                Affiliations
                [1 ] Oslo Centre for Biostatistics and Epidemiology, Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway
                [2 ] Department of Infectious Disease Epidemiology and Modelling, Division for Infection Control and Environmental Health, Norwegian Institute of Public Health, Oslo, Norway
                [3 ] Telenor Research, Telenor Group, Fornebu, Norway
                [4 ] Oslo Centre for Biostatistics and Epidemiology, Oslo University Hospital, Oslo, Norway
                London School of Hygiene & Tropical Medicine, UNITED KINGDOM
                Author notes

                The authors have declared that no competing interests exist.

                Author information
                http://orcid.org/0000-0002-7064-0869
                http://orcid.org/0000-0003-1618-7597
                Article
                PCOMPBIOL-D-18-01548
                10.1371/journal.pcbi.1006879
                6424465
                30845153
                4ca0d55f-0984-451a-b41d-a609965b0ed2
                © 2019 Engebretsen et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 6 September 2018
                : 18 February 2019
                Page count
                Figures: 14, Tables: 7, Pages: 36
                Funding
                SE and AF acknowledge partial funding from the Norwegian Research Council centre BigInsight project 237718. The funders had no role in study resign, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology and Life Sciences
                Immunology
                Vaccination and Immunization
                Medicine and Health Sciences
                Immunology
                Vaccination and Immunization
                Medicine and Health Sciences
                Public and Occupational Health
                Preventive Medicine
                Vaccination and Immunization
                Earth Sciences
                Geography
                Human Geography
                Human Mobility
                Social Sciences
                Human Geography
                Human Mobility
                Medicine and Health Sciences
                Infectious Diseases
                Earth Sciences
                Geography
                Geographic Areas
                Urban Areas
                Medicine and Health Sciences
                Epidemiology
                Disease Dynamics
                People and Places
                Geographical Locations
                Europe
                Norway
                Medicine and Health Sciences
                Infectious Diseases
                Viral Diseases
                Influenza
                Earth Sciences
                Geography
                Geographic Areas
                Rural Areas
                Custom metadata
                vor-update-to-uncorrected-proof
                2019-03-19
                The population size data for Norway are available at Statistics Norway ( http://www.ssb.no/en/statbank/table/11342/). The commuting data for Norway are available at Statistics Norway ( https://www.ssb.no/statbank/table/03321). The population sizes for Iceland are available at Statistics Iceland ( https://px.hagstofa.is/pxis/pxweb/is/Ibuar/Ibuar__mannfjoldi__2_byggdir__Byggdakjarnarhverfi/MAN03200.px/). Population data for the UK are available at the Office for National Statistics GB ( https://www.ons.gov.uk/peoplepopulationandcommunity/populationandmigration/populationestimates/datasets/populationestimatesforukenglandandwalesscotlandandnorthernireland).

                Quantitative & Systems biology
                Quantitative & Systems biology

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