{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T04:10:58Z","timestamp":1785903058971,"version":"3.56.0"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,12,16]],"date-time":"2019-12-16T00:00:00Z","timestamp":1576454400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,12,16]],"date-time":"2019-12-16T00:00:00Z","timestamp":1576454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["MOST 108-2638-H-002-002-MY2"],"award-info":[{"award-number":["MOST 108-2638-H-002-002-MY2"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004737","name":"National Health Research Institutes","doi-asserted-by":"publisher","award":["NHRI-108A1-MRCO-0619191"],"award-info":[{"award-number":["NHRI-108A1-MRCO-0619191"]}],"id":[{"id":"10.13039\/501100004737","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The basic reproductive number (<jats:italic>R<\/jats:italic><jats:sub>0<\/jats:sub>) is a fundamental measure used to quantify the transmission potential of an epidemic in public health practice. However, <jats:italic>R<\/jats:italic><jats:sub>0<\/jats:sub> cannot reflect the time-varying nature of an epidemic. A time-varying effective reproductive number <jats:italic>R<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> can provide more information because it tracks the subsequent evolution of transmission. However, since it neglects individual-level geographical variations in exposure risk, <jats:italic>R<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> may smooth out interpersonal heterogeneous transmission potential, obscure high-risk spreaders, and hence hamper the effectiveness of control measures in spatial dimension. Therefore, this study proposes a new method for quantifying spatially adjusted (time-varying) reproductive numbers that reflects spatial heterogeneity in transmission potential among individuals. This new method estimates individual-level effective reproductive numbers (<jats:italic>R<\/jats:italic><jats:sup><jats:italic>j<\/jats:italic><\/jats:sup>) and a summarized indicator for population-level time-varying reproductive number (<jats:italic>R<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub>). Data from the five most severe dengue outbreaks in southern Taiwan from 1998\u20132015 were used to demonstrate the ability of the method to highlight early spreaders contributing to the geographic expansion of dengue transmission. Our results show spatial heterogeneity in the transmission potential of dengue among individuals and identify the spreaders with the highest <jats:italic>R<\/jats:italic><jats:sup><jats:italic>j<\/jats:italic><\/jats:sup> during the epidemic period. The results also reveal that super-spreaders are usually early spreaders that locate at the edges of the epidemic foci, which means that these cases could be the drivers of the expansion of the outbreak. Therefore, our proposed method depicts a more detailed spatial-temporal dengue transmission process and identifies the significant role of the edges of the epidemic foci, which could be weak spots in disease control and prevention.<\/jats:p>","DOI":"10.1038\/s41598-019-55574-0","type":"journal-article","created":{"date-parts":[[2019,12,16]],"date-time":"2019-12-16T11:03:32Z","timestamp":1576494212000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Spatially Adjusted Time-varying Reproductive Numbers: Understanding the Geographical Expansion of Urban Dengue Outbreaks"],"prefix":"10.1038","volume":"9","author":[{"given":"Ta-Chou","family":"Ng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tzai-Hung","family":"Wen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,12,16]]},"reference":[{"key":"55574_CR1","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1111\/j.1467-9574.1996.tb01482.x","volume":"50","author":"J Heesterbeek","year":"1996","unstructured":"Heesterbeek, J. & Dietz, K. The concept of Ro in epidemic theory. Statistica Neerlandica 50, 89\u2013110 (1996).","journal-title":"Statistica Neerlandica"},{"key":"55574_CR2","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1177\/096228029300200103","volume":"2","author":"K Dietz","year":"1993","unstructured":"Dietz, K. The estimation of the basic reproduction number for infectious diseases. Statistical methods in medical research 2, 23\u201341 (1993).","journal-title":"Statistical methods in medical research"},{"key":"55574_CR3","unstructured":"Vynnycky, E. & White, R. An introduction to infectious disease modelling. OUP oxford, (2010)."},{"key":"55574_CR4","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1098\/rsif.2005.0042","volume":"2","author":"JM Heffernan","year":"2005","unstructured":"Heffernan, J. M., Smith, R. J. & Wahl, L. M. Perspectives on the basic reproductive ratio. Journal of the Royal Society Interface 2, 281\u2013293 (2005).","journal-title":"Journal of the Royal Society Interface"},{"key":"55574_CR5","doi-asserted-by":"crossref","unstructured":"Yi, W. & JinDe, C. Final size of network epidemic models: Properties and connections. SCIENCE CHINA Information Sciences. Advance online publication. doi:10.1007\/s11432-019-2656-2 (2019).","DOI":"10.1007\/s11432-019-2656-2"},{"key":"55574_CR6","doi-asserted-by":"crossref","unstructured":"Cauchemez, S., Hoze, N., Cousien, A. & Nikolay, B. How Modelling Can Enhance the Analysis of Imperfect Epidemic Data. Trends in parasitology (2019).","DOI":"10.1016\/j.pt.2019.01.009"},{"key":"55574_CR7","doi-asserted-by":"publisher","first-page":"1557","DOI":"10.1126\/science.1176062","volume":"324","author":"C Fraser","year":"2009","unstructured":"Fraser, C. et al. Pandemic potential of a strain of influenza A (H1N1): early findings. Science 324, 1557\u20131561 (2009).","journal-title":"Science"},{"key":"55574_CR8","doi-asserted-by":"publisher","first-page":"1966","DOI":"10.1126\/science.1086616","volume":"300","author":"M Lipsitch","year":"2003","unstructured":"Lipsitch, M. et al. Transmission dynamics and control of severe acute respiratory syndrome. Science 300, 1966\u20131970 (2003).","journal-title":"Science"},{"key":"55574_CR9","doi-asserted-by":"publisher","first-page":"e420","DOI":"10.1016\/S1473-3099(17)30307-9","volume":"17","author":"FM Guerra","year":"2017","unstructured":"Guerra, F. M. et al. The basic reproduction number (R0) of measles: a systematic review. The Lancet Infectious Diseases 17, e420\u2013e428 (2017).","journal-title":"The Lancet Infectious Diseases"},{"key":"55574_CR10","doi-asserted-by":"publisher","first-page":"12680","DOI":"10.1073\/pnas.1811115115","volume":"115","author":"Q-H Liu","year":"2018","unstructured":"Liu, Q.-H. et al. Measurability of the epidemic reproduction number in data-driven contact networks. Proceedings of the National Academy of Sciences 115, 12680\u201312685 (2018).","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"55574_CR11","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1098\/rspb.2006.3754","volume":"274","author":"J Wallinga","year":"2006","unstructured":"Wallinga, J. & Lipsitch, M. How generation intervals shape the relationship between growth rates and reproductive numbers. Proceedings of the Royal Society B: Biological Sciences 274, 599\u2013604 (2006).","journal-title":"Proceedings of the Royal Society B: Biological Sciences"},{"key":"55574_CR12","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1016\/S1473-3099(14)71075-8","volume":"15","author":"O Faye","year":"2015","unstructured":"Faye, O. et al. Chains of transmission and control of Ebola virus disease in Conakry, Guinea, in 2014: an observational study. The Lancet Infectious Diseases 15, 320\u2013326 (2015).","journal-title":"The Lancet Infectious Diseases"},{"key":"55574_CR13","doi-asserted-by":"publisher","first-page":"1505","DOI":"10.1093\/aje\/kwt133","volume":"178","author":"A Cori","year":"2013","unstructured":"Cori, A., Ferguson, N. M., Fraser, C. & Cauchemez, S. A new framework and software to estimate time-varying reproduction numbers during epidemics. American journal of epidemiology 178, 1505\u20131512 (2013).","journal-title":"American journal of epidemiology"},{"key":"55574_CR14","doi-asserted-by":"publisher","first-page":"1481","DOI":"10.1056\/NEJMoa1411100","volume":"371","author":"WER Team","year":"2014","unstructured":"Team, W. E. R. Ebola virus disease in West Africa\u2014the first 9 months of the epidemic and forward projections. New England Journal of Medicine 371, 1481\u20131495 (2014).","journal-title":"New England Journal of Medicine"},{"key":"55574_CR15","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1093\/aje\/kwh255","volume":"160","author":"J Wallinga","year":"2004","unstructured":"Wallinga, J. & Teunis, P. Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. American Journal of epidemiology 160, 509\u2013516 (2004).","journal-title":"American Journal of epidemiology"},{"key":"55574_CR16","doi-asserted-by":"publisher","first-page":"21484","DOI":"10.1073\/pnas.0906910106","volume":"106","author":"D Balcan","year":"2009","unstructured":"Balcan, D. et al. Multiscale mobility networks and the spatial spreading of infectious diseases. Proceedings of the National Academy of Sciences 106, 21484\u201321489 (2009).","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"55574_CR17","doi-asserted-by":"publisher","first-page":"e74","DOI":"10.1371\/journal.pmed.0050074","volume":"5","author":"J Mossong","year":"2008","unstructured":"Mossong, J. et al. Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS medicine 5, e74 (2008).","journal-title":"PLoS medicine"},{"key":"55574_CR18","doi-asserted-by":"publisher","first-page":"e15923","DOI":"10.1371\/journal.pone.0015923","volume":"6","author":"C Roth","year":"2011","unstructured":"Roth, C., Kang, S. M., Batty, M. & Barth\u00e9lemy, M. Structure of urban movements: polycentric activity and entangled hierarchical flows. PloS one 6, e15923 (2011).","journal-title":"PloS one"},{"key":"55574_CR19","doi-asserted-by":"publisher","first-page":"1298","DOI":"10.1126\/science.1134695","volume":"316","author":"S Riley","year":"2007","unstructured":"Riley, S. Large-scale spatial-transmission models of infectious disease. Science 316, 1298\u20131301 (2007).","journal-title":"Science"},{"key":"55574_CR20","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1098\/rspb.2004.3020","volume":"272","author":"C Favier","year":"2005","unstructured":"Favier, C. et al. Influence of spatial heterogeneity on an emerging infectious disease: the case of dengue epidemics. Proceedings of the Royal Society B: Biological Sciences 272, 1171\u20131177 (2005).","journal-title":"Proceedings of the Royal Society B: Biological Sciences"},{"key":"55574_CR21","doi-asserted-by":"publisher","first-page":"593","DOI":"10.7326\/0003-4819-154-9-201105030-00334","volume":"154","author":"AR Tuite","year":"2011","unstructured":"Tuite, A. R. et al. Cholera epidemic in Haiti, 2010: using a transmission model to explain spatial spread of disease and identify optimal control interventions. Annals of internal medicine 154, 593\u2013601 (2011).","journal-title":"Annals of internal medicine"},{"key":"55574_CR22","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1126\/science.1125237","volume":"312","author":"C Viboud","year":"2006","unstructured":"Viboud, C. et al. Synchrony, waves, and spatial hierarchies in the spread of influenza. Science 312, 447\u2013451 (2006).","journal-title":"Science"},{"key":"55574_CR23","doi-asserted-by":"publisher","DOI":"10.1186\/1746-6148-2-3","volume":"2","author":"NJ Savill","year":"2006","unstructured":"Savill, N. J. et al. Topographic determinants of foot and mouth disease transmission in the UK 2001 epidemic. BMC Veterinary Research 2, 3 (2006).","journal-title":"BMC Veterinary Research"},{"key":"55574_CR24","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1097\/EDE.0000000000000751","volume":"29","author":"AN Kraay","year":"2018","unstructured":"Kraay, A. N., Trostle, J., Brouwer, A. F., Cevallos, W. & Eisenberg, J. N. Determinants of Short-term Movement in a Developing Region and Implications for Disease Transmission. Epidemiology 29, 117\u2013125 (2018).","journal-title":"Epidemiology"},{"key":"55574_CR25","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-018-05230-4","volume":"9","author":"G Guzzetta","year":"2018","unstructured":"Guzzetta, G., Marques-Toledo, C. A., Ros\u00e0, R., Teixeira, M. & Merler, S. Quantifying the spatial spread of dengue in a non-endemic Brazilian metropolis via transmission chain reconstruction. Nature communications 9, 2837 (2018).","journal-title":"Nature communications"},{"key":"55574_CR26","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1098\/rspb.2011.0913","volume":"279","author":"RJ Ypma","year":"2011","unstructured":"Ypma, R. J. et al. Unravelling transmission trees of infectious diseases by combining genetic and epidemiological data. Proceedings of the Royal Society B: Biological Sciences 279, 444\u2013450 (2011).","journal-title":"Proceedings of the Royal Society B: Biological Sciences"},{"key":"55574_CR27","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-017-12852-z","volume":"7","author":"T-H Wen","year":"2017","unstructured":"Wen, T.-H., Sabel, C. E. & Wang, I.-H. A geo-computational algorithm for exploring the structure of diffusion progression in time and space. Scientific reports 7, 12565 (2017).","journal-title":"Scientific reports"},{"key":"55574_CR28","unstructured":"Center for Diseases Control, M. o. H. a. W., Taiwan. Guidelines for dengue control. (2009)."},{"key":"55574_CR29","unstructured":"Center for Diseases Control, M. o. H. a. W., Taiwan. Dengue daily Confirmed cases since 1998, https:\/\/data.cdc.gov.tw\/dataset\/dengue-daily-determined-cases-1998 (2019)."},{"key":"55574_CR30","doi-asserted-by":"publisher","first-page":"3258","DOI":"10.1137\/18M1186411","volume":"78","author":"D Champredon","year":"2018","unstructured":"Champredon, D., Dushoff, J. & Earn, D. J. Equivalence of the Erlang-distributed SEIR epidemic model and the renewal equation. SIAM Journal on Applied Mathematics 78, 3258\u20133278 (2018).","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"55574_CR31","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/j.epidem.2018.05.011","volume":"25","author":"CT Code\u00e7o","year":"2018","unstructured":"Code\u00e7o, C. T., Villela, D. A. & Coelho, F. C. Estimating the effective reproduction number of dengue considering temperature-dependent generation intervals. Epidemics 25, 101\u2013111 (2018).","journal-title":"Epidemics"},{"key":"55574_CR32","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1097\/EDE.0b013e31819d1092","volume":"20","author":"BJ Cowling","year":"2009","unstructured":"Cowling, B. J., Fang, V. J., Riley, S., Peiris, J. M. & Leung, G. M. Estimation of the serial interval of influenza. Epidemiology 20, 344 (2009).","journal-title":"Epidemiology"},{"key":"55574_CR33","doi-asserted-by":"publisher","first-page":"1612","DOI":"10.1214\/14-AOAS743","volume":"8","author":"S Meyer","year":"2014","unstructured":"Meyer, S. & Held, L. Power-law models for infectious disease spread. The Annals of Applied Statistics 8, 1612\u20131639 (2014).","journal-title":"The Annals of Applied Statistics"},{"key":"55574_CR34","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1080\/13658810902950625","volume":"24","author":"X Shi","year":"2010","unstructured":"Shi, X. Selection of bandwidth type and adjustment side in kernel density estimation over inhomogeneous backgrounds. International Journal of Geographical Information Science 24, 643\u2013660 (2010).","journal-title":"International Journal of Geographical Information Science"},{"key":"55574_CR35","doi-asserted-by":"publisher","first-page":"e510","DOI":"10.1016\/j.ijid.2010.06.020","volume":"15","author":"RA Stein","year":"2011","unstructured":"Stein, R. A. Super-spreaders in infectious diseases. International Journal of Infectious Diseases 15, e510\u2013e513 (2011).","journal-title":"International Journal of Infectious Diseases"},{"key":"55574_CR36","doi-asserted-by":"publisher","first-page":"460","DOI":"10.4103\/1995-7645.240081","volume":"11","author":"Y-H Hsieh","year":"2018","unstructured":"Hsieh, Y.-H. Dengue outbreaks in Taiwan, 1998-2017: importation, serotype and temporal pattern. Asian Pacific Journal of Tropical Medicine 11, 460 (2018).","journal-title":"Asian Pacific Journal of Tropical Medicine"},{"key":"55574_CR37","doi-asserted-by":"publisher","first-page":"5679","DOI":"10.1098\/rsta.2010.0278","volume":"368","author":"SD Pinho","year":"2010","unstructured":"Pinho, S. D. et al. Modelling the dynamics of dengue real epidemics. Philosophical Transactions of the Royal Society A: Mathematical, Physical Engineering Sciences 368, 5679\u20135693 (2010).","journal-title":"Philosophical Transactions of the Royal Society A: Mathematical, Physical Engineering Sciences"},{"key":"55574_CR38","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1038\/35097116","volume":"413","author":"NM Ferguson","year":"2001","unstructured":"Ferguson, N. M., Donnelly, C. A. & Anderson, R. M. Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain. Nature 413, 542 (2001).","journal-title":"Nature"},{"key":"55574_CR39","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1098\/rspb.2002.2191","volume":"270","author":"DT Haydon","year":"2003","unstructured":"Haydon, D. T. et al. The construction and analysis of epidemic trees with reference to the 2001 UK foot\u2013and\u2013mouth outbreak. Proceedings of the Royal Society of London. Series B: Biological Sciences 270, 121\u2013127 (2003).","journal-title":"Proceedings of the Royal Society of London. Series B: Biological Sciences"},{"key":"55574_CR40","doi-asserted-by":"publisher","first-page":"e1005210","DOI":"10.1371\/journal.pcbi.1005210","volume":"12","author":"JA Backer","year":"2016","unstructured":"Backer, J. A. & Wallinga, J. Spatiotemporal analysis of the 2014 Ebola epidemic in West Africa. PLoS computational biology 12, e1005210 (2016).","journal-title":"PLoS computational biology"},{"key":"55574_CR41","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-019-39057-w","volume":"9","author":"T Yamauchi","year":"2019","unstructured":"Yamauchi, T., Takeuchi, S., Yamano, Y., Kuroda, Y. & Nakadate, T. Estimation of the effective reproduction number of influenza based on weekly reports in Miyazaki Prefecture. Scientific reports 9, 2539 (2019).","journal-title":"Scientific reports"},{"key":"55574_CR42","doi-asserted-by":"publisher","first-page":"e1002500","DOI":"10.1371\/journal.pcbi.1002500","volume":"8","author":"B Cummins","year":"2012","unstructured":"Cummins, B., Cortez, R., Foppa, I. M., Walbeck, J. & Hyman, J. M. A spatial model of mosquito host-seeking behavior. PLoS computational biology 8, e1002500 (2012).","journal-title":"PLoS computational biology"},{"key":"55574_CR43","doi-asserted-by":"publisher","first-page":"209","DOI":"10.4269\/ajtmh.2005.72.209","volume":"72","author":"LC Harrington","year":"2005","unstructured":"Harrington, L. C. et al. Dispersal of the dengue vector Aedes aegypti within and between rural communities. The American journal of tropical medicine 72, 209\u2013220 (2005).","journal-title":"The American journal of tropical medicine"},{"key":"55574_CR44","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1038\/nature10856","volume":"484","author":"F Simini","year":"2012","unstructured":"Simini, F., Gonz\u00e1lez, M. C., Maritan, A. & Barab\u00e1si, A.-L. A universal model for mobility and migration patterns. Nature 484, 96 (2012).","journal-title":"Nature"},{"key":"55574_CR45","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.epidem.2018.10.002","volume":"26","author":"SM Kissler","year":"2019","unstructured":"Kissler, S. M. et al. Geographic transmission hubs of the 2009 influenza pandemic in the United States. Epidemics 26, 86\u201394 (2019).","journal-title":"Epidemics"},{"key":"55574_CR46","doi-asserted-by":"publisher","first-page":"e59","DOI":"10.1371\/journal.pmed.0020059","volume":"2","author":"M Kulldorff","year":"2005","unstructured":"Kulldorff, M., Heffernan, R., Hartman, J., Assun\u00e7ao, R. & Mostashari, F. A space\u2013time permutation scan statistic for disease outbreak detection. PLoS medicine 2, e59 (2005).","journal-title":"PLoS medicine"},{"key":"55574_CR47","doi-asserted-by":"crossref","unstructured":"Gatrell, A. C., Bailey, T. C., Diggle, P. J. & Rowlingson, B. S. Spatial point pattern analysis and its application in geographical epidemiology. Transactions of the Institute of British geographers, 256\u2013274 (1996).","DOI":"10.2307\/622936"},{"key":"55574_CR48","doi-asserted-by":"publisher","DOI":"10.1186\/1476-072X-12-28","volume":"12","author":"DF Cuadros","year":"2013","unstructured":"Cuadros, D. F., Awad, S. F. & Abu-Raddad, L. J. Mapping HIV clustering: a strategy for identifying populations at high risk ofHIV infection in sub-Saharan Africa. International journal of health geographics 12, 28 (2013).","journal-title":"International journal of health geographics"},{"key":"55574_CR49","doi-asserted-by":"publisher","first-page":"e63447","DOI":"10.1371\/journal.pone.0063447","volume":"8","author":"Y Liu","year":"2013","unstructured":"Liu, Y. et al. Detecting spatial-temporal clusters of HFMD from 2007 to 2011 in Shandong Province, China. PloS one 8, e63447 (2013).","journal-title":"PloS one"},{"key":"55574_CR50","doi-asserted-by":"publisher","first-page":"e0007350","DOI":"10.1371\/journal.pntd.0007350","volume":"13","author":"H Ren","year":"2019","unstructured":"Ren, H., Wu, W., Li, T. & Yang, Z. Urban villages as transfer stations for dengue fever epidemic: A case study in the Guangzhou, China. PLoS neglected tropical diseases 13, e0007350 (2019).","journal-title":"PLoS neglected tropical diseases"},{"key":"55574_CR51","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1006\/tpbi.2000.1517","volume":"59","author":"T Caraco","year":"2001","unstructured":"Caraco, T., Duryea, M. C., Glavanakov, S., Maniatty, W. & Szymanski, B. K. Host spatial heterogeneity and the spread of vector-borne infection. Theoretical Population Biology 59, 185\u2013206 (2001).","journal-title":"Theoretical Population Biology"},{"key":"55574_CR52","doi-asserted-by":"publisher","first-page":"e481","DOI":"10.1371\/journal.pntd.0000481","volume":"3","author":"ST Stoddard","year":"2009","unstructured":"Stoddard, S. T. et al. The role of human movement in the transmission of vector-borne pathogens. PLoS neglected tropical diseases 3, e481 (2009).","journal-title":"PLoS neglected tropical diseases"},{"key":"55574_CR53","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1038\/nature04024","volume":"438","author":"D Smith","year":"2005","unstructured":"Smith, D., Dushoff, J., Snow, R. & Hay, S. The entomological inoculation rate and Plasmodium falciparum infection in African children. Nature 438, 492 (2005).","journal-title":"Nature"},{"key":"55574_CR54","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/s11071-017-3877-3","volume":"91","author":"Y Wang","year":"2018","unstructured":"Wang, Y., Cao, J., Li, X. & Alsaedi, A. Edge-based epidemic dynamics with multiple routes of transmission on random networks. Nonlinear Dynamics 91, 403\u2013420 (2018).","journal-title":"Nonlinear Dynamics"}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-019-55574-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-019-55574-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-019-55574-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,17]],"date-time":"2022-12-17T17:34:15Z","timestamp":1671298455000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-019-55574-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,16]]},"references-count":54,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["55574"],"URL":"https:\/\/doi.org\/10.1038\/s41598-019-55574-0","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,16]]},"assertion":[{"value":"30 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 November 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 December 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"19172"}}