{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T05:15:27Z","timestamp":1771996527030,"version":"3.50.1"},"reference-count":58,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T00:00:00Z","timestamp":1697760000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T00:00:00Z","timestamp":1697760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"crossref","award":["1641020"],"award-info":[{"award-number":["1641020"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"crossref","award":["1916439"],"award-info":[{"award-number":["1916439"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Math. Biol."],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Infectious diseases continue to pose a significant threat to the health of humans globally. While the spread of pathogens transcends geographical boundaries, the management of infectious diseases typically occurs within distinct spatial units, determined by geopolitical boundaries. The allocation of management resources within and across regions (the \u201cgovernance structure\u201d) can affect epidemiological outcomes considerably, and policy-makers are often confronted with a choice between applying control measures uniformly or differentially across regions. Here, we investigate the extent to which uniform and non-uniform governance structures affect the costs of an infectious disease outbreak in two-patch systems using an optimal control framework. A uniform policy implements control measures with the same time varying rate functions across both patches, while these measures are allowed to differ between the patches in a non-uniform policy. We compare results from two systems of differential equations representing transmission of cholera and Ebola, respectively, to understand the interplay between transmission mode, governance structure and the optimal control of outbreaks. In our case studies, the governance structure has a meaningful impact on the allocation of resources and burden of cases, although the difference in total costs is minimal. Understanding how governance structure affects both the optimal control functions and epidemiological outcomes is crucial for the effective management of infectious diseases going forward.<\/jats:p>","DOI":"10.1007\/s00285-023-02001-8","type":"journal-article","created":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T07:02:48Z","timestamp":1697785368000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The effect of governance structures on optimal control of two-patch epidemic models"],"prefix":"10.1007","volume":"87","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0639-3728","authenticated-orcid":false,"given":"Emily","family":"Howerton","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1116-8074","authenticated-orcid":false,"given":"Kyle","family":"Dahlin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7922-7758","authenticated-orcid":false,"given":"Christina J.","family":"Edholm","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6252-5839","authenticated-orcid":false,"given":"Lindsey","family":"Fox","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9762-8851","authenticated-orcid":false,"given":"Margaret","family":"Reynolds","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1772-8191","authenticated-orcid":false,"given":"Brandon","family":"Hollingsworth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8290-3021","authenticated-orcid":false,"given":"George","family":"Lytle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Melody","family":"Walker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julie","family":"Blackwood","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suzanne","family":"Lenhart","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,10,20]]},"reference":[{"key":"2001_CR1","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/978-3-030-57129-0_5","volume-title":"Using mathematics to understand biological complexity: from cells to populations","author":"F Agusto","year":"2021","unstructured":"Agusto F, Goldberg A, Ortega O et al (2021) How do interventions impact malaria dynamics between neighboring countries? A case study with Botswana and Zimbabwe. In: Segal R, Shtylla B, Sindi S (eds) Using mathematics to understand biological complexity: from cells to populations. Springer, Cham, pp 83\u2013109. https:\/\/doi.org\/10.1007\/978-3-030-57129-0_5"},{"key":"2001_CR2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198545996.001.0001","volume-title":"Infectious diseases of humans","author":"R Anderson","year":"1991","unstructured":"Anderson R, May R (1991) Infectious diseases of humans. Oxford University Press, New York"},{"issue":"2","key":"2001_CR3","doi-asserted-by":"publisher","first-page":"219","DOI":"10.3934\/mbe.2008.5.219","volume":"5","author":"E Asano","year":"2008","unstructured":"Asano E, Gross LJ, Lenhart S et al (2008) Optimal control of vaccine distribution in a rabies metapopulation model. Math Biosci Eng MBE 5(2):219\u2013238. https:\/\/doi.org\/10.3934\/mbe.2008.5.219","journal-title":"Math Biosci Eng MBE"},{"issue":"1","key":"2001_CR4","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1179\/2047773214Y.0000000169","volume":"109","author":"SM Bartsch","year":"2015","unstructured":"Bartsch SM, Gorham K, Lee BY (2015) The cost of an Ebola case. Pathog Global Health 109(1):4\u20139. https:\/\/doi.org\/10.1179\/2047773214Y.0000000169","journal-title":"Pathog Global Health"},{"issue":"3","key":"2001_CR5","doi-asserted-by":"publisher","first-page":"4","DOI":"10.15585\/mmwr.su6503a2","volume":"65","author":"BP Bell","year":"2016","unstructured":"Bell BP, Damon IK, Jernigan DB et al (2016) Overview, control strategies, and lessons learned in the CDC response to the 2014\u20132016 Ebola epidemic. MMWR Suppl 65(3):4\u201311. https:\/\/doi.org\/10.15585\/mmwr.su6503a2","journal-title":"MMWR Suppl"},{"issue":"29","key":"2001_CR6","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1038\/srep29262","volume":"6","author":"JC Blackwood","year":"2016","unstructured":"Blackwood JC, Childs LM (2016) The role of interconnectivity in control of an Ebola epidemic. Sci Rep 6(29):262. https:\/\/doi.org\/10.1038\/srep29262","journal-title":"Sci Rep"},{"issue":"1","key":"2001_CR7","doi-asserted-by":"publisher","first-page":"1782","DOI":"10.1186\/s12889-021-11797-3","volume":"21","author":"JC Blackwood","year":"2021","unstructured":"Blackwood JC, Malakhov MM, Duan J et al (2021) Governance structure affects transboundary disease management under alternative objectives. BMC Public Health 21(1):1782. https:\/\/doi.org\/10.1186\/s12889-021-11797-3","journal-title":"BMC Public Health"},{"issue":"4","key":"2001_CR8","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.apjtb.2016.01.012","volume":"6","author":"E Bonyah","year":"2016","unstructured":"Bonyah E, Badu K, Asiedu-Addo SK (2016) Optimal control application to an Ebola model. Asian Pac J Trop Biomed 6(4):283\u2013289. https:\/\/doi.org\/10.1016\/j.apjtb.2016.01.012","journal-title":"Asian Pac J Trop Biomed"},{"key":"2001_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-9828-9","volume-title":"Mathematical models in epidemiology","author":"F Brauer","year":"2019","unstructured":"Brauer F, Castillo-Chavez C, Feng Z (2019) Mathematical models in epidemiology. Springer, New York. https:\/\/doi.org\/10.1007\/978-1-4939-9828-9"},{"issue":"6","key":"2001_CR10","doi-asserted-by":"publisher","first-page":"608","DOI":"10.3390\/math9060608","volume":"9","author":"D Burton","year":"2021","unstructured":"Burton D, Lenhart S, Edholm CJ et al (2021) A mathematical model of contact tracing during the 2014\u20132016 West African Ebola outbreak. Sci China Ser A Math 9(6):608. https:\/\/doi.org\/10.3390\/math9060608","journal-title":"Sci China Ser A Math"},{"issue":"6","key":"2001_CR11","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0156674","volume":"11","author":"G Bwire","year":"2016","unstructured":"Bwire G, Mwesawina M, Baluku Y et al (2016) Cross-border cholera outbreaks in sub-Saharan Africa, the mystery behind the silent illness: What needs to be done? PLOS ONE 11(6):e0156674. https:\/\/doi.org\/10.1371\/journal.pone.0156674","journal-title":"PLOS ONE"},{"issue":"6","key":"2001_CR12","doi-asserted-by":"publisher","first-page":"8374","DOI":"10.3934\/mbe.2021415","volume":"18","author":"E Che","year":"2021","unstructured":"Che E, Numfor E, Lenhart S et al (2021) Mathematical modeling of the influence of cultural practices on cholera infections in Cameroon. Math Biosci Eng MBE 18(6):8374\u20138391. https:\/\/doi.org\/10.3934\/mbe.2021415","journal-title":"Math Biosci Eng MBE"},{"issue":"Pt B","key":"2001_CR13","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1016\/j.mbs.2015.06.015","volume":"270","author":"C Cosner","year":"2015","unstructured":"Cosner C (2015) Models for the effects of host movement in vector-borne disease systems. Math Biosci 270(Pt B):192\u2013197. https:\/\/doi.org\/10.1016\/j.mbs.2015.06.015","journal-title":"Math Biosci"},{"issue":"5452","key":"2001_CR14","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1126\/science.287.5452.443","volume":"287","author":"P Daszak","year":"2000","unstructured":"Daszak P, Cunningham AA, Hyatt AD (2000) Emerging infectious diseases of wildlife-Threats] to biodiversity and human health. Science 287(5452):443\u2013449. https:\/\/doi.org\/10.1126\/science.287.5452.443","journal-title":"Science"},{"key":"2001_CR15","series-title":"Wiley series in mathematical and computational biology","volume-title":"Mathematical epidemiology of infectious diseases: model building, analysis and interpretation","author":"O Diekmann","year":"2000","unstructured":"Diekmann O, Heesterbeek JAP (2000) Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. Wiley series in mathematical and computational biology. Wiley, Chichester"},{"issue":"4","key":"2001_CR16","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1080\/17513750701605515","volume":"1","author":"W Ding","year":"2007","unstructured":"Ding W, Gross LJ, Langston K et al (2007) Rabies in raccoons: optimal control for a discrete time model on a spatial grid. J Biol Dyn 1(4):379\u2013393. https:\/\/doi.org\/10.1080\/17513750701605515","journal-title":"J Biol Dyn"},{"key":"2001_CR17","first-page":"1","volume":"237","author":"W Ding","year":"2012","unstructured":"Ding W, Hrynkiv V, Mu X (2012) Optimal control applied to native-invasive species competition via a PDE model. Electron J Differ Equ 237:1\u201318","journal-title":"Electron J Differ Equ"},{"key":"2001_CR18","doi-asserted-by":"publisher","unstructured":"Dowell SF, Mukunu R, Ksiazek TG, et\u00a0al (1999) Transmission of Ebola hemorrhagic fever: a study of risk factors in family members, Kikwit, Democratic Republic of the Congo, 1995. Commission de Lutte contre les Epid\u00e9mies \u00e0 Kikwit. J Infect Dis 179(Suppl 1):S87\u201391. https:\/\/doi.org\/10.1086\/514284","DOI":"10.1086\/514284"},{"key":"2001_CR19","doi-asserted-by":"publisher","DOI":"10.1142\/8884","volume-title":"Applications of epidemiological models to public health policymaking the role of heterogeneity in model predictions","author":"Z Feng","year":"2014","unstructured":"Feng Z (2014) Applications of epidemiological models to public health policymaking the role of heterogeneity in model predictions. World Scientific Publishing Company, New Jersey"},{"issue":"169","key":"2001_CR20","doi-asserted-by":"publisher","first-page":"20200429","DOI":"10.1098\/rsif.2020.0429","volume":"17","author":"WE Fitzgibbon","year":"2020","unstructured":"Fitzgibbon WE, Morgan JJ, Webb GF et al (2020) Modelling the aqueous transport of an infectious pathogen in regional communities: application to the cholera outbreak in Haiti. J Roy Soc Interface Roy Soc 17(169):20200429. https:\/\/doi.org\/10.1098\/rsif.2020.0429","journal-title":"J Roy Soc Interface Roy Soc"},{"issue":"7820","key":"2001_CR21","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1038\/s41586-020-2405-7","volume":"584","author":"S Flaxman","year":"2020","unstructured":"Flaxman S, Mishra S, Gandy A et al (2020) Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe. Nature 584(7820):257\u2013261. https:\/\/doi.org\/10.1038\/s41586-020-2405-7","journal-title":"Nature"},{"key":"2001_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6380-7","volume-title":"Deterministic and stochastic optimal control","author":"W Fleming","year":"1975","unstructured":"Fleming W, Rishel R (1975) Deterministic and stochastic optimal control. Springer, New York. https:\/\/doi.org\/10.1007\/978-1-4612-6380-7"},{"issue":"1775","key":"2001_CR23","doi-asserted-by":"publisher","first-page":"20180282","DOI":"10.1098\/rstb.2018.0282","volume":"374","author":"WM Getz","year":"2019","unstructured":"Getz WM, Salter R, Mgbara W (2019) Adequacy of SEIR models when epidemics have spatial structure: Ebola in Sierra Leone. Philos Trans Roy Soc Lond Ser B Biol Sci 374(1775):20180282. https:\/\/doi.org\/10.1098\/rstb.2018.0282","journal-title":"Philos Trans Roy Soc Lond Ser B Biol Sci"},{"key":"2001_CR24","unstructured":"Global Burden (2019) Global burden of 369 diseases and injuries in 204 countries and territories, 1990\u20132019: a systematic analysis for the global burden of disease study 2019"},{"key":"2001_CR25","doi-asserted-by":"publisher","DOI":"10.1002\/9781444398557","volume-title":"Structured decision making: a practical guide to environmental management choices","author":"R Gregory","year":"2012","unstructured":"Gregory R, Failing L, Harstone M et al (2012) Structured decision making: a practical guide to environmental management choices. Wiley, London"},{"issue":"8","key":"2001_CR26","doi-asserted-by":"publisher","first-page":"1525","DOI":"10.1007\/s11425-016-0300-6","volume":"59","author":"WW Hager","year":"2016","unstructured":"Hager WW, Zhang H (2016) An active set algorithm for nonlinear optimization with polyhedral constraints. Sci China Math 59(8):1525\u20131542. https:\/\/doi.org\/10.1007\/s11425-016-0300-6","journal-title":"Sci China Math"},{"issue":"2","key":"2001_CR27","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1111\/tbed.12401","volume":"64","author":"MG Hemida","year":"2017","unstructured":"Hemida MG, Elmoslemany A, Al-Hizab F et al (2017) Dromedary camels and the transmission of middle east respiratory syndrome coronavirus (MERS-CoV). Transbound Emerg Dis 64(2):344\u2013353. https:\/\/doi.org\/10.1111\/tbed.12401","journal-title":"Transbound Emerg Dis"},{"issue":"7181","key":"2001_CR28","doi-asserted-by":"publisher","first-page":"990","DOI":"10.1038\/nature06536","volume":"451","author":"KE Jones","year":"2008","unstructured":"Jones KE, Patel NG, Levy MA et al (2008) Global trends in emerging infectious diseases. Nature 451(7181):990\u2013993. https:\/\/doi.org\/10.1038\/nature06536","journal-title":"Nature"},{"key":"2001_CR29","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1080\/17513758.2016.1156172","volume":"10","author":"MR Kelly","year":"2016","unstructured":"Kelly MR, Tien JH, Eisenberg MC et al (2016) The impact of spatial arrangements on epidemic disease dynamics and intervention strategies. J Biol Dyn 10:222\u2013249. https:\/\/doi.org\/10.1080\/17513758.2016.1156172","journal-title":"J Biol Dyn"},{"issue":"772","key":"2001_CR30","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1098\/rspa.1927.0118","volume":"115","author":"WO Kermack","year":"1927","unstructured":"Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc Roy Soc A Math Phys Eng Sci 115(772):700\u2013721. https:\/\/doi.org\/10.1098\/rspa.1927.0118","journal-title":"Proc Roy Soc A Math Phys Eng Sci"},{"issue":"1","key":"2001_CR31","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1017\/dmp.2020.361","volume":"16","author":"A Lal","year":"2022","unstructured":"Lal A, Ashworth HC, Dada S et al (2022) Optimizing pandemic preparedness and response through health information systems: Lessons learned from Ebola to COVID-19. Disaster Med Public Health Prep 16(1):333\u2013340. https:\/\/doi.org\/10.1017\/dmp.2020.361","journal-title":"Disaster Med Public Health Prep"},{"issue":"8","key":"2001_CR32","doi-asserted-by":"publisher","first-page":"e1081","DOI":"10.1016\/S2214-109X(20)30310-7","volume":"8","author":"EC Lee","year":"2020","unstructured":"Lee EC, Chao DL, Lemaitre JC et al (2020a) Achieving coordinated national immunity and cholera elimination in Haiti through vaccination: a modelling study. Lancet Glob Health 8(8):e1081\u2013e1089. https:\/\/doi.org\/10.1016\/S2214-109X(20)30310-7","journal-title":"Lancet Glob Health"},{"issue":"9","key":"2001_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3390\/pr8091087","volume":"8","author":"S Lee","year":"2020","unstructured":"Lee S, Baek O, Melara L (2020b) Resource allocation in two-patch epidemic model with state-dependent dispersal behaviors using optimal control. Processes 8(9):1\u201319. https:\/\/doi.org\/10.3390\/pr8091087","journal-title":"Processes"},{"issue":"suppl-3","key":"2001_CR34","doi-asserted-by":"publisher","first-page":"S137","DOI":"10.1093\/infdis\/jiy486","volume":"218","author":"Legros D, Partners of the Global Task Force on Cholera Control","year":"2018","unstructured":"Legros D, Partners of the Global Task Force on Cholera Control (2018) Global cholera epidemiology: opportunities to reduce the burden of cholera by 2030. J Infect Dis 218(suppl-3):S137\u2013S140. https:\/\/doi.org\/10.1093\/infdis\/jiy486","journal-title":"J Infect Dis"},{"key":"2001_CR35","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011418","volume-title":"Optimal control applied to biological models","author":"S Lenhart","year":"2007","unstructured":"Lenhart S, Workman J (2007) Optimal control applied to biological models. Chapman and Hall\/CRC, New York"},{"key":"2001_CR36","volume-title":"An introduction to mathematical epidemiology","author":"M Martcheva","year":"2013","unstructured":"Martcheva M (2013) An introduction to mathematical epidemiology, a. Springer, New York","edition":"a"},{"key":"2001_CR37","volume-title":"Cholera: symptoms, diagnosis, and treatment. Tropical diseases-etiology, pathogenesis and treatments","year":"2011","unstructured":"Melbourne EL (ed) (2011) Cholera: symptoms, diagnosis, and treatment. Tropical diseases-etiology, pathogenesis and treatments. Nova Science Publishers, New York"},{"issue":"8","key":"2001_CR38","doi-asserted-by":"publisher","first-page":"2004","DOI":"10.1007\/s11538-010-9521-8","volume":"72","author":"RL Miller Neilan","year":"2010","unstructured":"Miller Neilan RL, Schaefer E, Gaff H et al (2010) Modeling optimal intervention strategies for cholera. Bull Math Biol 72(8):2004\u20132018. https:\/\/doi.org\/10.1007\/s11538-010-9521-8","journal-title":"Bull Math Biol"},{"issue":"39","key":"2001_CR39","first-page":"873","volume":"63","author":"K Mirkovic","year":"2014","unstructured":"Mirkovic K, Thwing J, Diack PA et al (2014) Importation and containment of Ebola virus disease\u2014Senegal, August\u2013September 2014. MMWR Morb Mortal Wkly Rep 63(39):873\u2013874","journal-title":"MMWR Morb Mortal Wkly Rep"},{"issue":"3","key":"2001_CR40","doi-asserted-by":"publisher","first-page":"1077","DOI":"10.1007\/s00285-019-01390-z","volume":"79","author":"TY Miyaoka","year":"2019","unstructured":"Miyaoka TY, Lenhart S, Meyer JFCA (2019) Optimal control of vaccination in a vector-borne reaction-diffusion model applied to Zika virus. J Math Biol 79(3):1077\u20131104. https:\/\/doi.org\/10.1007\/s00285-019-01390-z","journal-title":"J Math Biol"},{"issue":"35","key":"2001_CR41","doi-asserted-by":"publisher","first-page":"1198","DOI":"10.15585\/mmwr.mm6935a2","volume":"69","author":"A Moreland","year":"2020","unstructured":"Moreland A, Herlihy C, Tynan MA et al (2020) Timing of state and territorial COVID-19 stay-at-home orders and changes in population movement-United States, March 1\u2013May 31. MMWR Morbid Mortal Wkl Rep 69(35):1198\u20131203. https:\/\/doi.org\/10.15585\/mmwr.mm6935a2","journal-title":"MMWR Morbid Mortal Wkl Rep"},{"key":"2001_CR42","doi-asserted-by":"publisher","unstructured":"Morens DM, Fauci AS (2012) Emerging infectious diseases in 2012: 20 years after the Institute of Medicine report. mBio 3(6). https:\/\/doi.org\/10.1128\/mBio.00494-12","DOI":"10.1128\/mBio.00494-12"},{"issue":"9857","key":"2001_CR43","doi-asserted-by":"publisher","first-page":"1956","DOI":"10.1016\/S0140-6736(12)61684-5","volume":"380","author":"SS Morse","year":"2012","unstructured":"Morse SS, Mazet JAK, Woolhouse M et al (2012) Prediction and prevention of the next pandemic zoonosis. The Lancet 380(9857):1956\u20131965. https:\/\/doi.org\/10.1016\/S0140-6736(12)61684-5","journal-title":"The Lancet"},{"issue":"21","key":"2001_CR44","doi-asserted-by":"publisher","first-page":"8767","DOI":"10.1073\/pnas.1019712108","volume":"108","author":"Z Mukandavire","year":"2011","unstructured":"Mukandavire Z, Liao S, Wang J et al (2011) Estimating the reproductive numbers for the 2008\u20132009 cholera outbreaks in Zimbabwe. Proc Natl Acad Sci USA 108(21):8767\u20138772. https:\/\/doi.org\/10.1073\/pnas.1019712108","journal-title":"Proc Natl Acad Sci USA"},{"issue":"1","key":"2001_CR45","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2558904","volume":"41","author":"MA Patterson","year":"2014","unstructured":"Patterson MA, Rao AV (2014) GPOPS-II: a MATLAB software for solving multiple-phase optimal control problems using hp-adaptive gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans Math Softw Assoc Comput Mach 41(1):1\u201337. https:\/\/doi.org\/10.1145\/2558904","journal-title":"ACM Trans Math Softw Assoc Comput Mach"},{"key":"2001_CR46","volume-title":"The mathematical theory of optimal processes","author":"LS Pontryagin","year":"1962","unstructured":"Pontryagin LS, Boltyanskii VG, Gamkrelize RV et al (1962) The mathematical theory of optimal processes. Wiley, New York"},{"key":"2001_CR47","unstructured":"R Core Team (2021) R: a language and environment for statistical computing"},{"issue":"3","key":"2001_CR48","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/eap.2276","volume":"31","author":"JN Sanchirico","year":"2021","unstructured":"Sanchirico JN, Blackwood JC, Fitzpatrick B et al (2021) Political economy of renewable resource federalism. Ecol Appl Publ Ecol Soc Am 31(3):1\u201314. https:\/\/doi.org\/10.1002\/eap.2276","journal-title":"Ecol Appl Publ Ecol Soc Am"},{"issue":"5","key":"2001_CR49","doi-asserted-by":"publisher","first-page":"1136","DOI":"10.4269\/ajtmh.15-0700","volume":"94","author":"K S\u00e9v\u00e8re","year":"2016","unstructured":"S\u00e9v\u00e8re K, Rouzier V, Anglade SB et al (2016) Effectiveness of oral cholera vaccine in Haiti: 37-month follow-up. Am J Trop Med Hyg 94(5):1136\u20131142. https:\/\/doi.org\/10.4269\/ajtmh.15-0700","journal-title":"Am J Trop Med Hyg"},{"issue":"10","key":"2001_CR50","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pbio.1001970","volume":"12","author":"K Shea","year":"2014","unstructured":"Shea K, Tildesley MJ, Runge MC et al (2014) Adaptive management and the value of information: learning via intervention in epidemiology. PLOS Biol 12(10):e1001970. https:\/\/doi.org\/10.1371\/journal.pbio.1001970","journal-title":"PLOS Biol"},{"key":"2001_CR51","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v033.i09","volume":"33","author":"K Soetaert","year":"2010","unstructured":"Soetaert K, Petzoldt T, Woodrow Setzer R (2010) Solving differential equations in R: Package deSolve. J Stat Softw 33:1\u201325. https:\/\/doi.org\/10.18637\/jss.v033.i09","journal-title":"J Stat Softw"},{"issue":"6","key":"2001_CR52","doi-asserted-by":"publisher","first-page":"1506","DOI":"10.1007\/s11538-010-9507-6","volume":"72","author":"JH Tien","year":"2010","unstructured":"Tien JH, Earn DJD (2010) Multiple transmission pathways and disease dynamics in a waterborne pathogen model. Bull Math Biol 72(6):1506\u20131533. https:\/\/doi.org\/10.1007\/s11538-010-9507-6","journal-title":"Bull Math Biol"},{"issue":"9","key":"2001_CR53","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 AR, Tien J, Eisenberg M et al (2011) Cholera epidemic in Haiti, 2010: using a transmission model to explain spatial spread of disease and identify optimal control interventions. Ann Intern Med 154(9):593\u2013601. https:\/\/doi.org\/10.7326\/0003-4819-154-9-201105030-00334","journal-title":"Ann Intern Med"},{"key":"2001_CR54","unstructured":"UNICEF (2021) Ebola vaccine price data. https:\/\/www.unicef.org\/supply\/documents\/ebola-vaccine-pricing-data"},{"issue":"1\u20132","key":"2001_CR55","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","volume":"180","author":"P van den Driessche","year":"2002","unstructured":"van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180(1\u20132):29\u201348. https:\/\/doi.org\/10.1016\/S0025-5564(02)00108-6","journal-title":"Math Biosci"},{"issue":"7","key":"2001_CR56","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s00285-022-01761-z","volume":"84","author":"E Vargas Bernal","year":"2022","unstructured":"Vargas Bernal E, Saucedo O, Tien JH (2022) Relating Eulerian and Lagrangian spatial models for vector-host disease dynamics through a fundamental matrix. J Math Biol 84(7):57. https:\/\/doi.org\/10.1007\/s00285-022-01761-z","journal-title":"J Math Biol"},{"issue":"5","key":"2001_CR57","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1007\/s11908-015-0480-y","volume":"17","author":"J Weyer","year":"2015","unstructured":"Weyer J, Grobbelaar A, Blumberg L (2015) Ebola virus disease: history, epidemiology and outbreaks. Curr Infect Dis Rep 17(5):480. https:\/\/doi.org\/10.1007\/s11908-015-0480-y","journal-title":"Curr Infect Dis Rep"},{"key":"2001_CR58","unstructured":"WHO (2014) Ebola response roadmap. Technical report. World Health Organization. https:\/\/apps.who.int\/iris\/handle\/10665\/131596"}],"container-title":["Journal of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-023-02001-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00285-023-02001-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-023-02001-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T08:17:03Z","timestamp":1703405823000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00285-023-02001-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,20]]},"references-count":58,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["2001"],"URL":"https:\/\/doi.org\/10.1007\/s00285-023-02001-8","relation":{},"ISSN":["0303-6812","1432-1416"],"issn-type":[{"value":"0303-6812","type":"print"},{"value":"1432-1416","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,20]]},"assertion":[{"value":"9 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 September 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 October 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"74"}}