{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,20]],"date-time":"2026-09-20T03:33:37Z","timestamp":1789875217337,"version":"4.0.1"},"reference-count":98,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2017,6,6]],"date-time":"2017-06-06T00:00:00Z","timestamp":1496707200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Math. Biol."],"published-print":{"date-parts":[[2018,1]]},"DOI":"10.1007\/s00285-017-1146-1","type":"journal-article","created":{"date-parts":[[2017,6,6]],"date-time":"2017-06-06T04:27:19Z","timestamp":1496723239000},"page":"379-427","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":50,"title":["Bifurcation thresholds and optimal control in transmission dynamics of arboviral diseases"],"prefix":"10.1007","volume":"76","author":[{"given":"Hamadjam","family":"Abboubakar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean Claude","family":"Kamgang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leontine Nkague","family":"Nkamba","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Tieudjo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,6,6]]},"reference":[{"issue":"1507241","key":"1146_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.11145\/j.biomath.2015.07.241","volume":"4","author":"H Abboubakar","year":"2015","unstructured":"Abboubakar H, Kamgang JC, Nkamba LN, Tieudjo D, Emini L (2015) Modeling the dynamics of arboviral diseases with vaccination perspective. Biomath 4(1507241):1\u201330. doi: 10.11145\/j.biomath.2015.07.241","journal-title":"Biomath"},{"key":"1146_CR2","doi-asserted-by":"publisher","unstructured":"Abboubakar H, Buonomo B, Chitnis N (2016a) Modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans. Ric Mat. doi: 10.1007\/s11587-016-0293-9","DOI":"10.1007\/s11587-016-0293-9"},{"key":"1146_CR3","doi-asserted-by":"crossref","unstructured":"Abboubakar H, Kamgang JC, Tieudjo D (2016b) Backward bifurcation and control in transmission dynamics of arboviral diseases. Math Biosci 278:100\u2013129","DOI":"10.1016\/j.mbs.2016.06.002"},{"issue":"2","key":"1146_CR4","doi-asserted-by":"crossref","first-page":"223","DOI":"10.3934\/mbe.2004.1.223","volume":"1","author":"BM Adams","year":"2004","unstructured":"Adams BM, Banks HT, Kwon H, Tran HT (2004) Dynamic multidrug therapies for HIV: optimal and sti control approaches. Math Biosci Eng 1(2):223\u2013241","journal-title":"Math Biosci Eng"},{"issue":"4","key":"1146_CR5","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1137\/110860318","volume":"72","author":"S Ai","year":"2012","unstructured":"Ai S, Li J, Lu J (2012) Mosquito-stage-structured malaria models and their global dynamics. SIAM J Appl Math 72(4):1213\u20131237","journal-title":"SIAM J Appl Math"},{"key":"1146_CR6","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.biocon.2007.06.006","volume":"139","author":"C Alcaraz","year":"2007","unstructured":"Alcaraz C, Garc\u00eda-Berthou E (2007) Life history variation of invasive mosquitofish (Gambusia holbrooki) along a salinity gradient. Biol Conserv 139:83\u201392","journal-title":"Biol Conserv"},{"key":"1146_CR7","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.mbs.2012.11.014","volume":"242","author":"D Aldila","year":"2013","unstructured":"Aldila D, G\u00f6tz T, Soewono E (2013) An optimal control problem arising from a dengue disease transmission model. Math Biosci 242:9\u201316","journal-title":"Math Biosci"},{"issue":"22","key":"1146_CR8","first-page":"63","volume":"63","author":"M Antonio","year":"2001","unstructured":"Antonio M, Yoneyama T (2001) Optimal and sub-optimal control in dengue epidemics. Optim Control Appl Methods 63(22):63\u201373","journal-title":"Optim Control Appl Methods"},{"key":"1146_CR9","unstructured":"Brasseur A (2011) Analyse des pratiques actuelles destin\u00e9es \u00e1 limiter la propagation d\u2019aedes albopictus dans la zone sud est de la france et propositions d\u2019am\u00e9lioration. Ph.D. thesis, \u00c9coles des Hautes \u00c9tudes en Sant\u00e9 Publique (EHESP)"},{"issue":"4","key":"1146_CR10","doi-asserted-by":"crossref","first-page":"e10165","DOI":"10.1371\/journal.pone.0010165","volume":"5","author":"SE Bellan","year":"2010","unstructured":"Bellan SE (2010) The importance of age dependent mortality and the extrinsic incubation period in models of mosquito-borne disease transmission and control. PLoS ONE 5(4):e10165","journal-title":"PLoS ONE"},{"issue":"3","key":"1146_CR11","doi-asserted-by":"crossref","first-page":"587","DOI":"10.3934\/dcdsb.2009.11.587","volume":"11","author":"K Blayneh","year":"2009","unstructured":"Blayneh K, Cao Y, Kwon HD (2009) Optimal control of vector-borne diseases: treatment and prevention. Discrete Continuous Dyn Syst B 11(3):587\u2013611","journal-title":"Discrete Continuous Dyn Syst B"},{"key":"1146_CR12","doi-asserted-by":"publisher","first-page":"1006","DOI":"10.1007\/s11538-009-9480-0","volume":"72","author":"KW Blayneh","year":"2010","unstructured":"Blayneh KW, Gumel AB, Lenhart S, Clayton T (2010) Backward bifurcation and optimal control in transmission dynamics of West Nile virus. Bull Math Biol 72:1006\u20131028. doi: 10.1007\/s11538-009-9480-0","journal-title":"Bull Math Biol"},{"key":"1146_CR13","unstructured":"Bosc P, Boullet V, Echaubard M, Corre ML, Quilici S, Quod JP, Rochat J, Ribes S, Salamolard M, Thybaud E (2006) Premier Bilan sur les Impacts des Traitements Anti-moustiques, dans le cadre de la lutte Contre le Chikungunya, sur les Esp\u00e8ces et les Milieux de l\u2019\u00eele de la R\u00e9union"},{"issue":"3","key":"1146_CR14","doi-asserted-by":"crossref","first-page":"677","DOI":"10.3934\/mbe.2011.8.677","volume":"8","author":"B Buonomo","year":"2011","unstructured":"Buonomo B (2011) A simple analysis of vaccination strategies for rubella. Math Biosci Eng 8(3):677\u2013687","journal-title":"Math Biosci Eng"},{"issue":"4","key":"1146_CR15","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.3390\/math3041241","volume":"3","author":"B Buonomo","year":"2015","unstructured":"Buonomo B (2015) Modeling itns usage: optimal promotion programs versus pure voluntary adoptions. Mathematics 3(4):1241\u20131254","journal-title":"Mathematics"},{"key":"1146_CR16","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1002\/mma.1556","volume":"35","author":"JR Cannon","year":"2012","unstructured":"Cannon JR, Galiffa DJ (2012) An epidemiology model suggested by yellow fever. Math Methods Appl Sci 35:196\u2013206","journal-title":"Math Methods Appl Sci"},{"key":"1146_CR17","unstructured":"Carvalho SA, da Silva SO, da Cunha Charret I (2015) Mathematical modeling of dengue epidemic: control methods and vaccination strategies. arXiv:1508.00961v1 pp. 1\u201311"},{"key":"1146_CR18","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/S0399-077X(03)00204-X","volume":"33","author":"A Chippaux","year":"2003","unstructured":"Chippaux A (2003) G\u00e9n\u00e9ralit\u00e9s sur arbovirus et arboviroses\u2014overview of arbovirus and arbovirosis. Med Mal Infect 33:377\u2013384","journal-title":"Med Mal Infect"},{"key":"1146_CR19","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1007\/s11538-008-9299-0","volume":"70","author":"N Chitnis","year":"2008","unstructured":"Chitnis N, Hyman JM, Cushing JM (2008) Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull Math Biol 70:1272\u20131296","journal-title":"Bull Math Biol"},{"key":"1146_CR20","doi-asserted-by":"crossref","first-page":"2263","DOI":"10.1007\/s11538-006-9108-6","volume":"68","author":"FAB Coutinho","year":"2006","unstructured":"Coutinho FAB, Burattini MN, Lopez LF, Massad E (2006) Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue. Bull Math Biol 68:2263\u20132282","journal-title":"Bull Math Biol"},{"key":"1146_CR21","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1016\/j.bulm.2004.11.008","volume":"67","author":"G Cruz-Pacheco","year":"2005","unstructured":"Cruz-Pacheco G, Esteva L, Monta\u00f1o-Hirose JA, Vargas C (2005) Seasonality and outbreaks in West Nile virus infection. Bull Math Biol 67:1157\u20131172","journal-title":"Bull Math Biol"},{"key":"1146_CR22","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1007\/s11538-009-9406-x","volume":"71","author":"G Cruz-Pacheco","year":"2009","unstructured":"Cruz-Pacheco G, Esteva L, Vargas C (2009) Seasonality and outbreaks in West Nile virus infection. Bull Math Biol 71:1378\u20131393","journal-title":"Bull Math Biol"},{"key":"1146_CR23","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970005","volume-title":"An introduction to structured population dynamics","author":"JM Cushing","year":"1998","unstructured":"Cushing JM (1998) An introduction to structured population dynamics, vol 71. SIAM, Philadelphia"},{"key":"1146_CR24","unstructured":"Darriet F, Marcombe S, Corbel V (2007) Insecticides larvicides et adulticides alternatifs pour les op\u00e9rations de d\u00e9moustication en france, synth\u00e8se bibliographique. IRD, pp 1\u201346"},{"key":"1146_CR25","doi-asserted-by":"publisher","unstructured":"de Pinho M, Nogueira FN (2017) On application of optimal control to SEIR normalized models: pros and cons. Math Biosci Eng 14(1):111\u2013126. doi: 10.3934\/mbe.2017008","DOI":"10.3934\/mbe.2017008"},{"issue":"2","key":"1146_CR26","first-page":"528","volume":"177","author":"M Derouich","year":"2006","unstructured":"Derouich M, Boutayeb A (2006) Dengue fever: mathematical modelling and computer simulation. Appl Math Comput 177(2):528\u2013544","journal-title":"Appl Math Comput"},{"key":"1146_CR27","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.mbs.2015.08.019","volume":"269","author":"WO Dias","year":"2015","unstructured":"Dias WO, Wanner EF, Cardoso RTN (2015) A multiobjective optimization approach for combating Aedes aegypti using chemical and biological alternated step-size control. Math Biosci 269:37\u201347","journal-title":"Math Biosci"},{"key":"1146_CR28","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, Chichester"},{"key":"1146_CR29","unstructured":"Djamila M (2011) Mod\u00e9lisation et analyse math\u00e9matique de syst\u00e8mes dynamiques en \u00e9pid\u00e9miologie. application au cas du chikungunya. Ph.D. thesis, Universit\u00e9 du Havre"},{"issue":"01","key":"1146_CR30","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1142\/S0218339016500029","volume":"24","author":"SD Djiomba Njankou","year":"2016","unstructured":"Djiomba Njankou SD, Nyabadza F (2016) An optimal control model for Ebola virus disease. J Biol Syst 24(01):29\u201349","journal-title":"J Biol Syst"},{"key":"1146_CR31","doi-asserted-by":"crossref","first-page":"313","DOI":"10.3934\/mbe.2010.7.313","volume":"7","author":"Y Dumont","year":"2010","unstructured":"Dumont Y, Chiroleu F (2010) Vector control for the Chikungunya disease. Math Biosci Eng 7:313\u2013345","journal-title":"Math Biosci Eng"},{"key":"1146_CR32","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.mbs.2016.08.011","volume":"281","author":"Y Dumont","year":"2016","unstructured":"Dumont Y, Thuilliez J (2016) Human behaviors: a threat to mosquito control? Math Biosci 281:9\u201323","journal-title":"Math Biosci"},{"key":"1146_CR33","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s002850050099","volume":"36","author":"J Dushoff","year":"1998","unstructured":"Dushoff J, Huang W, Castillo-Chavez C (1998) Backward bifurcations and catastrophe in simple models of fatal diseases. J Math Biol 36:227\u2013248","journal-title":"J Math Biol"},{"key":"1146_CR34","doi-asserted-by":"crossref","unstructured":"Eshita Y, Takasaki T, Takashima I, Komalamisra N, Ushijima H, Kurane I (2007) Vector competence of Japanese mosquitoes for dengue and West Nile viruses, chap 23. Pesticide Chemistry, pp 260\u2013268","DOI":"10.1002\/9783527611249.ch23"},{"key":"1146_CR35","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/S0025-5564(98)10003-2","volume":"150","author":"L Esteva","year":"1998","unstructured":"Esteva L, Vargas C (1998) Analysis of a dengue disease transmission model. Math Biosci 150:131\u2013151","journal-title":"Math Biosci"},{"key":"1146_CR36","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1007\/s002850050147","volume":"38","author":"L Esteva","year":"1999","unstructured":"Esteva L, Vargas C (1999) A model for dengue disease with variable human population. J Math Biol 38:220\u2013240","journal-title":"J Math Biol"},{"key":"1146_CR37","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1007\/s002850050064","volume":"35","author":"Z Feng","year":"1997","unstructured":"Feng Z, Velasco-Hernadez V (1997) Competitive exclusion in a vector-host model for the dengue fever. J Math Biol 35:523\u2013544","journal-title":"J Math Biol"},{"key":"1146_CR38","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6380-7","volume-title":"Deterministic and stochastic optimal control","author":"WH Fleming","year":"1975","unstructured":"Fleming WH, Rishel RW (1975) Deterministic and stochastic optimal control. Springer, Berlin"},{"issue":"1","key":"1146_CR39","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/BF02547925","volume":"41","author":"H Freedman","year":"1979","unstructured":"Freedman H (1979) Stability analysis of a predator\u2013prey system with mutual interference and density-dependent death rates. Bull Math Biol 41(1):67\u201378","journal-title":"Bull Math Biol"},{"key":"1146_CR40","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.mbs.2008.05.002","volume":"215","author":"SM Garba","year":"2008","unstructured":"Garba SM, Gumel AB, Bakar MRA (2008) Backward bifurcations in dengue transmission dynamics. Math Biosci 215:11\u201325","journal-title":"Math Biosci"},{"issue":"4","key":"1146_CR41","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/BF02460776","volume":"40","author":"BS Goh","year":"1978","unstructured":"Goh BS (1978) Global stability in a class of prey\u2013predator models. Bull Math Biol 40(4):525\u2013533","journal-title":"Bull Math Biol"},{"issue":"1","key":"1146_CR42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00285-008-0206-y","volume":"59","author":"D Greenhalgh","year":"2009","unstructured":"Greenhalgh D, Griffiths M (2009) Backward bifurcation, equilibrium and stability phenomena in a three-stage extended brsv epidemic model. J Math Biol 59(1):1\u201336","journal-title":"J Math Biol"},{"key":"1146_CR43","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1111\/j.1749-6632.2001.tb02681.x","volume":"951","author":"DJ Gubler","year":"2001","unstructured":"Gubler DJ (2001) Human arbovirus infections worldwide. Ann N Y Acad Sci 951:13\u201324","journal-title":"Ann N Y Acad Sci"},{"issue":"3","key":"1146_CR44","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/BF00250793","volume":"54","author":"ME Gurtin","year":"1974","unstructured":"Gurtin ME, MacCamy RC (1974) Non-linear age-dependent population dynamics. Arch Ration Mech Anal 54(3):281\u2013300","journal-title":"Arch Ration Mech Anal"},{"issue":"3\u20134","key":"1146_CR45","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0025-5564(79)90049-X","volume":"43","author":"ME Gurtin","year":"1979","unstructured":"Gurtin ME, MacCamy RC (1979) Some simple models for nonlinear age-dependent population dynamics. Math Biosci 43(3\u20134):199\u2013211","journal-title":"Math Biosci"},{"issue":"13","key":"1146_CR46","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1056\/NEJMoa1506223","volume":"373","author":"SR Hadinegoro","year":"2015","unstructured":"Hadinegoro SR, Arredondo-Garc\u00eda JL, Capeding MR, Deseda C, Chotpitayasunondh T, Dietze R, Hj Muhammad Ismail H, Reynales H, Limkittikul K, Rivera-Medina DM et al (2015) Efficacy and long-term safety of a dengue vaccine in regions of endemic disease. N Engl J Med 373(13):1195\u20131206","journal-title":"N Engl J Med"},{"key":"1146_CR47","volume-title":"Ordinary differential equations","author":"JK Hale","year":"1969","unstructured":"Hale JK (1969) Ordinary differential equations. Wiley, New York"},{"issue":"6","key":"1146_CR48","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1086\/382077","volume":"38","author":"PJ Hotez","year":"2004","unstructured":"Hotez PJ, Remme JH, Buss P, George G, Morel C, Breman JG (2004) Combating tropical infectious diseases: report of the disease control priorities in developing countries project. Clin Infect Dis 38(6):871\u2013878","journal-title":"Clin Infect Dis"},{"issue":"4","key":"1146_CR49","doi-asserted-by":"crossref","first-page":"473","DOI":"10.3934\/dcdsb.2002.2.473","volume":"2","author":"E Jung","year":"2002","unstructured":"Jung E, Lenhart S, Feng Z (2002) Optimal control of treatments in a two-strain tuberculosis model. Discrete Continuous Dyn Syst Ser B 2(4):473\u2013482","journal-title":"Discrete Continuous Dyn Syst Ser B"},{"key":"1146_CR50","unstructured":"Kane H (2015) N\u00e9gocier la gu\u00e9rison du petit malade. Configurations denfance et accessibilit\u00e9 des soins \u00e0 nouakchott. Ph.D. thesis, EHESS-Paris, Centre Norbert Elias, UMR 8562"},{"key":"1146_CR51","unstructured":"Karabatsos N (1985) International Catalogue of Arboviruses, including certain other viruses of vertebrates. American Society of Tropical Medicine and Hygiene, San Antonio, TX (2001 update)"},{"issue":"6","key":"1146_CR52","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1002\/oca.2088","volume":"35","author":"SM Kassa","year":"2014","unstructured":"Kassa SM, Hove-Musekwa SD (2014) Optimal control of allocation of resources and the economic growth in HIV-infected communities. Optim Control Appl Methods 35(6):627\u2013646","journal-title":"Optim Control Appl Methods"},{"key":"1146_CR53","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/0022-0396(68)90048-X","volume":"4","author":"JP LaSalle","year":"1968","unstructured":"LaSalle JP (1968) Stability theory for ordinary differential equations. J Differ Equ 4:57\u201365","journal-title":"J Differ Equ"},{"key":"1146_CR54","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970432","volume-title":"The stability of dynamical systems","author":"JP LaSalle","year":"1976","unstructured":"LaSalle JP (1976) The stability of dynamical systems. Society for Industrial and Applied Mathematics, Philadelphia"},{"key":"1146_CR55","unstructured":"Le Monde Economie: Sanofi lance son vaccin contre la dengue. Accessed 09\/12\/2015 at 16:30 Updated 10\/12\/2015 at 11:26"},{"key":"1146_CR56","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011418","volume-title":"Optimal control applied to biological models","author":"S Lenhart","year":"2007","unstructured":"Lenhart S, Workman JT (2007) Optimal control applied to biological models. Chapman and Hall, New York"},{"key":"1146_CR57","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1111\/j.1365-2915.1996.tb00077.x","volume":"10","author":"CC Lord","year":"1996","unstructured":"Lord CC, Woolhouse MEJ, Heesterbeek JAP (1996) Vector-borne diseases and the basic reproduction number: a case study of African horse sickness. Med Vet Entomol 10:19\u201328","journal-title":"Med Vet Entomol"},{"key":"1146_CR58","volume-title":"Differential equations: classical to controlled","author":"DL Lukes","year":"1982","unstructured":"Lukes DL (1982) Differential equations: classical to controlled. Academic Press, New York"},{"key":"1146_CR59","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1016\/j.mcm.2010.12.008","volume":"53","author":"NA Maidana","year":"2011","unstructured":"Maidana NA, Yang HM (2011) Dynamic of West Nile virus transmission considering several coexisting avian populations. Math Comput Model 53:1247\u20131260","journal-title":"Math Comput Model"},{"key":"1146_CR60","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.mbs.2010.10.008","volume":"229","author":"D Moulay","year":"2011","unstructured":"Moulay D, Aziz-Alaoui MA, Cadivel M (2011) The Chikungunya disease: modeling, vector and transmission global dynamics. Math Biosci 229:50\u201363","journal-title":"Math Biosci"},{"issue":"2","key":"1146_CR61","doi-asserted-by":"crossref","first-page":"369","DOI":"10.3934\/mbe.2012.9.369","volume":"9","author":"D Moulay","year":"2012","unstructured":"Moulay D, Aziz-Alaoui MA, Hee-Dae K (2012) Optimal control of Chikungunya disease: larvae reduction, treatment and prevention. Math Biosci Eng 9(2):369\u2013393","journal-title":"Math Biosci Eng"},{"issue":"7","key":"1146_CR62","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1016\/S0895-7177(00)00169-2","volume":"32","author":"GA Ngwa","year":"2000","unstructured":"Ngwa GA, Shu WS (2000) A mathematical model for endemic malaria with variable human and mosquito populations. Math Comput Model 32(7):747\u2013763","journal-title":"Math Comput Model"},{"key":"1146_CR63","first-page":"51","volume":"30","author":"H Nishiura","year":"2006","unstructured":"Nishiura H (2006) Mathematical and statistical analyses of the spread of dengue. Dengue Bull 30:51\u201367","journal-title":"Dengue Bull"},{"key":"1146_CR64","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.biosystems.2011.07.006","volume":"106","author":"KO Okosun","year":"2011","unstructured":"Okosun KO, Ouifki R, Marcus N (2011) Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity. Biosystems 106:136\u2013145","journal-title":"Biosystems"},{"key":"1146_CR65","volume-title":"Planning social mobilization and communication for dengue fever prevention and control","author":"W Parks","year":"2004","unstructured":"Parks W, Lloyd L (2004) Planning social mobilization and communication for dengue fever prevention and control. World Health Organization, Geneva"},{"issue":"10","key":"1146_CR66","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3201\/eid1210.060610","volume":"12","author":"P Parola","year":"2006","unstructured":"Parola P, de Lamballerie X, Jourdan J, Rovery C, Vaillant V, Minodier P, Brouqui P, Flahault A, Raoult D, Charrel RN (2006) Novel Chikungunya virus variant in travelers returning from Indian ocean islands. Emerg Infect Dis 12(10):1\u201312","journal-title":"Emerg Infect Dis"},{"issue":"1177","key":"1146_CR67","first-page":"14","volume":"1","author":"C Paupy","year":"2009","unstructured":"Paupy C, Delatte H, Bagny L, Corbel V, Fontenille D (2009) Aedes albopictus, an arbovirus vector: from the darkness to the light. Microbes Infect 1(1177):14\u201315","journal-title":"Microbes Infect"},{"issue":"e18860","key":"1146_CR68","first-page":"1","volume":"6","author":"P Poletti","year":"2011","unstructured":"Poletti P, Messeri G, Ajelli M, Vallorani R, Rizzo C, Merler S (2011) Transmission potential of Chikungunya virus and control measures: the case of Italy. PLoS ONE 6(e18860):1\u201312","journal-title":"PLoS ONE"},{"key":"1146_CR69","volume-title":"The mathematical theory of optimal processes","author":"LS Pontryagin","year":"1962","unstructured":"Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF (1962) The mathematical theory of optimal processes. Wiley, New York"},{"key":"1146_CR70","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.matcom.2015.09.005","volume":"121","author":"E Rivero-Esquivel","year":"2016","unstructured":"Rivero-Esquivel E, Avila-Vales E, Garc\u00eda-Almeida G (2016) Stability and bifurcation analysis of a SIR model with saturated incidence rate and saturated treatment. Math Comput Simul 121:109\u2013132","journal-title":"Math Comput Simul"},{"key":"1146_CR71","unstructured":"Rodrigues HSF (2012) Optimal control and numerical optimization applied to epidemiological models. Ph.D. thesis, Universidade de Aveiro Departamento de Matematica"},{"key":"1146_CR72","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.mbs.2013.10.006","volume":"247","author":"HS Rodrigues","year":"2014","unstructured":"Rodrigues HS, Monteiro MTT, Torres DFM (2014) Vaccination models and optimal control strategies to dengue. Math Biosci 247:1\u201312","journal-title":"Math Biosci"},{"key":"1146_CR73","doi-asserted-by":"crossref","first-page":"1559","DOI":"10.1016\/S0140-6736(12)61428-7","volume":"380","author":"A Sabchareon","year":"2012","unstructured":"Sabchareon A, Wallace D, Sirivichayakul C, Limkittikul K, Chanthavanich P, Suvannadabba S, Jiwariyavej V, Dulyachai W, Pengsaa K, Anh Wartel T, Moureau A, Saville M, Bouckenooghe A, Viviani S, Tornieporth NG, Lang J (2012) Protective efficacy of the recombinant, live-attenuated, CYD tetravalent dengue vaccine in Thai schoolchildren: a randomised, controlled phase 2b trial. Lancet 380:1559\u20131567","journal-title":"Lancet"},{"key":"1146_CR74","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1007\/s00285-012-0582-1","volume":"67","author":"M Safan","year":"2013","unstructured":"Safan M, Kretzschmar M, Hadeler KP (2013) Vaccination based control of infections in SIRS models with reinfection: special reference to pertussis. J Math Biol 67:1083\u20131110","journal-title":"J Math Biol"},{"key":"1146_CR75","unstructured":"Sanofi P (2013) Dengue vaccine, a priority for global health. http:\/\/www.sanofipasteur.com\/en\/Documents\/PDF\/Dengue_Priority_for_Global_Health_EN_2013-09.pdf"},{"key":"1146_CR76","unstructured":"Sanofi P (2014) Communiqu\u00e9 de presse: the new England Journal of Medicine publie les r\u00e9sultats de l\u2019\u00e9tude clinique d\u2019efficacit\u00e9 de phase iii du candidat vaccin dengue de sanofi pasteur"},{"key":"1146_CR77","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-3834-2","volume-title":"Geometric optimal control: theory, methods and examples","author":"H Sch\u00e4ttler","year":"2012","unstructured":"Sch\u00e4ttler H, Ledzewicz U (2012) Geometric optimal control: theory, methods and examples, vol 38. Springer Science and Business Media, Berlin"},{"key":"1146_CR78","first-page":"115","volume":"338","author":"TW Scott","year":"2010","unstructured":"Scott TW, Morrison AC (2010) Vector dynamics and transmission of dengue virus: implications for dengue surveillance and prevention strategies: vector dynamics and dengue prevention. Curr Top Microbiol Immunol 338:115\u2013128","journal-title":"Curr Top Microbiol Immunol"},{"key":"1146_CR79","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1016\/j.mbs.2007.05.012","volume":"210","author":"O Sharomi","year":"2007","unstructured":"Sharomi O, Podder C, Gumel A, Elbasha E, Watmough J (2007) Role of incidence function in vaccine-induced backward bifurcation in some HIV models. Math Biosci 210:436\u2013463","journal-title":"Math Biosci"},{"key":"1146_CR80","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1111\/j.1570-7458.1992.tb01570.x","volume":"63","author":"T Sota","year":"1992","unstructured":"Sota T, Mogi M (1992) Survival time and resistance to desiccation of diapause and non-diapause eggs of temperate Aedes (Stegomyia) mosquitoe. Entomol Exp Appl 63:155","journal-title":"Entomol Exp Appl"},{"issue":"10","key":"1146_CR81","doi-asserted-by":"crossref","first-page":"e107700","DOI":"10.1371\/journal.pone.0107700","volume":"9","author":"EM Stuckey","year":"2014","unstructured":"Stuckey EM, Stevenson J, Galactionova K, Baidjoe AY, Bousema T, Odongo W, Kariuki S, Drakeley C, Smith TA, Cox J et al (2014) Modeling the cost effectiveness of malaria control interventions in the highlands of western Kenya. PLoS ONE 9(10):e107700","journal-title":"PLoS ONE"},{"issue":"85","key":"1146_CR82","doi-asserted-by":"crossref","first-page":"20130325","DOI":"10.1098\/rsif.2013.0325","volume":"10","author":"EB Stukalin","year":"2013","unstructured":"Stukalin EB, Aifuwa I, Kim JS, Wirtz D, Sun SX (2013) Age-dependent stochastic models for understanding population fluctuations in continuously cultured cells. J R Soc Interface 10(85):20130325","journal-title":"J R Soc Interface"},{"issue":"9","key":"1146_CR83","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1111\/j.1365-3156.2007.01889.x","volume":"12","author":"JA Suaya","year":"2007","unstructured":"Suaya JA, Shepard DS, Chang MS, Caram M, Hoyer S, Socheat D, Chantha N, Nathan MB (2007) Cost-effectiveness of annual targeted larviciding campaigns in Cambodia against the dengue vector Aedes aegypti. Trop Med Int Health 12(9):1026\u20131036","journal-title":"Trop Med Int Health"},{"key":"1146_CR84","unstructured":"The Verge: Dengue vaccine protects people nine years or older\u2014but harms younger kids. July 27, 2015. Accessed 21 Oct 2016. http:\/\/www.theverge.com\/2015\/7\/27\/9048425\/dengue-vaccine-side-effects-r isks-children"},{"issue":"2","key":"1146_CR85","first-page":"79","volume":"92","author":"J Thonnon","year":"1999","unstructured":"Thonnon J, Spiegel A, Diallo M, Diallo A, Fontenille D (1999) Epid\u00e9mies \u00e0 virus chikungunya en 1996 et 1997 au s\u00e9n\u00e9gal. Bull Soc Pathol Exot 92(2):79\u201382","journal-title":"Bull Soc Pathol Exot"},{"issue":"3","key":"1146_CR86","first-page":"40","volume":"29","author":"M Togora","year":"2014","unstructured":"Togora M, Kpoz\u00e8houen A, Saizonou J, Sossa C, Ou\u00e9graogo L, Makoutod\u00e9 M (2014) Facteurs associ\u00e9s a la faible couverture en vaccin antit\u00e9tanique chez les femmes enceintes dans la zone sanitaire de Zogbodomey\u2013Bohicon\u2013Zakpota au b\u00e9nin. Mali M\u00e9d 29(3):40\u201348","journal-title":"Mali M\u00e9d"},{"key":"1146_CR87","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","volume":"180","author":"P Driessche van den","year":"2002","unstructured":"van den Driessche P, Watmough J (2002) Reproduction numbers and the sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180:29\u201348","journal-title":"Math Biosci"},{"issue":"2","key":"1146_CR88","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1056\/NEJMoa1411037","volume":"372","author":"L Villar","year":"2015","unstructured":"Villar L, Dayan GH, Arredondo-Garc\u00eda JL, Rivera DM, Cunha R, Deseda C, Reynales H, Costa MS, Morales-Ramrez JO, Carrasquilla G, Rey LC, Dietze R, Luz K, Rivas E, Montoya MCM, Supelano MC, Zambrano B, Langevin E, Boaz M, Tornieporth N, Saville M, Noriega F (2015) Efficacy of a tetravalent dengue vaccine in children in Latin America. N Eng J Med 372(2):113\u2013123","journal-title":"N Eng J Med"},{"key":"1146_CR89","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2015.07.022","author":"IM Wangari","year":"2015","unstructured":"Wangari IM, Davis S, Stone L (2015) Backward bifurcation in epidemic models: technical note. Appl Math Model. doi: 10.1016\/j.apm.2015.07.022","journal-title":"Appl Math Model"},{"issue":"2","key":"1146_CR90","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1046\/j.1365-3156.2003.01177.x","volume":"9","author":"A Wilder-Smith","year":"2004","unstructured":"Wilder-Smith A, Foo W, Earnest A, Sremulanathan S, Paton NI (2004) Seroepidemiology of dengue in the adult population of Singapore. Trop Med Int Health 9(2):305\u2013308","journal-title":"Trop Med Int Health"},{"key":"1146_CR91","unstructured":"World Health Organization (2009) Dengue and dengue haemorrhagic fever. www.who.int\/mediacentre\/factsheets\/fs117\/en"},{"key":"1146_CR92","unstructured":"World Health Organization (2016) Dengue vaccine. Weekly epidemiological record (April)"},{"key":"1146_CR93","unstructured":"World Health Organization (2013) Dengue and severe dengue. www.who.int\/mediacentre\/factsheets\/fs117\/en \u00a0(updated September)"},{"issue":"1","key":"1146_CR94","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s13149-010-0123-3","volume":"104","author":"T Yam\u00e9ogo","year":"2011","unstructured":"Yam\u00e9ogo T, Kyelem C, Poda G, Sombi\u00e9 I, Ou\u00e9draogo M, Millogo A (2011) \u00c9pid\u00e9mie de m\u00e9ningite: \u00e9valuation de la surveillance et du traitement des cas dans les formations sanitaires dun district du Burkina Faso. Bull Soc Pathol Exot 104(1):68\u201373","journal-title":"Bull Soc Pathol Exot"},{"key":"1146_CR95","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/j.amc.2007.08.046","volume":"198","author":"HM Yang","year":"2008","unstructured":"Yang HM, Ferreira CP (2008) Assessing the effects of vector control on dengue transmission. Appl Math Comput 198:401\u2013413","journal-title":"Appl Math Comput"},{"issue":"5","key":"1146_CR96","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1111\/j.1365-3156.2004.01241.x","volume":"9","author":"A Y\u00e9bakima","year":"2004","unstructured":"Y\u00e9bakima A, Charles C, Mousson L, Vazeille M, Yp-Tcha MM, Failloux AB (2004) Genetic heterogeneity of the dengue vector Aedes aegypti in martinique. Trop Med Int Health 9(5):582\u2013587","journal-title":"Trop Med Int Health"},{"issue":"3","key":"1146_CR97","first-page":"194","volume":"8","author":"TT Yusuf","year":"2012","unstructured":"Yusuf TT, Benyah F (2012) Optimal control of vaccination and treatment for an SIR epidemiological model. World J Model Simul 8(3):194\u2013204","journal-title":"World J Model Simul"},{"key":"1146_CR98","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.biosystems.2008.05.004","volume":"93","author":"G Zaman","year":"2008","unstructured":"Zaman G, Kang YH, Jung IH (2008) Stability analysis and optimal vaccination of an SIR epidemic model. BioSystems 93:240\u2013249","journal-title":"BioSystems"}],"container-title":["Journal of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00285-017-1146-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-017-1146-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-017-1146-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T04:59:16Z","timestamp":1659070756000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00285-017-1146-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,6]]},"references-count":98,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["1146"],"URL":"https:\/\/doi.org\/10.1007\/s00285-017-1146-1","relation":{},"ISSN":["0303-6812","1432-1416"],"issn-type":[{"value":"0303-6812","type":"print"},{"value":"1432-1416","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,6,6]]}}}