{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T09:57:52Z","timestamp":1792403872041,"version":"4.4.0"},"reference-count":65,"publisher":"Springer Science and Business Media LLC","issue":"15","license":[{"start":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T00:00:00Z","timestamp":1685664000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T00:00:00Z","timestamp":1685664000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004410","name":"T\u00fcrkiye Bilimsel ve Teknolojik Ara\u015ft\u0131rma Kurumu","doi-asserted-by":"publisher","award":["119F162"],"award-info":[{"award-number":["119F162"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nonlinear Dyn"],"published-print":{"date-parts":[[2023,8]]},"DOI":"10.1007\/s11071-023-08577-6","type":"journal-article","created":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T04:31:08Z","timestamp":1685680268000},"page":"14467-14484","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A mathematical interpretation for outbreaks of bacterial meningitis under the effect of time-dependent transmission parameters"],"prefix":"10.1007","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5248-3118","authenticated-orcid":false,"given":"Can","family":"T\u00fcrk\u00fcn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3671-6225","authenticated-orcid":false,"given":"Meltem","family":"G\u00f6lgeli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6277-6830","authenticated-orcid":false,"given":"Fatihcan M.","family":"Atay","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,6,2]]},"reference":[{"issue":"Supplement\u20134","key":"8577_CR1","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1093\/infdis\/jiz358","volume":"220","author":"HM Soeters","year":"2019","unstructured":"Soeters, H.M., Diallo, A.O., Bicaba, B.W., et al.: Bacterial meningitis epidemiology in five countries in the meningitis belt of sub-Saharan Africa, 2015\u20132017. J. Inf. Dis. 220(Supplement\u20134), 165\u2013174 (2019). https:\/\/doi.org\/10.1093\/infdis\/jiz358","journal-title":"J. Inf. Dis."},{"issue":"4","key":"8577_CR2","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1016\/j.jinf.2020.05.079","volume":"81","author":"SR Parikh","year":"2020","unstructured":"Parikh, S.R., Campbell, H., Bettinger, J.A., et al.: The everchanging epidemiology of meningococcal disease worldwide and the potential for prevention through vaccination. J. Infect. 81(4), 483\u2013498 (2020). https:\/\/doi.org\/10.1016\/j.jinf.2020.05.079","journal-title":"J. Infect."},{"key":"8577_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/s10719-021-09990-y","author":"F Berti","year":"2021","unstructured":"Berti, F., Romano, M.R., Micoli, F., Adamo, R.: Carbohydrate based meningococcal vaccines: past and present overview. Glycoconj. J. (2021). https:\/\/doi.org\/10.1007\/s10719-021-09990-y","journal-title":"Glycoconj. J."},{"key":"8577_CR4","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.tmaid.2018.05.003","volume":"24","author":"S Yezli","year":"2018","unstructured":"Yezli, S.: The threat of meningococcal disease during the Hajj and Umrah mass gatherings: a comprehensive review. Travel Med. Infect. Dis. 24, 51\u201358 (2018). https:\/\/doi.org\/10.1016\/j.tmaid.2018.05.003","journal-title":"Travel Med. Infect. Dis."},{"issue":"s2","key":"8577_CR5","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1086\/596498","volume":"48","author":"Y Traore","year":"2009","unstructured":"Traore, Y., Tameklo, T.A., Njanpop-Lafourcade, B.-M., et al.: Incidence, seasonality, age distribution, and mortality of pneumococcal meningitis in Burkina Faso and Togo. Clin. Infect. Dis. 48(s2), 181\u2013189 (2009). https:\/\/doi.org\/10.1086\/596498","journal-title":"Clin. Infect. Dis."},{"issue":"79","key":"8577_CR6","doi-asserted-by":"publisher","first-page":"20120814","DOI":"10.1098\/rsif.2012.0814","volume":"10","author":"L Agier","year":"2013","unstructured":"Agier, L., Deroubaix, A., Martiny, N., et al.: Seasonality of meningitis in Africa and climate forcing: aerosols stand out. J. R. Soc. Interface 10(79), 20120814 (2013). https:\/\/doi.org\/10.1098\/rsif.2012.0814","journal-title":"J. R. Soc. Interface"},{"issue":"10","key":"8577_CR7","doi-asserted-by":"publisher","first-page":"0008634","DOI":"10.1371\/journal.pntd.0008634","volume":"14","author":"S Mazamay","year":"2020","unstructured":"Mazamay, S., Broutin, H., Bompangue, D., et al.: The environmental drivers of bacterial meningitis epidemics in the Democratic Republic of Congo, Central Africa. PLOS Negl. Trop. Dis. 14(10), 0008634 (2020). https:\/\/doi.org\/10.1371\/journal.pntd.0008634","journal-title":"PLOS Negl. Trop. Dis."},{"issue":"6","key":"8577_CR8","doi-asserted-by":"publisher","first-page":"665","DOI":"10.3201\/eid0906.020565","volume":"9","author":"JR Lingappa","year":"2003","unstructured":"Lingappa, J.R., Al-Rabeah, A.M., Hajjeh, R., et al.: Serogroup W-135 meningococcal disease during the Hajj, 2000. Emerg. Infect. Dis. 9(6), 665\u2013671 (2003). https:\/\/doi.org\/10.3201\/eid0906.020565","journal-title":"Emerg. Infect. Dis."},{"key":"8577_CR9","unstructured":"GASTAT, K.o.S.A.: Hajj statistics 2019. Technical report, General Authority for Statistics (2020). https:\/\/www.stats.gov.sa\/en\/28"},{"issue":"6","key":"8577_CR10","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1016\/j.tmaid.2015.09.008","volume":"13","author":"P Gautret","year":"2015","unstructured":"Gautret, P., Benkouiten, S., Griffiths, K., Sridhar, S.: The inevitable Hajj cough: surveillance data in French pilgrims, 2012\u20132014. Travel Med. Infect. Dis. 13(6), 485\u2013489 (2015). https:\/\/doi.org\/10.1016\/j.tmaid.2015.09.008","journal-title":"Travel Med. Infect. Dis."},{"issue":"6","key":"8577_CR11","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1086\/367858","volume":"36","author":"A Wilder-Smith","year":"2003","unstructured":"Wilder-Smith, A., Goh, K.T., Barkham, T., Paton, N.I.: Hajj-associated outbreak strain of Neisseria meningitidis Serogroup W135: estimates of the attack rate in a defined population and the risk of invasive disease developing in carriers. Clin. Infect. Dis. 36(6), 679\u2013683 (2003). https:\/\/doi.org\/10.1086\/367858","journal-title":"Clin. Infect. Dis."},{"issue":"8","key":"8577_CR12","doi-asserted-by":"publisher","first-page":"574","DOI":"10.1016\/j.ijid.2012.03.011","volume":"16","author":"M Ceyhan","year":"2012","unstructured":"Ceyhan, M., Anis, S., Htun-Myint, L., et al.: Meningococcal disease in the Middle East and North Africa: an important public health consideration that requires further attention. Int. J. Infect. Dis. 16(8), 574\u2013582 (2012). https:\/\/doi.org\/10.1016\/j.ijid.2012.03.011","journal-title":"Int. J. Infect. Dis."},{"key":"8577_CR13","doi-asserted-by":"publisher","DOI":"10.1111\/tmi.13546","author":"A Alasmari","year":"2021","unstructured":"Alasmari, A., Houghton, J., Greenwood, B., et al.: Meningococcal carriage among Hajj pilgrims, risk factors for carriage and records of vaccination: a study of pilgrims to Mecca. Trop. Med. Int. Health (2021). https:\/\/doi.org\/10.1111\/tmi.13546","journal-title":"Trop. Med. Int. Health"},{"key":"8577_CR14","doi-asserted-by":"publisher","DOI":"10.1186\/s12879-021-06781-6","author":"AG Dogu","year":"2021","unstructured":"Dogu, A.G., Oordt-Speets, A.M., Kessel-de Bruijn, F., et al.: Systematic review of invasive meningococcal disease epidemiology in the Eastern Mediterranean and North Africa region. BMC Infect. Dis. (2021). https:\/\/doi.org\/10.1186\/s12879-021-06781-6","journal-title":"BMC Infect. Dis."},{"issue":"4","key":"8577_CR15","doi-asserted-by":"publisher","first-page":"127","DOI":"10.3390\/tropicalmed4040127","volume":"4","author":"A-M Badahdah","year":"2019","unstructured":"Badahdah, A.-M., Alghabban, F., Falemban, W., et al.: Meningococcal vaccine for Hajj pilgrims: compliance, predictors, and barriers. Trop. Med. Infect. Dis. 4(4), 127 (2019). https:\/\/doi.org\/10.3390\/tropicalmed4040127","journal-title":"Trop. Med. Infect. Dis."},{"key":"8577_CR16","doi-asserted-by":"publisher","DOI":"10.2991\/jegh.k.190705.001","author":"JA Al-Tawfiq","year":"2019","unstructured":"Al-Tawfiq, J.A., Memish, Z.A.: The Hajj 2019 vaccine requirements and possible new challenges. J. Epidemiol. Global Health (2019). https:\/\/doi.org\/10.2991\/jegh.k.190705.001","journal-title":"J. Epidemiol. Global Health"},{"issue":"7","key":"8577_CR17","doi-asserted-by":"publisher","first-page":"976","DOI":"10.1017\/s095026880999104x","volume":"138","author":"A Wilder-Smith","year":"2009","unstructured":"Wilder-Smith, A., Chow, A., Goh, K.T.: Emergence and disappearance of W135 meningococcal disease. Epidemiol. Infect. 138(7), 976\u2013978 (2009). https:\/\/doi.org\/10.1017\/s095026880999104x","journal-title":"Epidemiol. Infect."},{"issue":"1","key":"8577_CR18","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1128\/cvi.00314-12","volume":"20","author":"M Ceyhan","year":"2013","unstructured":"Ceyhan, M., Celik, M., Demir, E.T., et al.: Acquisition of meningococcal serogroup W-135 carriage in Turkish Hajj pilgrims who had received the quadrivalent meningococcal polysaccharide vaccine. Clin. Vaccine Immunol. 20(1), 66\u201368 (2013). https:\/\/doi.org\/10.1128\/cvi.00314-12","journal-title":"Clin. Vaccine Immunol."},{"issue":"6","key":"8577_CR19","doi-asserted-by":"publisher","first-page":"1268","DOI":"10.1080\/21645515.2019.1680084","volume":"16","author":"H Tezer","year":"2019","unstructured":"Tezer, H., G\u00fclhan, B., Gi\u015fi, A.S., et al.: The impact of meningococcal conjugate vaccine (MenACWY-TT) on meningococcal carriage in Hajj pilgrims returning to Turkey. Human Vaccines Immunother. 16(6), 1268\u20131271 (2019). https:\/\/doi.org\/10.1080\/21645515.2019.1680084","journal-title":"Human Vaccines Immunother."},{"issue":"12","key":"8577_CR20","doi-asserted-by":"publisher","first-page":"6923","DOI":"10.3390\/su13126923","volume":"13","author":"AM Al-Shaery","year":"2021","unstructured":"Al-Shaery, A.M., Hejase, B., Tridane, A., et al.: Agent-based modeling of the Hajj rituals with the possible spread of COVID-19. Sustainability 13(12), 6923 (2021). https:\/\/doi.org\/10.3390\/su13126923","journal-title":"Sustainability"},{"key":"8577_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/s13369-021-05838-7","author":"MK Shambour","year":"2021","unstructured":"Shambour, M.K., Gutub, A.: Progress of IoT research technologies and applications serving Hajj and Umrah. Arab. J. Sci. Eng. (2021). https:\/\/doi.org\/10.1007\/s13369-021-05838-7","journal-title":"Arab. J. Sci. Eng."},{"issue":"5","key":"8577_CR22","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1002\/rmv.443","volume":"14","author":"D Bernoulli","year":"2004","unstructured":"Bernoulli, D., Blower, S.: An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it. Rev. Med. Virol. 14(5), 275\u2013288 (2004). https:\/\/doi.org\/10.1002\/rmv.443","journal-title":"Rev. Med. Virol."},{"issue":"1","key":"8577_CR23","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1186\/1476-072x-6-29","volume":"6","author":"H Broutin","year":"2007","unstructured":"Broutin, H., Philippon, S., Magny, G.C., et al.: Comparative study of meningitis dynamics across nine African countries: a global perspective. Int. J. Health Geogr. 6(1), 29 (2007). https:\/\/doi.org\/10.1186\/1476-072x-6-29","journal-title":"Int. J. Health Geogr."},{"issue":"5","key":"8577_CR24","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1017\/s0950268811001385","volume":"140","author":"TJ Irving","year":"2011","unstructured":"Irving, T.J., Blyuss, K.B., Colijn, C., Trotter, C.L.: Modelling meningococcal meningitis in the African meningitis belt. Epidemiol. Infect. 140(5), 897\u2013905 (2011). https:\/\/doi.org\/10.1017\/s0950268811001385","journal-title":"Epidemiol. Infect."},{"key":"8577_CR25","doi-asserted-by":"publisher","first-page":"2492","DOI":"10.1016\/j.procs.2013.05.426","volume":"18","author":"MJF Mart\u00ednez","year":"2013","unstructured":"Mart\u00ednez, M.J.F., Merino, E.G., S\u00e1nchez, E.G., et al.: A mathematical model to study the meningococcal meningitis. Procedia Comput. Sci. 18, 2492\u20132495 (2013). https:\/\/doi.org\/10.1016\/j.procs.2013.05.426","journal-title":"Procedia Comput. Sci."},{"key":"8577_CR26","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/2657461","author":"JKK Asamoah","year":"2018","unstructured":"Asamoah, J.K.K., Nyabadza, F., Seidu, B., et al.: Mathematical modelling of bacterial meningitis transmission dynamics with control measures. Comput. Math. Methods Med. (2018). https:\/\/doi.org\/10.1155\/2018\/2657461","journal-title":"Comput. Math. Methods Med."},{"key":"8577_CR27","doi-asserted-by":"publisher","unstructured":"Blyuss, K.B.: In: Aston, P.J., Mulholland, A.J., Tant, K.M.M. (eds.) Mathematical Modelling of the Dynamics of Meningococcal Meningitis in Africa, pp. 221\u2013226. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-25454-8_28","DOI":"10.1007\/978-3-319-25454-8_28"},{"issue":"1","key":"8577_CR28","doi-asserted-by":"publisher","first-page":"34","DOI":"10.2307\/2341437","volume":"92","author":"HE Soper","year":"1929","unstructured":"Soper, H.E.: The interpretation of periodicity in disease prevalence. J. Roy. Stat. Soc. 92(1), 34 (1929). https:\/\/doi.org\/10.2307\/2341437","journal-title":"J. Roy. Stat. Soc."},{"issue":"7135","key":"8577_CR29","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1038\/nature05638","volume":"446","author":"L Stone","year":"2007","unstructured":"Stone, L., Olinky, R., Huppert, A.: Seasonal dynamics of recurrent epidemics. Nature 446(7135), 533\u2013536 (2007). https:\/\/doi.org\/10.1038\/nature05638","journal-title":"Nature"},{"issue":"5","key":"8577_CR30","doi-asserted-by":"publisher","first-page":"1098","DOI":"10.1007\/s11538-011-9710-0","volume":"74","author":"N Chitnis","year":"2012","unstructured":"Chitnis, N., Hardy, D., Smith, T.: A periodically-forced mathematical model for the seasonal dynamics of malaria in mosquitoes. Bull. Math. Biol. 74(5), 1098\u20131124 (2012). https:\/\/doi.org\/10.1007\/s11538-011-9710-0","journal-title":"Bull. Math. Biol."},{"issue":"3","key":"8577_CR31","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1007\/s00285-013-0648-8","volume":"68","author":"NO Onyango","year":"2013","unstructured":"Onyango, N.O., M\u00fcller, J.: Determination of optimal vaccination strategies using an orbital stability threshold from periodically driven systems. J. Math. Biol. 68(3), 763\u2013784 (2013). https:\/\/doi.org\/10.1007\/s00285-013-0648-8","journal-title":"J. Math. Biol."},{"issue":"6\u20137","key":"8577_CR32","doi-asserted-by":"publisher","first-page":"1437","DOI":"10.1007\/s00285-016-0997-1","volume":"73","author":"P Doutor","year":"2016","unstructured":"Doutor, P., Rodrigues, P., C\u00e9u Soares, M., Chalub, F.A.C.C.: Optimal vaccination strategies and rational behaviour in seasonal epidemics. J. Math. Biol. 73(6\u20137), 1437\u20131465 (2016). https:\/\/doi.org\/10.1007\/s00285-016-0997-1","journal-title":"J. Math. Biol."},{"issue":"1","key":"8577_CR33","doi-asserted-by":"publisher","DOI":"10.1098\/rsos.191187","volume":"7","author":"M Greer","year":"2020","unstructured":"Greer, M., Saha, R., Gogliettino, A., et al.: Emergence of oscillations in a simple epidemic model with demographic data. R. Soc. Open Sci. 7(1), 191187 (2020). https:\/\/doi.org\/10.1098\/rsos.191187","journal-title":"R. Soc. Open Sci."},{"key":"8577_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-021-01430-9","author":"AJ Arenas","year":"2021","unstructured":"Arenas, A.J., Gonz\u00e1lez-Parra, G., Espriella, N.D.L.: Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate. Comput. Appl. Math. (2021). https:\/\/doi.org\/10.1007\/s40314-021-01430-9","journal-title":"Comput. Appl. Math."},{"issue":"3","key":"8577_CR35","doi-asserted-by":"publisher","first-page":"921","DOI":"10.15672\/hujms.624042","volume":"49","author":"M G\u00f6lgeli","year":"2020","unstructured":"G\u00f6lgeli, M., Atay, F.M.: Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes. Hacet. J. Math. Stat. 49(3), 921\u2013934 (2020). https:\/\/doi.org\/10.15672\/hujms.624042","journal-title":"Hacet. J. Math. Stat."},{"issue":"6","key":"8577_CR36","doi-asserted-by":"publisher","first-page":"0198772","DOI":"10.1371\/journal.pone.0198772","volume":"13","author":"AM Oordt-Speets","year":"2018","unstructured":"Oordt-Speets, A.M., Bolijn, R., Hoorn, R.C., et al.: Global etiology of bacterial meningitis: a systematic review and meta-analysis. PLoS ONE 13(6), 0198772 (2018). https:\/\/doi.org\/10.1371\/journal.pone.0198772","journal-title":"PLoS ONE"},{"issue":"4","key":"8577_CR37","doi-asserted-by":"publisher","first-page":"1343","DOI":"10.1007\/s40121-022-00620-0","volume":"11","author":"S Badur","year":"2022","unstructured":"Badur, S., Khalaf, M., \u00d6zt\u00fcrk, S., et al.: Meningococcal disease and immunization activities in Hajj and Umrah pilgrimage: a review. Infect. Dis. Therapy 11(4), 1343\u20131369 (2022). https:\/\/doi.org\/10.1007\/s40121-022-00620-0","journal-title":"Infect. Dis. Therapy"},{"issue":"10","key":"8577_CR38","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.3201\/eid0910.030182","volume":"9","author":"AM Molesworth","year":"2003","unstructured":"Molesworth, A.M., Cuevas, L.E., Connor, S.J., et al.: Environmental risk and meningitis epidemics in Africa. Emerg. Infect. Dis. 9(10), 1287\u20131293 (2003). https:\/\/doi.org\/10.3201\/eid0910.030182","journal-title":"Emerg. Infect. Dis."},{"issue":"5","key":"8577_CR39","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/0169-4758(92)90018-w","volume":"8","author":"K Dietz","year":"1992","unstructured":"Dietz, K.: Infectious diseases of humans: dynamics and control. Parasitol. Today 8(5), 179 (1992). https:\/\/doi.org\/10.1016\/0169-4758(92)90018-w","journal-title":"Parasitol. Today"},{"issue":"1\u20132","key":"8577_CR40","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/s0025-5564(02)00108-6","volume":"180","author":"P Driessche","year":"2002","unstructured":"Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1\u20132), 29\u201348 (2002). https:\/\/doi.org\/10.1016\/s0025-5564(02)00108-6","journal-title":"Math. Biosci."},{"issue":"1600","key":"8577_CR41","doi-asserted-by":"publisher","first-page":"2541","DOI":"10.1098\/rspb.2006.3604","volume":"273","author":"NC Grassly","year":"2006","unstructured":"Grassly, N.C., Fraser, C.: Seasonal infectious disease epidemiology. Proc. R. Soc. B Biol. Sci. 273(1600), 2541\u20132550 (2006). https:\/\/doi.org\/10.1098\/rspb.2006.3604","journal-title":"Proc. R. Soc. B Biol. Sci."},{"issue":"3","key":"8577_CR42","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1007\/s00285-006-0015-0","volume":"53","author":"N Baca\u00ebr","year":"2006","unstructured":"Baca\u00ebr, N., Guernaoui, S.: The epidemic threshold of vector-borne diseases with seasonality. J. Math. Biol. 53(3), 421\u2013436 (2006). https:\/\/doi.org\/10.1007\/s00285-006-0015-0","journal-title":"J. Math. Biol."},{"issue":"3","key":"8577_CR43","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1007\/s10884-008-9111-8","volume":"20","author":"W Wang","year":"2008","unstructured":"Wang, W., Zhao, X.-Q.: Threshold dynamics for compartmental epidemic models in periodic environments. J. Dyn. Diff. Equat. 20(3), 699\u2013717 (2008). https:\/\/doi.org\/10.1007\/s10884-008-9111-8","journal-title":"J. Dyn. Diff. Equat."},{"issue":"1","key":"8577_CR44","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1137\/080732870","volume":"70","author":"HR Thieme","year":"2009","unstructured":"Thieme, H.R.: Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity. SIAM J. Appl. Math. 70(1), 188\u2013211 (2009). https:\/\/doi.org\/10.1137\/080732870","journal-title":"SIAM J. Appl. Math."},{"issue":"1","key":"8577_CR45","doi-asserted-by":"publisher","first-page":"1004057","DOI":"10.1371\/journal.pcbi.1004057","volume":"11","author":"JT Griffin","year":"2015","unstructured":"Griffin, J.T.: The interaction between seasonality and pulsed interventions against malaria in their effects on the reproduction number. PLoS Comput. Biol. 11(1), 1004057 (2015). https:\/\/doi.org\/10.1371\/journal.pcbi.1004057","journal-title":"PLoS Comput. Biol."},{"issue":"4","key":"8577_CR46","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. J. R. Soc. Interface 2(4), 281\u2013293 (2005). https:\/\/doi.org\/10.1098\/rsif.2005.0042","journal-title":"J. R. Soc. Interface"},{"key":"8577_CR47","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-009-9433-7","author":"N Baca\u00ebr","year":"2009","unstructured":"Baca\u00ebr, N., Gomes, M.G.M.: On the final size of epidemics with seasonality. Bull. Math. Biol. (2009). https:\/\/doi.org\/10.1007\/s11538-009-9433-7","journal-title":"Bull. Math. Biol."},{"issue":"3","key":"8577_CR48","doi-asserted-by":"publisher","first-page":"1067","DOI":"10.1007\/s11538-006-9166-9","volume":"69","author":"N Baca\u00ebr","year":"2007","unstructured":"Baca\u00ebr, N.: Approximation of the basic reproduction number $$r_0$$ for vector-borne diseases with a periodic vector population. Bull. Math. Biol. 69(3), 1067\u20131091 (2007). https:\/\/doi.org\/10.1007\/s11538-006-9166-9","journal-title":"Bull. Math. Biol."},{"issue":"1","key":"8577_CR49","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/j.jmaa.2009.08.027","volume":"363","author":"Y Nakata","year":"2010","unstructured":"Nakata, Y., Kuniya, T.: Global dynamics of a class of SEIRS epidemic models in a periodic environment. J. Math. Anal. Appl. 363(1), 230\u2013237 (2010). https:\/\/doi.org\/10.1016\/j.jmaa.2009.08.027","journal-title":"J. Math. Anal. Appl."},{"key":"8577_CR50","unstructured":"Inc., T.M.: MATLAB Version: 9.13.0 (R2022b. The MathWorks Inc., Natick, Massachusetts, United States (2022)"},{"issue":"5","key":"8577_CR51","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1586\/erv.12.29","volume":"11","author":"EC Dinleyici","year":"2012","unstructured":"Dinleyici, E.C., Ceyhan, M.: The dynamic and changing epidemiology of meningococcal disease at the country-based level: the experience in Turkey. Expert Rev. Vaccines 11(5), 515\u2013518 (2012). https:\/\/doi.org\/10.1586\/erv.12.29","journal-title":"Expert Rev. Vaccines"},{"key":"8577_CR52","doi-asserted-by":"publisher","DOI":"10.1017\/s0950268819001134","author":"LV Cooper","year":"2019","unstructured":"Cooper, L.V., Kristiansen, P.A., Christensen, H., et al.: Meningococcal carriage by age in the African meningitis belt: a systematic review and meta-analysis. Epidemiol Infect. (2019). https:\/\/doi.org\/10.1017\/s0950268819001134","journal-title":"Epidemiol Infect."},{"key":"8577_CR53","doi-asserted-by":"publisher","first-page":"1317","DOI":"10.3906\/sag-1405-7","volume":"45","author":"M Metanat","year":"2015","unstructured":"Metanat, M., Sharifi-Mood, B., Sanei-Moghaddam, S., Rad, N.S.: Pharyngeal carriage rate of Neisseria meningitidis before and after the Hajj pilgrimage, in Zahedan (southeastern Iran), 2012. Turkish J. Med. Sci. 45, 1317\u20131320 (2015). https:\/\/doi.org\/10.3906\/sag-1405-7","journal-title":"Turkish J. Med. Sci."},{"issue":"4","key":"8577_CR54","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1159\/000312721","volume":"19","author":"EH Husain","year":"2010","unstructured":"Husain, E.H., Dashti, A.A., Electricwala, Q.Y., et al.: Absence of neisseria meningitidis from throat swabs of Kuwaiti pilgrims after returning from the Hajj. Med. Princ. Pract. 19(4), 321\u2013323 (2010). https:\/\/doi.org\/10.1159\/000312721","journal-title":"Med. Princ. Pract."},{"key":"8577_CR55","doi-asserted-by":"publisher","DOI":"10.1128\/msphere.00060-20","author":"M Ceyhan","year":"2020","unstructured":"Ceyhan, M., Ozsurekci, Y., Basaranoglu, S.T., et al.: Multicenter hospital-based prospective surveillance study of bacterial agents causing meningitis and seroprevalence of different serogroups of neisseria meningitidis, haemophilus influenzae type b, and streptococcus pneumoniae during 2015 to 2018 in Turkey. Sphere (2020). https:\/\/doi.org\/10.1128\/msphere.00060-20","journal-title":"Sphere"},{"issue":"7","key":"8577_CR56","doi-asserted-by":"publisher","first-page":"891","DOI":"10.3923\/pjbs.2020.891.897","volume":"23","author":"A Loutfi","year":"2020","unstructured":"Loutfi, A., Hioui, M.E., Jayche, S., et al.: Epidemiological, cytochemical and bacteriological profile of meningitis among adults and children in north west of Morocco. Pak. J. Biol. Sci. 23(7), 891\u2013897 (2020). https:\/\/doi.org\/10.3923\/pjbs.2020.891.897","journal-title":"Pak. J. Biol. Sci."},{"issue":"01","key":"8577_CR57","doi-asserted-by":"publisher","first-page":"2050006","DOI":"10.1142\/s1793524520500060","volume":"13","author":"SS Musa","year":"2020","unstructured":"Musa, S.S., Zhao, S., Hussaini, N., et al.: Mathematical modeling and analysis of meningococcal meningitis transmission dynamics. Int. J. Biomath. 13(01), 2050006 (2020). https:\/\/doi.org\/10.1142\/s1793524520500060","journal-title":"Int. J. Biomath."},{"key":"8577_CR58","unstructured":"World Bank: Data, Population Website. https:\/\/data.worldbank.org\/income-level\/upper-middle-income"},{"key":"8577_CR59","doi-asserted-by":"publisher","first-page":"4077","DOI":"10.2147\/idr.s240162","volume":"13","author":"Z Alamarat","year":"2020","unstructured":"Alamarat, Z., Hasbun, R.: Management of acute bacterial meningitis in children. Infect Drug Resist 13, 4077\u20134089 (2020). https:\/\/doi.org\/10.2147\/idr.s240162","journal-title":"Infect Drug Resist"},{"key":"8577_CR60","unstructured":"TUIK: Adrese dayal\u0131 n\u00fcfus kay\u0131t sistemi sonu\u00e7lar\u0131, 2019. Technical report, Turkish Statistical Institute (2020). https:\/\/data.tuik.gov.tr\/Kategori\/GetKategori?p=Nufus-ve-Demografi-109"},{"key":"8577_CR61","doi-asserted-by":"publisher","DOI":"10.3389\/fpubh.2016.00280","author":"M Aleeban","year":"2016","unstructured":"Aleeban, M., Mackey, T.K.: Global health and visa policy reform to address dangers of Hajj during summer seasons. Front. Public Health (2016). https:\/\/doi.org\/10.3389\/fpubh.2016.00280","journal-title":"Front. Public Health"},{"key":"8577_CR62","doi-asserted-by":"publisher","unstructured":"Kessel, F., Ende, C., Oordt-Speets, A.M., Kyaw, M.H.: Outbreaks of meningococcal meningitis in non-African countries over the last 50 years: a systematic review. J. Global Health (2019). https:\/\/doi.org\/10.7189\/jogh.09.010411","DOI":"10.7189\/jogh.09.010411"},{"key":"8577_CR63","doi-asserted-by":"publisher","unstructured":"Mazamay, S., Gu\u00e9gan, J.-F., Diallo, N., et al.: An overview of bacterial meningitis epidemics in Africa from 1928 to 2018 with a focus on epidemics outside-the-belt. BMC Infect. Dis. (2021). https:\/\/doi.org\/10.1186\/s12879-021-06724-1","DOI":"10.1186\/s12879-021-06724-1"},{"key":"8577_CR64","doi-asserted-by":"publisher","unstructured":"Sebastian, S., Badahdah, A.-M., Khatami, A., Rashid, H.: In: Laher, I. (ed.) Meningococcal Disease During Hajj, Umrah, and Other Mass Gatherings, pp. 1\u201322. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-319-74365-3_52-1","DOI":"10.1007\/978-3-319-74365-3_52-1"},{"issue":"11","key":"8577_CR65","doi-asserted-by":"publisher","first-page":"2781","DOI":"10.1080\/21645515.2020.1744979","volume":"16","author":"EC Dinleyici","year":"2020","unstructured":"Dinleyici, E.C., Borrow, R.: Meningococcal infections among refugees and immigrants: silent threats of past, present and future. Hum. Vaccin. Immunother. 16(11), 2781\u20132786 (2020). https:\/\/doi.org\/10.1080\/21645515.2020.1744979","journal-title":"Hum. Vaccin. Immunother."}],"container-title":["Nonlinear Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-023-08577-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11071-023-08577-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-023-08577-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T12:30:24Z","timestamp":1744201824000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11071-023-08577-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,2]]},"references-count":65,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["8577"],"URL":"https:\/\/doi.org\/10.1007\/s11071-023-08577-6","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-2585865\/v1","asserted-by":"object"}]},"ISSN":["0924-090X","1573-269X"],"issn-type":[{"value":"0924-090X","type":"print"},{"value":"1573-269X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,2]]},"assertion":[{"value":"21 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 May 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}