{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T14:17:28Z","timestamp":1764857848491,"version":"3.37.3"},"reference-count":52,"publisher":"World Scientific Pub Co Pte Ltd","issue":"15","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11401002","11771001"],"award-info":[{"award-number":["11401002","11771001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009558","name":"University Natural Science Research Project of Anhui Province","doi-asserted-by":"publisher","award":["KJ2018A0029"],"award-info":[{"award-number":["KJ2018A0029"]}],"id":[{"id":"10.13039\/501100009558","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012422","name":"Anhui Provincial University Teaching Quality and Teaching Reform Project","doi-asserted-by":"publisher","award":["KJ2019A005"],"award-info":[{"award-number":["KJ2019A005"]}],"id":[{"id":"10.13039\/501100012422","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009558","name":"University Natural Science Research Project of Anhui Province","doi-asserted-by":"publisher","award":["ZLTS2016065"],"award-info":[{"award-number":["ZLTS2016065"]}],"id":[{"id":"10.13039\/501100009558","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003995","name":"Natural Science Foundation of Anhui Province","doi-asserted-by":"publisher","award":["2008085MA02"],"award-info":[{"award-number":["2008085MA02"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,12,15]]},"abstract":"<jats:p> In this paper, the influence of PM[Formula: see text] on children\u2019s respiratory diseases is taken as the main research focus. Based on the real monitoring data of children\u2019s respiratory diseases in Anhui province, the traditional model is modified substantially, leading to the establishment of two mathematical models. First of all, considering that the PM[Formula: see text] changes over time, a nonautonomous air pollution-related disease model is constructed to study its permanence and extinction. Furthermore, regarding lag days of PM[Formula: see text] exposure, an air pollution-related disease model with the lag effect is installed and its local and global stabilities and Hopf bifurcation are investigated. Meanwhile, the above two models are numerically simulated, respectively. Our study demonstrates that the threshold conditions of permanence and extinction are obtained by the nonautonomous air pollution-related disease model, and the optimal parameters are obtained through the annual revision of the data by integrating the mathematical model, such that the number of children with respiratory diseases in the future can be checked and predicted. Also our study finds that the lag days of PM[Formula: see text] exposure have little effect on children with respiratory diseases in the air pollution-related disease model with a lag effect, but the PM[Formula: see text] has a tremendous influence on the number of patients. Once the lag days are combined with the effect of the PM[Formula: see text], it can have a significant impact on the patients\u2019 number, e.g. an emergence of periodic oscillations, with an approximate period of 11 days in Anhui Province, due to the Hopf bifurcation. <\/jats:p>","DOI":"10.1142\/s0218127420502351","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T10:44:48Z","timestamp":1607597088000},"page":"2050235","source":"Crossref","is-referenced-by-count":8,"title":["Modeling and Predicting the Influence of PM2.5 on Children\u2019s Respiratory Diseases"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7823-5684","authenticated-orcid":false,"given":"Lei","family":"Shi","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, 111 Jiulong Road, Shushan District, Hefei 230601, P. R. China"}]},{"given":"Xiaoliang","family":"Feng","sequence":"additional","affiliation":[{"name":"Anhui Provincial Center for Disease Control and Prevention, Hefei 230601, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6326-5274","authenticated-orcid":false,"given":"Longxing","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, 111 Jiulong Road, Shushan District, Hefei 230601, P. R. China"}]},{"given":"Yanlong","family":"Xu","sequence":"additional","affiliation":[{"name":"Anhui Provincial Center for Disease Control and Prevention, Hefei 230601, P. R. China"}]},{"given":"Sulan","family":"Zhai","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, 111 Jiulong Road, Shushan District, Hefei 230601, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2020,12,9]]},"reference":[{"key":"S0218127420502351BIB001","first-page":"167","volume":"21","author":"Abdurhaman X.","year":"2006","journal-title":"J. Biomath."},{"key":"S0218127420502351BIB002","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1007\/BF00276147","volume":"26","author":"Beretta E.","year":"1988","journal-title":"J. Math. Biol."},{"key":"S0218127420502351BIB003","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.amc.2017.02.003","volume":"305","author":"Cai Y.","year":"2017","journal-title":"Appl. Math. Comp."},{"key":"S0218127420502351BIB004","doi-asserted-by":"crossref","first-page":"8442","DOI":"10.1016\/j.atmosenv.2007.07.003","volume":"41","author":"Cairncross E. K.","year":"2007","journal-title":"Atm. Env."},{"key":"S0218127420502351BIB005","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.jtbi.2005.11.026","volume":"241","author":"Chowell G.","year":"2006","journal-title":"J. Th. Biol."},{"key":"S0218127420502351BIB006","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1111\/rssc.12239","volume":"67","author":"De Souza J. B.","year":"2018","journal-title":"J. R. Stat. Soc.: Ser. C (Appl. Stat.)"},{"key":"S0218127420502351BIB007","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12940-016-0115-2","volume":"15","author":"Feng C.","year":"2016","journal-title":"Env. Heal."},{"key":"S0218127420502351BIB008","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1016\/j.scitotenv.2015.01.005","volume":"511","author":"Gao M.","year":"2015","journal-title":"Sci. Tot. Env."},{"key":"S0218127420502351BIB009","first-page":"1","volume":"532","author":"He S.","year":"2019","journal-title":"Physica A: Stat. Mech. Appl."},{"key":"S0218127420502351BIB010","first-page":"89","volume":"30","author":"Laine M.","year":"2008","journal-title":"Soc. Sci. Elec. Publ."},{"key":"S0218127420502351BIB011","first-page":"575","volume":"69","author":"Leisch F.","year":"2002","journal-title":"Comput. Stat."},{"key":"S0218127420502351BIB012","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/S0025-5564(99)00030-9","volume":"160","author":"Li M. Y.","year":"1999","journal-title":"Math. Biosci."},{"key":"S0218127420502351BIB013","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-016-0001-8","volume":"6","author":"Li L.","year":"2016","journal-title":"Sci. Rep."},{"key":"S0218127420502351BIB014","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.amc.2018.11.042","volume":"347","author":"Li L.","year":"2019","journal-title":"Appl. Math. Comp."},{"key":"S0218127420502351BIB015","doi-asserted-by":"crossref","first-page":"4339","DOI":"10.3934\/mbe.2019216","volume":"16","author":"Lin J.","year":"2019","journal-title":"Math. Biosci. Eng."},{"key":"S0218127420502351BIB016","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1016\/j.aml.2003.11.005","volume":"17","author":"Ma W. B.","year":"2004","journal-title":"Appl. Math. Lett."},{"key":"S0218127420502351BIB017","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.atmosenv.2018.08.027","volume":"191","author":"Ma Y.","year":"2018","journal-title":"Atm. Env."},{"key":"S0218127420502351BIB018","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1016\/j.envsoft.2006.06.016","volume":"22","author":"Malve O.","year":"2007","journal-title":"Env. Mod. Soft."},{"key":"S0218127420502351BIB019","first-page":"1","volume":"486","author":"Maria D. V. R.","year":"2020","journal-title":"J. Th. Biol."},{"key":"S0218127420502351BIB020","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/17513750802638712","volume":"3","author":"Martcheva M.","year":"2009","journal-title":"J. Biol. Dyn."},{"key":"S0218127420502351BIB021","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.nonrwa.2008.10.014","volume":"11","author":"Mccluskey C. C.","year":"2010","journal-title":"Nonlin. Anal.: Real World Appl."},{"key":"S0218127420502351BIB022","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-017-17765-5","volume":"8","author":"Mo Z.","year":"2018","journal-title":"Sci. Rep."},{"key":"S0218127420502351BIB023","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.envint.2017.10.024","volume":"110","author":"Nhung N. T. T.","year":"2018","journal-title":"Env. Int."},{"key":"S0218127420502351BIB024","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1016\/j.scitotenv.2018.09.183","volume":"651","author":"Phosri A.","year":"2019","journal-title":"Sci. T. Env."},{"key":"S0218127420502351BIB025","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1016\/j.cam.2011.05.040","volume":"236","author":"Sekiguchi M.","year":"2011","journal-title":"J. Comput. Appl. Math."},{"key":"S0218127420502351BIB026","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1016\/j.jde.2014.05.030","volume":"257","author":"Shan C.","year":"2014","journal-title":"J. Diff. Eqs."},{"key":"S0218127420502351BIB027","first-page":"1","volume":"33","author":"Soetaert K.","year":"2010","journal-title":"J. Stat. Soft."},{"key":"S0218127420502351BIB028","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12890-018-0716-3","volume":"18","author":"Song J.","year":"2018","journal-title":"BMC Pulm. Med."},{"key":"S0218127420502351BIB029","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1016\/S0362-546X(99)00138-8","volume":"42","author":"Takeuchi Y.","year":"2000","journal-title":"Nonlin. Anal.: Th. Meth. Appl."},{"key":"S0218127420502351BIB030","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.envpol.2017.09.071","volume":"232","author":"Tang S.","year":"2018","journal-title":"Env. Poll."},{"key":"S0218127420502351BIB031","doi-asserted-by":"crossref","first-page":"2599","DOI":"10.1016\/j.na.2007.08.036","volume":"69","author":"Teng Z. D.","year":"2008","journal-title":"Nonlin. Anal."},{"key":"S0218127420502351BIB032","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S0025-5564(00)00018-3","volume":"166","author":"Thieme H. R.","year":"2000","journal-title":"Math. Biosci."},{"key":"S0218127420502351BIB033","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.jtbi.2019.05.020","volume":"476","author":"Timothy C. R.","year":"2019","journal-title":"J. Th. Biol."},{"key":"S0218127420502351BIB034","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1007\/s10884-008-9111-8","volume":"20","author":"Wang W.","year":"2008","journal-title":"J. Dyn. Diff. Eqs."},{"key":"S0218127420502351BIB035","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1007\/s00285-018-1245-7","volume":"77","author":"Wang L.","year":"2018","journal-title":"J. Math. Biol."},{"key":"S0218127420502351BIB036","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1016\/j.jmaa.2007.12.058","volume":"342","author":"Wei H. M.","year":"2008","journal-title":"J. Math. Anal. Appl."},{"key":"S0218127420502351BIB037","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1289\/ehp.11257","volume":"116","author":"Wong C. M.","year":"2008","journal-title":"Env. Heal. Persp."},{"key":"S0218127420502351BIB038","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1007\/s11538-007-9279-9","volume":"70","author":"Wu H.","year":"2008","journal-title":"Bull. Math. Biol."},{"key":"S0218127420502351BIB039","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10666-018-9625-3","volume":"24","author":"Xia C.","year":"2019","journal-title":"Env. Mod. Assess."},{"key":"S0218127420502351BIB040","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/s00484-018-01665-y","volume":"63","author":"Xie J.","year":"2019","journal-title":"Int. J. Biom."},{"key":"S0218127420502351BIB041","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.amc.2017.04.007","volume":"309","author":"Xing Y.","year":"2017","journal-title":"Appl. Math. Comp."},{"key":"S0218127420502351BIB042","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.cam.2008.11.009","volume":"230","author":"Xu R.","year":"2009","journal-title":"J. Comput. Appl. Math."},{"key":"S0218127420502351BIB043","first-page":"1","volume":"25","author":"Xue X.","year":"2018","journal-title":"Env. Sci. Poll. Res."},{"key":"S0218127420502351BIB044","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.envint.2018.12.012","volume":"123","author":"Yang B.","year":"2019","journal-title":"Env. Int."},{"key":"S0218127420502351BIB045","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s10255-003-0093-3","volume":"19","author":"Yuan S. L.","year":"2003","journal-title":"Acta. Math. Appl. Sin."},{"key":"S0218127420502351BIB046","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/j.amc.2018.03.050","volume":"332","author":"Zhan X. X.","year":"2018","journal-title":"Appl. Math. Comp."},{"key":"S0218127420502351BIB047","doi-asserted-by":"crossref","first-page":"2537","DOI":"10.1007\/s11538-007-9231-z","volume":"69","author":"Zhang T. L.","year":"2007","journal-title":"Bull. Math. Biol."},{"key":"S0218127420502351BIB048","doi-asserted-by":"crossref","first-page":"4236","DOI":"10.1007\/s11356-013-2374-6","volume":"21","author":"Zhang Z.","year":"2014","journal-title":"Env. Sci. Poll. Res."},{"key":"S0218127420502351BIB049","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.jtbi.2018.09.027","volume":"460","author":"Zhang J.","year":"2019","journal-title":"J. Th. Biol."},{"key":"S0218127420502351BIB050","first-page":"1","volume":"14","author":"Zhao Yu.","year":"2017","journal-title":"Int. J. Environ. Res. Public Health."},{"key":"S0218127420502351BIB051","first-page":"1","volume":"2018","author":"Zhao Y.","year":"2018","journal-title":"Comput. Math. Meth. Med."},{"key":"S0218127420502351BIB052","first-page":"1","volume":"2019","author":"Zhao Y.","year":"2019","journal-title":"Complexity"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127420502351","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T10:48:16Z","timestamp":1607597296000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127420502351"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,9]]},"references-count":52,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2020,12,15]]}},"alternative-id":["10.1142\/S0218127420502351"],"URL":"https:\/\/doi.org\/10.1142\/s0218127420502351","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2020,12,9]]}}}