{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T06:24:47Z","timestamp":1791440687873,"version":"4.3.3"},"reference-count":23,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2018,4,5]],"date-time":"2018-04-05T00:00:00Z","timestamp":1522886400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"DOI":"10.1371\/journal.pone.0191914","type":"journal-article","created":{"date-parts":[[2018,4,5]],"date-time":"2018-04-05T20:14:56Z","timestamp":1522959296000},"page":"e0191914","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":14,"title":["Spreading dynamic of acute and carrier hepatitis B with nonlinear incidence"],"prefix":"10.1371","volume":"13","author":[{"given":"Tahir","family":"Khan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8281-3432","authenticated-orcid":true,"given":"Gul","family":"Zaman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali","family":"Saleh Alshomrani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2018,4,5]]},"reference":[{"issue":"269","key":"ref1","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.jtbi.2010.10.028","article-title":"Modelling the epidemiology of hepatitis B in New Zealand","volume":"21","author":"J Mann","year":"2011","journal-title":"Journal of Theoretical Biology"},{"key":"ref2","unstructured":"WHO, Hepatitis B. Fact sheet No. 204. Updated June 2014(<ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"http:\/\/www.who.int\/meadiacenter\/factsheet\/fs204\/en\/index.html\" xlink:type=\"simple\">http:\/\/www.who.int\/meadiacenter\/factsheet\/fs204\/en\/index.html<\/ext-link>)(<italic>revised Agust<\/italic> 2014)."},{"issue":"369","key":"ref3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jtbi.2015.01.005","article-title":"On the sexual transmission dynamics of hepatitis B virus in China","volume":"21","author":"L Zou","year":"2015","journal-title":"Journal of Theoretical Biology"},{"issue":"256","key":"ref4","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.amc.2014.12.096","article-title":"Transmission dynamics and optimal control of measles epidemics","volume":"1","author":"L Pang","year":"2015","journal-title":"Applied Mathematics and Computation"},{"issue":"93","key":"ref5","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.biosystems.2008.05.004","article-title":"Stability analysis and optimal vaccination of an SIR epidemic model","volume":"30","author":"G Zaman","year":"2008","journal-title":"BioSystems"},{"issue":"37","key":"ref6","doi-asserted-by":"crossref","first-page":"5326","DOI":"10.1016\/j.apm.2012.10.005","article-title":"Square-root dynamics of a giving up smoking model","volume":"1","author":"A Zeb","year":"2013","journal-title":"Applied Mathematical Modelling"},{"issue":"98","key":"ref7","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.biosystems.2009.05.006","article-title":"Optimal treatment of an SIR epidemic model with time delay","volume":"31","author":"G Zaman","year":"2009","journal-title":"BioSystems"},{"issue":"5","key":"ref8","doi-asserted-by":"crossref","first-page":"1082","DOI":"10.1186\/s40064-016-2706-3","article-title":"Classification of different Hepatitis B infected individuals with saturated incidence rate","volume":"15","author":"T Khan","year":"2016","journal-title":"SpringerPlus"},{"issue":"11","key":"ref9","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1080\/17513758.2016.1256441","article-title":"The transmission dynamic and optimal control of acute and chronic hepatitis B","volume":"1","author":"T Khan","year":"2017","journal-title":"Journal of Biological Dynamics"},{"issue":"78","key":"ref10","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.chaos.2015.06.020","article-title":"Solution of optimal power flow using chaotic krill herd algorithm","volume":"30","author":"A Mukherjee","year":"2015","journal-title":"Chaos, Solitons and Fractals"},{"issue":"246","key":"ref11","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1016\/j.amc.2014.08.028","article-title":"Global stability for a sheep brucellosis model with immigration","volume":"1","author":"GQ Sun","year":"2014","journal-title":"Applied Mathematics and Computation"},{"issue":"252","key":"ref12","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.amc.2014.11.107","article-title":"Bifurcation and chaos in a discrete physiological control system","volume":"1","author":"L Li","year":"2015","journal-title":"Applied Mathematics and Computation"},{"issue":"45","key":"ref13","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.cnsns.2016.10.007","article-title":"Transmission dynamics of cholera: Mathematical modeling and control strategies","volume":"30","author":"GQ Sun","year":"2017","journal-title":"Communications in Nonlinear Science and Numerical Simulation"},{"issue":"446","key":"ref14","first-page":"1292","article-title":"Modeling direct and indirect disease transmission using multi-group model","volume":"15","author":"MT Li","year":"2017","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"04","key":"ref15","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1142\/S0218339016500261","article-title":"Monthly periodic outbreak of Hemorrhagic Fever with renal syndrome in China","volume":"24","author":"L Li","year":"2016","journal-title":"Journal of Biological Systems"},{"issue":"254","key":"ref16","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1016\/j.jtbi.2008.06.022","article-title":"Hepatitis B in a high prevalence New Zealand population: a mathematical model applied to infection control policy","volume":"7","author":"S Thornley","year":"2008","journal-title":"Journal of Theoretical Biology"},{"issue":"262","key":"ref17","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.jtbi.2009.09.035","article-title":"Modeling the transmission dynamics and control of hepatitis B virus in China","volume":"21","author":"L Zou","year":"2010","journal-title":"Journal of Theoretical Biology"},{"issue":"170","key":"ref18","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/S0025-5564(00)00067-5","article-title":"Global stability of an SEIS epidemic model with recruitment and a varying total population size","volume":"30","author":"M Fan","year":"2001","journal-title":"Mathematical Biosciences"},{"issue":"35","key":"ref19","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1016\/S0895-7177(02)00082-1","article-title":"Qualitative analyses of SIS epidemic model with vaccination and varying total population size","volume":"1","author":"J Li","year":"2002","journal-title":"Mathematical and Computer Modelling"},{"issue":"7","key":"ref20","doi-asserted-by":"crossref","first-page":"301","DOI":"10.12785\/amis\/070138","article-title":"Backward bifurcation and optimal control of a vector borne disease","volume":"1","author":"AA Lashari","year":"2013","journal-title":"Applied Mathematics and Information Sciences"},{"issue":"180","key":"ref21","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","article-title":"Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission","volume":"31","author":"P Van den Driessche","year":"2002","journal-title":"Mathematical Biosciences"},{"key":"ref22","article-title":"Mathematical epidemiology","author":"LJ Allen","year":"2008"},{"key":"ref23","article-title":"Dynamic optimization: the calculus of variations and optimal control in economics and management","author":"MI Kamien","year":"2012"}],"container-title":["PLOS ONE"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pone.0191914","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T01:46:04Z","timestamp":1540259164000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0191914"}},"subtitle":[],"editor":[{"given":"Oliver","family":"Schildgen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2018,4,5]]},"references-count":23,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4,5]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0191914","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,5]]}}}