{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:24:14Z","timestamp":1776831854658,"version":"3.51.2"},"reference-count":34,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2023,10]]},"DOI":"10.1016\/j.cnsns.2023.107318","type":"journal-article","created":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T21:08:43Z","timestamp":1685135323000},"page":"107318","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":7,"special_numbering":"C","title":["Dynamics and profiles of a degenerated reaction\u2013diffusion host-pathogen model with apparent and inapparent infection period"],"prefix":"10.1016","volume":"125","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9646-2765","authenticated-orcid":false,"given":"Jinliang","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Han","family":"Lu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.cnsns.2023.107318_b1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3934\/dcds.2008.21.1","article-title":"Asymptotic profiles of the steady states for an SIS epidemic reaction\u2013diffusion model","volume":"21","author":"Allen","year":"2008","journal-title":"Discrete Contin Dyn Syst"},{"key":"10.1016\/j.cnsns.2023.107318_b2","doi-asserted-by":"crossref","first-page":"3305","DOI":"10.1016\/j.jde.2016.05.025","article-title":"A spatial SIS model in advective heterogeneous environments","volume":"261","author":"Cui","year":"2016","journal-title":"J Differential Equations"},{"key":"10.1016\/j.cnsns.2023.107318_b3","doi-asserted-by":"crossref","first-page":"2343","DOI":"10.1016\/j.jde.2017.03.045","article-title":"Dynamics and asymptotic profiles of steady states of an epidemic model in advective environments","volume":"263","author":"Cui","year":"2017","journal-title":"J Differential Equations"},{"key":"10.1016\/j.cnsns.2023.107318_b4","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1017\/S0308210515000864","article-title":"Dynamics of a susceptible-infected-susceptible epidemic reaction diffusion model","volume":"146","author":"Deng","year":"2016","journal-title":"Proc Roy Soc Edinburgh Sect A"},{"key":"10.1016\/j.cnsns.2023.107318_b5","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1016\/j.jde.2009.05.002","article-title":"Asymptotic profiles of the positive steady state for an SIS epidemic reaction\u2013diffusion model. Part I","volume":"247","author":"Peng","year":"2009","journal-title":"J Differential Equations"},{"key":"10.1016\/j.cnsns.2023.107318_b6","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1016\/j.jde.2016.09.044","article-title":"Varying total population enhances disease persistence: Qualitative analysis on a diffusive SIS epidemic model","volume":"262","author":"Li","year":"2017","journal-title":"J Differential Equations"},{"issue":"4","key":"10.1016\/j.cnsns.2023.107318_b7","doi-asserted-by":"crossref","first-page":"2129","DOI":"10.1137\/18M1167863","article-title":"On a diffusive susceptible-infected-susceptible epidemic model with mass action mechanism and birth\u2013death effect: Analysis, simulations, and comparison with other mechanisms","volume":"78","author":"Li","year":"2018","journal-title":"SIAM J Appl Math"},{"key":"10.1016\/j.cnsns.2023.107318_b8","doi-asserted-by":"crossref","first-page":"1451","DOI":"10.1088\/0951-7715\/25\/5\/1451","article-title":"A reaction\u2013diffusion SIS epidemic model in a time-periodic environment","volume":"25","author":"Peng","year":"2012","journal-title":"Nonlinearity"},{"key":"10.1016\/j.cnsns.2023.107318_b9","doi-asserted-by":"crossref","first-page":"4424","DOI":"10.1016\/j.jde.2016.06.028","article-title":"Asymptotic profiles of steady states for a diffusive SIS epidemic model with mass action infection mechanism","volume":"261","author":"Wu","year":"2016","journal-title":"J Differential Equations"},{"key":"10.1016\/j.cnsns.2023.107318_b10","doi-asserted-by":"crossref","unstructured":"Wang J, Wu X. Dynamics and profiles of a diffusive cholera model with bacterial hyperinfectivity and distinct dispersal rates. J Dyn Differ Equ. http:\/\/dx.doi.org\/10.1007\/s10884-021-09975-3.","DOI":"10.1007\/s10884-021-09975-3"},{"key":"10.1016\/j.cnsns.2023.107318_b11","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1098\/rstb.1981.0005","article-title":"The population dynamics of microparasites and their invertebrate hosts","volume":"291","author":"Anderson","year":"1981","journal-title":"Philos Trans R Soc Lond Ser B"},{"key":"10.1016\/j.cnsns.2023.107318_b12","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1086\/285619","article-title":"Density tependence and spatial structure in the dynamics of insect pathogens","volume":"143","author":"Dwyer","year":"1994","journal-title":"Am Nat"},{"key":"10.1016\/j.cnsns.2023.107318_b13","doi-asserted-by":"crossref","first-page":"2535","DOI":"10.3934\/cpaa.2015.14.2535","article-title":"Dynamics of a host-pathogen system on a bounded spatial domain","volume":"14","author":"Wang","year":"2015","journal-title":"Commun Pure Appl Anal"},{"key":"10.1016\/j.cnsns.2023.107318_b14","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.physd.2013.05.006","article-title":"Asymptotic profile of the positive steady state for an SIS epidemic reaction\u2013diffusion model: Effects of epidemic risk and population movement","volume":"259","author":"Peng","year":"2013","journal-title":"Physica D"},{"key":"10.1016\/j.cnsns.2023.107318_b15","doi-asserted-by":"crossref","first-page":"4989","DOI":"10.1016\/j.jde.2017.12.027","article-title":"Dynamics and profiles of a diffusive host-pathogen system with distinct dispersal rates","volume":"264","author":"Wu","year":"2018","journal-title":"J Differential Equations"},{"key":"10.1016\/j.cnsns.2023.107318_b16","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1007\/s10884-019-09820-8","article-title":"Analysis of a reaction\u2013diffusion cholera model with distinct dispersal rates in the human population","volume":"33","author":"Wang","year":"2021","journal-title":"J Dyn Differ Equ"},{"issue":"3","key":"10.1016\/j.cnsns.2023.107318_b17","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1137\/110850761","article-title":"A multipatch malariamodel with logistic growth population","volume":"72","author":"Gao","year":"2012","journal-title":"SIAM J Appl Math"},{"key":"10.1016\/j.cnsns.2023.107318_b18","doi-asserted-by":"crossref","first-page":"383","DOI":"10.15835\/nsb11310436","article-title":"Generic salmonella in asymptomatic adult volunteers: occurrence, antibiogram, extended-spectrum \u03b2-lactamase production and carbapenem resistance","volume":"11","author":"Okpalanwa","year":"2019","journal-title":"Notulae Sci Biol"},{"key":"10.1016\/j.cnsns.2023.107318_b19","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1093\/oxfordjournals.aje.a113019","article-title":"Wateborne giardiasis: a communitywide outbreak of disease and a high rate of asymptomatic infection","volume":"112","author":"Lopez","year":"1980","journal-title":"Am J Epidemiol"},{"key":"10.1016\/j.cnsns.2023.107318_b20","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1038\/nrmicro2204","article-title":"Cholera transmission: the host, pathogen and bacteriophage dynamic","volume":"7","author":"Nelson","year":"2009","journal-title":"Nat Rev Microbiol"},{"key":"10.1016\/j.cnsns.2023.107318_b21","series-title":"Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, Vol. 41","author":"Smith","year":"1995"},{"key":"10.1016\/j.cnsns.2023.107318_b22","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1007\/s00285-010-0346-8","article-title":"A reaction\u2013diffusion malaria model with incubation period in the vector population","volume":"62","author":"Lou","year":"2011","journal-title":"J Math Biol"},{"key":"10.1016\/j.cnsns.2023.107318_b23","series-title":"Asymptotic behavior of dissipative systems","author":"Hale","year":"1989"},{"key":"10.1016\/j.cnsns.2023.107318_b24","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1137\/080732870","article-title":"Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity","volume":"70","author":"Thieme","year":"2009","journal-title":"SIAM J Appl Math"},{"key":"10.1016\/j.cnsns.2023.107318_b25","doi-asserted-by":"crossref","first-page":"1652","DOI":"10.1137\/120872942","article-title":"Basic reproduction numbers for reaction\u2013diffusion epidemic models","volume":"11","author":"Wang","year":"2012","journal-title":"SIAM J Appl Dyn Syst"},{"key":"10.1016\/j.cnsns.2023.107318_b26","series-title":"Partial differential equations","author":"Evans","year":"1998"},{"key":"10.1016\/j.cnsns.2023.107318_b27","series-title":"Fixed point theory","first-page":"309","article-title":"Eigenvectors of nonlinear positive operator and the linear Krein\u2013Rutman theorem","author":"Nussbaum","year":"1981"},{"key":"10.1016\/j.cnsns.2023.107318_b28","first-page":"1","article-title":"Abstract functional differential equtions and reaction\u2013diffusion systems","volume":"321","author":"Martin","year":"1990","journal-title":"Trans Amer Math Soc"},{"issue":"9","key":"10.1016\/j.cnsns.2023.107318_b29","doi-asserted-by":"crossref","first-page":"6169","DOI":"10.1016\/S0362-546X(01)00678-2","article-title":"Robust persistence for semidynamical systems","volume":"47","author":"Smith","year":"2001","journal-title":"Nonlinear Anal TMA"},{"key":"10.1016\/j.cnsns.2023.107318_b30","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1137\/S0036141003439173","article-title":"Global attractors and steady states for uniformly persistent dynamical systems","volume":"37","author":"Magal","year":"2005","journal-title":"SIAM J Math Anal"},{"key":"10.1016\/j.cnsns.2023.107318_b31","series-title":"Dynamical systems and population persistence","volume":"vol. 118","author":"Smith","year":"2011"},{"key":"10.1016\/j.cnsns.2023.107318_b32","series-title":"Maximum principles in differential equations","author":"Protter M.H.\u00a0Weinberger","year":"1984"},{"key":"10.1016\/j.cnsns.2023.107318_b33","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1007\/s11538-008-9299-0","article-title":"Determining inportant parameters in the spread of malaria through the sensistivity analysis of a mathematical model","volume":"70","author":"Chitnis","year":"2008","journal-title":"Bull Math Biol"},{"key":"10.1016\/j.cnsns.2023.107318_b34","doi-asserted-by":"crossref","first-page":"229","DOI":"10.2307\/1403510","article-title":"Sensitivity and uncertainty analysis of complex-models of disease transmission: an HIV model, as an example","volume":"62","author":"Blower","year":"1994","journal-title":"Int Stat Rev"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570423002368?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570423002368?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T14:08:22Z","timestamp":1760882902000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570423002368"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10]]},"references-count":34,"alternative-id":["S1007570423002368"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2023.107318","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2023,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Dynamics and profiles of a degenerated reaction\u2013diffusion host-pathogen model with apparent and inapparent infection period","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2023.107318","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2023 Elsevier B.V. All rights reserved.","name":"copyright","label":"Copyright"}],"article-number":"107318"}}