{"title":"On a Chemotactic Host–Pathogen Model: Boundedness, Aggregation, and Segregation","authors":"Guodong Liu, Hao Wang, Xiaoyan Zhang","doi":"10.1007/s00332-023-10010-6","DOIUrl":null,"url":null,"abstract":"<p>This study formulates a host–pathogen model driven by cross-diffusion to examine the effect of chemotaxis on solution dynamics and spatial structures. The negative binomial incidence mechanism is incorporated to illustrate the transmission process by pathogens. In terms of the magnitude of chemotaxis, the global solvability of the model is extensively studied by employing semigroup methods, loop arguments, and energy estimates. In a limiting case, the necessary conditions for chemotaxis-driven instability are established regarding the degree of chemotactic attraction. Spatial aggregation may occur along strong chemotaxis in a two-dimensional domain due to solution explosion. We further observe that spatial segregation appears for short-lived free pathogens in a one-dimensional domain, whereas strong chemotactic repulsion homogenizes the infected hosts and thus fails to segregate host groups effectively.\n</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"153 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Science","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00332-023-10010-6","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This study formulates a host–pathogen model driven by cross-diffusion to examine the effect of chemotaxis on solution dynamics and spatial structures. The negative binomial incidence mechanism is incorporated to illustrate the transmission process by pathogens. In terms of the magnitude of chemotaxis, the global solvability of the model is extensively studied by employing semigroup methods, loop arguments, and energy estimates. In a limiting case, the necessary conditions for chemotaxis-driven instability are established regarding the degree of chemotactic attraction. Spatial aggregation may occur along strong chemotaxis in a two-dimensional domain due to solution explosion. We further observe that spatial segregation appears for short-lived free pathogens in a one-dimensional domain, whereas strong chemotactic repulsion homogenizes the infected hosts and thus fails to segregate host groups effectively.
期刊介绍：
The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be.
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