2023/11/15 by Xiumei Deng, Qihua Huang, Zhi‐An Wang +1
Environmental Science · Mathematics · Medicine · #Ecosystem dynamics and resilience #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models
paper · doi:10.1137/22m1510881
crossref issued 2023/11/15 · crossref published 2023/11/15 · crossref published-online 2023/11/15 · openalex publication_date 2023/11/15 · crossref created 2023/11/15 · crossref deposited 2023/12/21 · crossref published-print 2023/12/31 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31
.Because of the significance of remediating contaminated ecosystems, many mathematical models have been developed to describe the interactions between populations and toxicants in polluted aquatic environments. These models typically neglect the consequences of toxicant-induced behavioral changes on population dynamics. Taking into account that individuals may flee from areas with high toxicant concentrations to areas with low toxicant concentrations in order to improve their chances of survival, growth, and reproduction, we develop a diffusive population-toxicant model with toxicant-taxis. We establish the global well-posedness of our model and prove the global stability of spatially homogeneous toxicant-only steady states and population-toxicant coexistence steady states under some conditions. We find conditions under which stable spatially inhomogeneous steady states become unstable to trigger spatial pattern formations as the toxicant-taxis is strong. We also identify a narrow parameter regime in which toxicant-only and population-toxicant coexistence steady states are bistable. Numerical simulations are performed to illustrate that spatial aggregation and segregation patterns between the population and the toxicant will typically emerge. Our study highlights the important effects of toxicant-induced movement responses on the spatial distributions of populations in polluted aquatic environments.Keywordspopulation-toxicant modeltoxicant-taxisglobal dynamicspattern formationspatial segregationMSC codes92D2535K5735K2