TY - JOUR
T1 - A Reaction-Diffusion Model with Spatially Inhomogeneous Delays
AU - Lou, Yijun
AU - Wang, Feng Bin
N1 - Funding Information:
Research of Y. Lou was supported in part by the NSF of China [12071393] and the General Research Fund from The Hong Kong Research Grants Council [15304821]. Research of F.-B. Wang was supported in part by National Science and Technology Council (NSTC), Taiwan.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/3/28
Y1 - 2023/3/28
N2 - Motivated by population growth in a heterogeneous environment, this manuscript builds a reaction-diffusion model with spatially dependent parameters. In particular, a term for spatially uneven maturation durations is included in the model, which puts the current investigation among the very few studies on reaction-diffusion systems with spatially dependent delays. Rigorous analysis is performed, including the well-posedness of the model, the basic reproduction ratio formulation and long-term behavior of solutions. Under mild assumptions on model parameters, extinction of the species is predicted when the basic reproduction ratio is less than one. When the birth rate is an increasing function and the basic reproduction ratio is greater than one, uniqueness and global attractivity of a positive equilibrium can be established with the help of a novel functional phase space. Permanence of the species is shown when the birth function is in a unimodal form and the basic reproduction ratio is greater than one. The synthesized approach proposed here is applicable to broader contexts of studies on the impact of spatial heterogeneity on population dynamics, in particular, when the delayed feedbacks are involved and the response time is spatially varying.
AB - Motivated by population growth in a heterogeneous environment, this manuscript builds a reaction-diffusion model with spatially dependent parameters. In particular, a term for spatially uneven maturation durations is included in the model, which puts the current investigation among the very few studies on reaction-diffusion systems with spatially dependent delays. Rigorous analysis is performed, including the well-posedness of the model, the basic reproduction ratio formulation and long-term behavior of solutions. Under mild assumptions on model parameters, extinction of the species is predicted when the basic reproduction ratio is less than one. When the birth rate is an increasing function and the basic reproduction ratio is greater than one, uniqueness and global attractivity of a positive equilibrium can be established with the help of a novel functional phase space. Permanence of the species is shown when the birth function is in a unimodal form and the basic reproduction ratio is greater than one. The synthesized approach proposed here is applicable to broader contexts of studies on the impact of spatial heterogeneity on population dynamics, in particular, when the delayed feedbacks are involved and the response time is spatially varying.
KW - Population dynamics
KW - Reaction-diffusion model
KW - Spatially inhomogeneous delay
KW - Stage-structured model
UR - http://www.scopus.com/inward/record.url?scp=85151081101&partnerID=8YFLogxK
U2 - 10.1007/s10884-023-10254-6
DO - 10.1007/s10884-023-10254-6
M3 - Journal article
AN - SCOPUS:85151081101
SN - 1040-7294
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
ER -