Growth bound and threshold dynamic for nonautonomous nondensely defined evolution problems

We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below d v ( t ) d t = A v ( t ) + F ( t ) v ( t ) - V ( t ) v ( t ) , where A : D ( A ) ⊂ X → X is a H...

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Published in	Journal of mathematical biology Vol. 87; no. 2; p. 32
Main Authors	Djidjou-Demasse, Ramsès, Goudiaby, Ibou, Seydi, Ousmane
Format	Journal Article
Language	English
Published	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2023 Springer Nature B.V Springer
Subjects	Analysis of PDEs Applications of Mathematics Banach spaces Dynamical Systems Epidemiology Evolution Linear operators Malaria Mathematical and Computational Biology Mathematics Mathematics and Statistics Operators (mathematics) Pathogens Population genetics Population growth Topology Threshold dynamics Evolutionary systems 47N60 92D25 37B55 47D62 Reproduction number Growth bound 34K20 Reproduction number Growth bound Threshold dynamics evolutionary systems Mathematics Subject Classification 34K20 37B55 47D62 47N60 92D25 evolutionary systems
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ISSN	0303-6812 1432-1416 1432-1416
DOI	10.1007/s00285-023-01966-w

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Abstract	We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below d v ( t ) d t = A v ( t ) + F ( t ) v ( t ) - V ( t ) v ( t ) , where A : D ( A ) ⊂ X → X is a Hille–Yosida linear operator (possibly unbounded, non-densely defined) on a Banach space ( X , ‖ · ‖ ) , and the maps t ∈ R ↦ V ( t ) ∈ L ( X 0 , X ) , t ∈ R ↦ F ( t ) ∈ L ( X 0 , X ) are p -periodic in time and continuous in the operator norm topology. We give applications of our approach for two general examples of an age-structured model, and a delay differential system. Other examples concern the dynamics of a nonlocal problem arising in population genetics and the dynamics of a structured human-vector malaria model.
AbstractList	We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below dv(t)dt=Av(t)+F(t)v(t)-V(t)v(t),where A:D(A)⊂X→X is a Hille–Yosida linear operator (possibly unbounded, non-densely defined) on a Banach space (X,‖·‖), and the maps t∈R↦V(t)∈L(X0,X), t∈R↦F(t)∈L(X0,X) are p-periodic in time and continuous in the operator norm topology. We give applications of our approach for two general examples of an age-structured model, and a delay differential system. Other examples concern the dynamics of a nonlocal problem arising in population genetics and the dynamics of a structured human-vector malaria model. We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below [Formula: see text]where [Formula: see text] is a Hille-Yosida linear operator (possibly unbounded, non-densely defined) on a Banach space [Formula: see text], and the maps [Formula: see text], [Formula: see text] are p-periodic in time and continuous in the operator norm topology. We give applications of our approach for two general examples of an age-structured model, and a delay differential system. Other examples concern the dynamics of a nonlocal problem arising in population genetics and the dynamics of a structured human-vector malaria model. We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below d v ( t ) d t = A v ( t ) + F ( t ) v ( t ) - V ( t ) v ( t ) , where A : D ( A ) ⊂ X → X is a Hille–Yosida linear operator (possibly unbounded, non-densely defined) on a Banach space ( X , ‖ · ‖ ) , and the maps t ∈ R ↦ V ( t ) ∈ L ( X 0 , X ) , t ∈ R ↦ F ( t ) ∈ L ( X 0 , X ) are p -periodic in time and continuous in the operator norm topology. We give applications of our approach for two general examples of an age-structured model, and a delay differential system. Other examples concern the dynamics of a nonlocal problem arising in population genetics and the dynamics of a structured human-vector malaria model. We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below dv(t) dt = Av(t) + F(t)v(t) − V(t)v(t), where A : D(A) ⊂ X → X is a Hille-Yosida linear operator (possibly unbounded, non-densely defined) on a Banach space (X, ∥ • ∥), and the maps t ∈ R → V(t) ∈ L(X 0 , X), t ∈ R → F(t) ∈ L(X 0 , X) are p-periodic in time and continuous in the operator norm topology. We give applications of our approach for two general examples of an age-structured model, and a delay differential system. Other examples concern the dynamics of a nonlocal problem arising in population genetics and the dynamics of a structured human-vector malaria model. We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below [Formula: see text]where [Formula: see text] is a Hille-Yosida linear operator (possibly unbounded, non-densely defined) on a Banach space [Formula: see text], and the maps [Formula: see text], [Formula: see text] are p-periodic in time and continuous in the operator norm topology. We give applications of our approach for two general examples of an age-structured model, and a delay differential system. Other examples concern the dynamics of a nonlocal problem arising in population genetics and the dynamics of a structured human-vector malaria model.We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below [Formula: see text]where [Formula: see text] is a Hille-Yosida linear operator (possibly unbounded, non-densely defined) on a Banach space [Formula: see text], and the maps [Formula: see text], [Formula: see text] are p-periodic in time and continuous in the operator norm topology. We give applications of our approach for two general examples of an age-structured model, and a delay differential system. Other examples concern the dynamics of a nonlocal problem arising in population genetics and the dynamics of a structured human-vector malaria model.
ArticleNumber	32
Author	Seydi, Ousmane Djidjou-Demasse, Ramsès Goudiaby, Ibou
Author_xml	– sequence: 1 givenname: Ramsès surname: Djidjou-Demasse fullname: Djidjou-Demasse, Ramsès organization: MIVEGEC, CNRS, IRD, University of Montpellier, Département Tronc Commun, École Polytechnique de Thiès – sequence: 2 givenname: Ibou surname: Goudiaby fullname: Goudiaby, Ibou organization: LMA, Université Assane Seck de Ziguinchor – sequence: 3 givenname: Ousmane orcidid: 0000-0001-5702-2575 surname: Seydi fullname: Seydi, Ousmane email: oseydi@ept.sn organization: Département Tronc Commun, École Polytechnique de Thiès
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Keywords	Threshold dynamics Evolutionary systems 47N60 92D25 37B55 47D62 Reproduction number Growth bound 34K20 Reproduction number Growth bound Threshold dynamics evolutionary systems Mathematics Subject Classification 34K20 37B55 47D62 47N60 92D25 evolutionary systems
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SubjectTerms	Analysis of PDEs Applications of Mathematics Banach spaces Dynamical Systems Epidemiology Evolution Linear operators Malaria Mathematical and Computational Biology Mathematics Mathematics and Statistics Operators (mathematics) Pathogens Population genetics Population growth Topology
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Title	Growth bound and threshold dynamic for nonautonomous nondensely defined evolution problems
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