%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Djidjou-Demasse, Ramsès
%A Goudiaby, I.
%A Seydi, O.
%T Growth bound and threshold dynamic for nonautonomous nondensely defined evolution problems
%D 2023
%L fdi:010090044
%G ENG
%J Journal of Mathematical Biology
%@ 0303-6812
%K Reproduction number ; Growth bound ; Threshold dynamics ; Evolutionary systems
%M ISI:001035577000001
%N 2
%P 32 [31 ]
%R 10.1007/s00285-023-01966-w
%U https://www.documentation.ird.fr/hor/fdi:010090044
%> https://www.documentation.ird.fr/intranet/publi/2023-09/010090044.pdf
%V 87
%W Horizon (IRD)
%X 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) subset of X -> X is a Hille-Yosida linear operator (possibly unbounded, non-densely defined) on a Banach space (X, vertical bar vertical bar center dot vertical bar vertical bar), and the maps t is an element of R bar right arrow V(t) is an element of L(X-0, X), t is an element of R bar right arrow F(t) is an element of 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.
%$ 020