Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior of the principal eigenvalue and basic reproduction
  ratio for periodic patch models   This paper is devoted to the study of the asymptotic behavior of the
principal eigenvalue and basic reproduction ratio associated with periodic
population models in a patchy environment for small and large dispersal rates.
We first deal with the eigenspace corresponding to the zero eigenvalue of the
connectivity matrix. Then we investigate the limiting profile of the principal
eigenvalue of an associated periodic eigenvalue problem as the dispersal rate
goes to zero and infinity, respectively. We further establish the asymptotic
behavior of the basic reproduction ratio in the case of small and large
dispersal rates. Finally, we apply these results to a periodic Ross-Macdonald
patch model.

9
The categories of this paper are: nlin
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat