Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems (2009.05544v1)

Published 11 Sep 2020 in math.AP and math.DS

Abstract: This paper is devoted to the study of asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems in the case of small and large diffusion coefficients. We first establish the continuity of the basic reproduction ratio with respect to parameters by developing the theory of resolvent positive operators. Then we investigate the limiting profile of the principal eigenvalue of an associated periodic eigenvalue problem for large diffusion coefficients. We then obtain the asymptotic behavior of the basic reproduction ratio as the diffusion coefficients go to zero and infinity, respectively. We also investigate the limiting behavior of positive periodic solution for periodic and cooperative reaction-diffusion systems with the Neumann boundary condition when the diffusion coefficients are large enough. Finally, we apply these results to a reaction-diffusion model of Zika virus transmission.

Summary

We haven't generated a summary for this paper yet.