Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
8 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

Fast Diffusion Inhibits Disease Outbreaks (1907.12229v1)

Published 29 Jul 2019 in q-bio.PE and math.DS

Abstract: We show that the basic reproduction number of an SIS patch model with standard incidence is either strictly decreasing and strictly convex with respect to the diffusion coefficient of infected subpopulation if the patch reproduction numbers of at least two patches in isolation are distinct or constant otherwise. Biologically, it means that fast diffusion of the infected people reduces the risk of infection. This completely solves and generalizes a conjecture by Allen et al. ({\it SIAM J Appl Math}, 67: 1283-1309, 2007). Furthermore, a substantially improved lower bound on the multipatch reproduction number, a generalized monotone result on the spectral bound the Jacobian matrix of the model system at the disease-free equilibrium, and the limiting endemic equilibrium are obtained. The approach and results can be applied to a class of epidemic patch models where only one class of infected compartments migrate between patches and one transmission route is involved.

Summary

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