Open AccessSpreading speeds of epidemic models with nonlocal delays
Author(s) -
Guo Lin,
Shinhwan Pan,
Xiang-Ping Yan
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019380
Subject(s) - monotone polygon , nonlinear system , mathematics , rate of convergence , wave speed , incidence (geometry) , saturation (graph theory) , convergence (economics) , epidemic model , quantum nonlocality , speedup , mathematical analysis , physics , computer science , geometry , combinatorics , quantum mechanics , key (lock) , population , demography , sociology , quantum entanglement , economics , quantum , economic growth , operating system , computer security
We estimate the spreading speeds in diffusive epidemic models with nonlocal delays, nonlinear incidence rate and constant recruitment rate. The purpose is to model the process that the infective invades the habitat of the susceptible, and they coexist eventually. In order to focus on our idea, a system with a nonlinear incidence rate is firstly studied, which implies a saturation level of the infective individuals and monotone incidence rate. When the initial value of the infective has nonempty compact support, we prove the rough spreading speed that equals the minimal wave speed of traveling wave solutions in the known results. Then for a general (nonmonotone) incidence rate, we obtain the spreading speeds by constructing auxiliary systems admitting a monotone incidence rate, and prove the convergence of solutions on any compact spatial interval. Furthermore, some numerical examples are given to estimate the invasion speed and show the nontrivial effect of time delay and spatial nonlocality, which implies that the stronger spatial nonlocality leads to larger spreading speeds.