A diffusive logistic equation with concentrated and nonlocal sources

2017 ◽  
Vol 40 (16) ◽  
pp. 5975-5985 ◽  
Author(s):  
A. Caicedo ◽  
F. W. Cruz ◽  
R. Limeira ◽  
A. Viana
Keyword(s):  
Logistic Equation ◽  
Nonlocal Sources ◽  
Diffusive Logistic Equation

scholarly journals Impact of Regional Difference in Recovery Rate on the Total Population of Infected for a Diffusive SIS Model

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 888
Author(s):  
Jumpei Inoue ◽  
Kousuke Kuto
Keyword(s):  
Recovery Rate ◽  
Regional Difference ◽  
Total Population ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Logistic Equation ◽  
Sis Model ◽  
Reaction Diffusion Model ◽  
Diffusive Logistic Equation ◽  
Sis Epidemic

This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on an application of our previous result on the unboundedness of the ratio of the species to the resource for a diffusive logistic equation. Our pure mathematical result can be epidemically interpreted as that a regional difference in the recovery rate can make the infected population grow in the case when the reproduction number is slightly larger than one.

scholarly journals On a Diffusive Logistic Equation

1998 ◽  
Vol 225 (1) ◽  
pp. 326-339 ◽  
Author(s):  
G.A Afrouzi ◽  
K.J Brown
Keyword(s):  
Logistic Equation ◽  
Diffusive Logistic Equation

Positive solutions for diffusive Logistic equation with refuge

2019 ◽  
Vol 9 (1) ◽  
pp. 1092-1101 ◽  
Author(s):  
Jian-Wen Sun
Keyword(s):  
Boundary Condition ◽  
Weight Function ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Critical Value ◽  
Stationary Solutions ◽  
Logistic Equation ◽  
Diffusion Equations ◽  
Diffusion Operator ◽  
Diffusive Logistic Equation

Abstract In this paper, we study the stationary solutions of the Logistic equation $$\begin{array}{} \displaystyle u_t=\mathcal {D}[u]+\lambda u-[b(x)+\varepsilon]u^p \text{ in }{\it\Omega} \end{array}$$ with Dirichlet boundary condition, here 𝓓 is a diffusion operator and ε > 0, p > 1. The weight function b(x) is nonnegative and vanishes in a smooth subdomain Ω0 of Ω. We investigate the asymptotic profiles of positive stationary solutions with the critical value λ when ε is sufficiently small. We find that the profiles are different between nonlocal and classical diffusion equations.

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