Wavefront solutions in diffusive Nicholson’s blowflies equation with nonlocal delay

2010 ◽  
Vol 31 (3) ◽  
pp. 385-392 ◽  
Author(s):  
Cun-hua Zhang ◽  
Xiang-ping Yan
Keyword(s):  
Nonlocal Delay ◽  
Nicholson’S Blowflies Equation

scholarly journals Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Wenzhen Gan ◽  
Canrong Tian ◽  
Qunying Zhang ◽  
Zhigui Lin
Keyword(s):  
Steady State ◽  
Functional Response ◽  
Neumann Boundary Condition ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Food Ingestion ◽  
Nonlocal Delay ◽  
Homogeneous Neumann Boundary Condition

This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results.

Minimal wave speed of a diffusive SIR epidemic model with nonlocal delay

2019 ◽  
Vol 12 (07) ◽  
pp. 1950081
Author(s):  
Fuzhen Wu ◽  
Dongfeng Li
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Nonlocal Delay ◽  
Spatial Nonlocality ◽  
Wave Solutions ◽  
Minimal Wave Speed

This paper is concerned with the minimal wave speed in a diffusive epidemic model with nonlocal delays. We define a threshold. By presenting the existence and the nonexistence of traveling wave solutions for all positive wave speed, we confirm that the threshold is the minimal wave speed of traveling wave solutions, which models that the infective invades the habitat of the susceptible. For some cases, it is proven that spatial nonlocality may increase the propagation threshold while time delay decreases the threshold.

scholarly journals Pattern Dynamics of Nonlocal Delay SI Epidemic Model with the Growth of the Susceptible following Logistic Mode

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zun-Guang Guo ◽  
Jing Li ◽  
Can Li ◽  
Juan Liang ◽  
Yiwei Yan
Keyword(s):  
Time Delay ◽  
Epidemic Model ◽  
Turing Instability ◽  
Average Density ◽  
Linear Stability Theory ◽  
Susceptible Population ◽  
Nonlocal Delay ◽  
Pattern Dynamics ◽  
And Control ◽  
Theoretical Results

In this paper, we investigate pattern dynamics of a nonlocal delay SI epidemic model with the growth of susceptible population following logistic mode. Applying the linear stability theory, the condition that the model generates Turing instability at the endemic steady state is analyzed; then, the exact Turing domain is found in the parameter space. Additionally, numerical results show that the time delay has key effect on the spatial distribution of the infected, that is, time delay induces the system to generate stripe patterns with different spatial structures and affects the average density of the infected. The numerical simulation is consistent with the theoretical results, which provides a reference for disease prevention and control.

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