SPREADING SPEED IN THE FISHER-KPP EQUATION WITH NONLOCAL DELAY

This paper is concerned with the Fisher-KPP equation with diffusion and nonlocal delay.Firstly,we establish the global existence and uniform boundedness of solutions to the Cauchy problem.Then,we establish the spreading speed for the solutions with compactly supported initial data.Finally,we investigate the long time behavior of solutions by numerical simulations.

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

This paper is concerned with the diffusive Nicholson＇s blowflies equation with nonlocal delay incorporated as an integral convolution over the entire past time up to now and the whole one-dimensional spatial domain R. Assume that the delay kernel is a strong generic kernel. By the linear chain techniques and the geometric singular perturbation theory, the existence of travelling front solutions is shown for small delay.

EXTINCTION IN AUTONOMOUS REACTION-DIFFUSION LOTKA-VOLTERRA SYSTEMS WITH NONLOCAL DELAYS

In this paper,we consider an autonomous reaction-diffusion Lotka-Volterra systems with nonlocal delays.Using an iterative technique,we prove that n- 1 species are driven to extinction while the remaining species are globally stable.Finally,we present an example to verify our main result.

TRAVELLING FRONT SOLUTIONS IN A DIFFUSIVE VECTOR DISEASE MODEL WITH SPATIO-TEMPORAL DELAY

This paper is concerned with travelling front solutions to a vector disease model with a spatio-temporal delay incorporated as an integral convolution over all the past time up to now and the whole one-dimensional spatial domain R.When the delay kernel is assumed to be the strong generic kernel,using the linear chain techniques and the geometric singular perturbation theory,the existence of travelling front solutions is shown for small delay.

Traveling wave solutions in a nonlocal dispersal SIR epidemic model with nonlocal time-delay and general nonlinear incidences

This paper investigates a nonlocal dispersal epidemic model under the multiple nonlocal distributed delays and nonlinear incidence effects.First,the minimal wave speed c*and the basic reproduction number Ro are defined,which determine the existence of traveling wave solutions.Second,with the help of the upper and lower solutions,Schauder's fixed point theorem,and limiting techniques,the traveling waves satisfying some asymptotic boundary conditions are discussed.Specifically,when Ro>1,for every speed c>c^(*) there exists a traveling wave solution satisfying the boundary conditions,and there is no such traveling wave solution for any 0<c<c^(*) when R_(0)>1 or c>0 when R_(0)<1.Finally,we analyze the effects of nonlocal time delay on the minimum wave speed.

Dynamical analysis of a diffusive malaria model with fixed latent period in the human and vector populations

To investigate the impact of the fixed latent periods in the human and vector populations on the disease transmission in heterogenous environment,we formulate a nonlocal and time-delayed reaction-diffusion(NLTD-RD)system.By appealing to the next generation operator(NGO),we define the basic reproduction number(BRN)Ro,and prove it as a threshold parameter for indicating whether disease persists or not.Specifically,if o<1,the disease-free equilibrium is globally asymptotically stable,while if Ro>1,the disease is shown to be uniformly persistent.In the homogeneous case that all parameters are assumed to be constants,the explicit expression of o is obtained.We further achieved the global attractivity of the constant equilibria by utilizing Lyapunov functionals.Numerical simulations are performed to verify the theoretical results and the effects of the diffusion rate on disease transmission.