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This paper is concerned with the propagation phenomenon of a three species predation-competition system with nonlocal dispersal and climate change effects. That is to say, there is not only competition for food, but also competitive interaction between two preys. The growth rate of each prey is nondecreasing along the $ x $-axis and shifts rightward at a speed $ s $. We mainly consider the population dynamics for three cases: (ⅰ) the predator spreads faster than the two preys, (ⅱ) the predator spreads between two preys and (ⅲ) the predator with slower speed spreads behind the two preys, including multiple layers with different speeds to achieve a complete picture. Due to lack of comparison principle in the prey-predator system and compactness of the nonlocal operator, we give some priori estimates of the solutions to obtain the persistence for three species, which depends on improving the regularity of the dispersal kernels and proposing some parameter conditions of the considered system. [ABSTRACT FROM AUTHOR]

This paper is concerned with the propagation dynamics of nonlocal dispersal monostable equations in time-space periodic habitats. We first show that such an equation admits a single spreading speed in every direction under certain conditions and then give several spreading properties in terms of spreading speeds such as asymptotic spreading ray speeds and asymptotic spreading sets. Furthermore, we consider the dependence of the spreading speed on the dispersal rate and reaction term and prove that taking the temporal average or spatial average can decrease the spreading speed. Finally, we employ the viscosity vanishing method to establish the existence of time-space periodic traveling fronts with the critical speed in every direction under the partially temporally homogeneous case and partially nearly flat case, which solves partially the open problem raised by Rawal, Shen, and Zhang (Discrete Contin. Dyn. Syst. 35 (2015) 1609–1640). [ABSTRACT FROM AUTHOR]

This paper is concerned with a nonlocal (convolution) dispersal susceptible-infected-susceptible (SIS) epidemic model with bilinear incidence and Neumann boundary conditions. First we establish the existence and uniqueness of stationary solutions by reducing the system to a single equation. Then we study the asymptotic profiles of the endemic steady states for large and small diffusion rates to illustrate the persistence or extinction of the infectious disease. The lack of regularity of the endemic steady state makes it more difficult to obtain the limit function of the sequence of endemic steady states. We also observe the concentration phenomenon which occurs when the diffusion rate of the infected individuals tends to zero. Our analytical results demonstrate that limiting the movement of susceptible individuals is not effective in eliminating the infectious disease unless the total population size is relatively small. [ABSTRACT FROM AUTHOR]

In this paper, we study the spreading properties of a nonlocal dispersal reducible cooperation model under a shifting habitat. By considering the corresponding upper and lower control systems, we find that the left and right expansion fronts of the solutions with exponentially unbounded kernels propagate with finite speed and infinite speed, respectively. This is quite different from the case of exponentially bounded kernels (Wang and Li, 2020), in which the expansion fronts of the solutions always spread to the left and right with finite speeds. That is to say, we have found a new phenomenon that linear extension and accelerating propagation appear at the same time for such a system. [ABSTRACT FROM AUTHOR]

This paper is concerned with the traveling wave solutions for a class of predator-prey model with nonlocal dispersal. By adopting the truncation method, we use Schauder's fixed-point theorem to obtain the existence of traveling waves connecting the semi-trivial equilibrium to non-trivial leftover concentrations for c > c*, in which c* is the minimal wave speed. Meanwhile, through the limiting approach and the delicate analysis, we establish the existence of traveling wave solutions with the critical speed. Finally, we show the nonexistence of traveling waves for 0 < c < c* by the characteristic equation corresponding to the linearization of original system at the semi-trivial equilibrium. Throughout the whole paper, we need to overcome the difficulties brought by the nonlocal dispersal and the non-preserving of system itself. [ABSTRACT FROM AUTHOR]

We investigate the existence and qualitative properties of conical traveling fronts for the bistable nonlocal equations. Based on the existence result of pyramidal traveling fronts (Li et al., 2021), we construct a sequence of pyramidal traveling fronts and take its limit. However, it is not easy to show that the limit function is a real conical traveling front, and the proofs of its qualitative properties are quite different from those of classical equations, although some of the ideas used are similar. [ABSTRACT FROM AUTHOR]