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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]

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]

This paper is concerned with traveling wave solutions of a nonlocal dispersal Susceptible–Infective–Removal–Healing (for short SIRH ) model with relapse. It is found that the existence and nonexistence of traveling waves of the system are not only determined by the critical wave speed c ∗ , but also by the basic reproduction number R 0 of the corresponding system of ordinary differential equations. More precisely, we use Schauder’s fixed-point theorem to obtain the existence of traveling waves for R 0 > 1 and c > c ∗ , and the nonexistence of traveling waves for R 0 > 1 and 0 < c < c ∗ . Some numerical simulations and discussions are also provided to illustrate our analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the blow-up profiles of the nonlocal dispersal equation. More precisely, we prove that the positive solution of nonlocal dispersal equation has different blow-up profiles, depending on the refuge domain. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence, nonexistence and minimal wave speed of traveling waves of a nonlocal dispersal delayed SIR model with constant external supplies and Holling-II incidence rate. We find that the existence and nonexistence of traveling waves of the system are not only determined by the minimal wave speed c ∗ , but also by the so-called basic reproduction number R 0 of the corresponding reaction system. That is, we establish the existence of traveling waves for R 0 > 1 and each wave speed c ⩾ c ∗ , and the nonexistence for R 0 > 1 and any 0 < c < c ∗ or R 0 < 1 . We also discuss how the latency of infection and the spatial movement of the infective individuals affect the minimal wave speed. Biologically speaking, the longer the latency of infection in a vector is, the slower the disease spreads. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with entire solutions of the Fisher-KPP equation with nonlocal dispersal, i.e., , which is a one-dimensional nonlocal version of the Fisher-KPP equation describing the spatial spread of a mutant in a given population and the dispersion of the genetic characters is assumed to follow a nonlocal diffusion law modeled by a convolution operator. Here the entire solutions are defined in the whole space and for all time . A comparison principle is employed to establish the existence of entire solutions by combining two traveling wave solutions with different speeds and coming from both ends of the real axis and some spatially independent solutions. The main difficulty is that a lack of regularizing effect occurs. This is probably the first time the existence of entire solutions of reaction equations with nonlocal dispersal has been studied. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence and asymptotic behavior of solutions of a nonlocal dispersal equation. By means of super-subsolution method and monotone iteration, we first study the existence and asymptotic behavior of solutions for a general nonlocal dispersal equation. Then, we apply these results to our equation and show that the nonnegative solution is unique, and the behavior of this solution depends on parameter in equation. For , the solution decays to zero as ; while for , the solution converges to the unique positive stationary solution as . In addition, we show that the solution blows up under some conditions. [Copyright &y& Elsevier]

Recently, the spreading speeds and periodic traveling wave solutions for a general class of partially degenerate nonlocal dispersal cooperative systems in time and space periodic habitats have been investigated. In this paper, we continue to study the stability and convergence rate for such time and space periodic traveling waves. We show that if the initial function perturbation is uniformly bounded with respect to a weighted maximum norm, the periodic traveling wave solution is globally exponentially stable when the wave speed is greater than the spreading speed. [ABSTRACT FROM AUTHOR]

This paper is concerned with propagation phenomena of a general class of partially degenerate nonlocal dispersal cooperative systems in time and space periodic habitats. We first show that such system has a finite spreading speed interval in any direction and there is a spreading speed for the partially degenerate system under certain conditions. Next, we prove that if the wave speed is greater than the spreading speed, there exists a time and space periodic traveling wave solution connecting the stable positive time and space periodic steady state and 0. Finally, we apply these results to two species partially degenerate competition systems and a partially degenerate epidemic model with nonlocal dispersal in time and space periodic habitats. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating the traveling wave solutions of a nonlocal dispersal SEIR epidemic model with standard incidence. We find that the existence and nonexistence of traveling wave solutions are determined by the basic reproduction number and the critical wave speed. Through considering a truncate problem, combining with Schauder's fixed-point theorem and applying a limiting argument, we prove the existence of traveling wave solutions. Meanwhile, the nonexistence of traveling wave solutions is showed by the Laplace transform method. Furthermore, the existence of traveling wave solutions with critical wave speed is also established by a delicate analysis. We also point out that both the nonlocal dispersal and coupling of system in the model bring some difficulties in the study of traveling wave solutions. [ABSTRACT FROM AUTHOR]