A West Nile virus nonlocal model with free boundaries and seasonal succession

On a partially degenerate West Nile virus model in closed advective environments

“…In recent years, many mathematical models have been used to study the transmission mechanism of WNv, leading to the development of effective measures for prevention and control (see e.g., [1,5,6,22,24,26,27,30,37,45,46,49,51]). This paper aims to study the effects of bird movements, including diffusion and advection, on virus transmission.…”

“…They demonstrated the existence of traveling wave solutions and calculated the rate of spatial spread of infection. For further related results on WNv epidemic models, see [1,[3][4][5]13,16,22,25,26,30,37,38,41,42,[47][48][49] and the references therein. It is worth noting that the virus primarily transmits between birds and mosquitoes, where birds act as primary reservoir hosts and mosquitoes as vectors.…”

The monostable cooperative system with nonlocal diffusion and free boundaries

“…Since these two works [4] and [7] appeared, some related research has emerged. For example, one can refer to [8] for the first attempt to the spreading speed of the model in [4], [5,15,22] for the Lotka-Volterra competition and prey-predator models, [21,28,29] for the systems where one species adopts the nonlocal diffusion strategy while the other takes the local diffusion, [13,14] for high dimensional and radial symmetric version of the model in [4], [20] for the model with a fixed boundary and a moving boundary, [19] for unbounded initial range, [23] for the mutualist model, [34,35] for SIR epidemic model, and [27] for the model with seasonal succession. Before introducing our results for (1.1), let us briefly review some conclusions obtained by Du and Ni [10,11].…”

Dynamics for a diffusive prey–predator model with advection and free boundaries

“…We end this introductory section by mentioning some related researches. In the absence of $$$ v $$$, the problem () with $$$ \alpha =0 $$$ is reduced to the one‐species free boundary problem, which has been systematically investigated by many authors (see, for instance, previous works [16–20]). When the species is affected by the advective environment, that is, when $$$ \alpha \ne 0 $$$, Gu et al [21, 22] first studied the asymptotic behavior of the solutions to the corresponding free boundary problem with the advection coefficient $$$ \alpha \in \left(0,2\right) $$$ and the nonlinearity term $$$ f(u)=u\left(1-u\right) $$$.…”