Interaction between prey and predator in the presence of an infectious pathogen is the main focus of this article. A non-local transmission, that encompasses the possibility of acquiring infection from a distanced potential infected individual, is incorporated by utilizing a convolution of a spatial kernel function of compact support with the spatial distribution of the infected population. The spatial kernel function characterizes the likelihood of contracting an infection from an infected individual located within a certain range and its compact support indicates the extent of the non-local disease transmission. The model is governed by a system of semilinear parabolic integro-differential equations whose global-in-time classical solution has been established. The basic reproduction numbers of two distinct disease-free homogeneous steady states are derived for the non-local diffusive eco-epidemiological model. The associated non-spatial model undergoes a supercritical Hopf-bifurcation and possesses a stable limit cycle bifurcated from the stable endemic equilibrium point. The Turing instability conditions of the endemic homogeneous steady state are derived for both the local and non-local systems. A wide variety of spatio-temporal solutions over a one-dimensional spatial domain have been explored for both the local model and the non-local model with parabolic kernel function. It has been observed that an increase in the extent of the non-local disease transmission increases the parametric region of the stable spatially homogeneous solution. On the other hand, the parametric region for the spatially heterogeneous solutions, characterizing the patchy distributions of interacting populations, shrinks with an increase in the extent of the non-local disease transmission.

中文翻译：

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空间异质生态流行模型：非本地疾病传播的稳定作用


在存在传染性病原体的情况下，猎物和捕食者之间的相互作用是本文的主要焦点。非本地传播包括从远处的潜在感染个体获得感染的可能性，通过利用紧凑支持的空间核函数与感染人群的空间分布的卷积来合并。空间核函数表征了一定范围内的感染个体受到感染的可能性，其紧支持度表明了非局部疾病传播的程度。该模型由半线性抛物型积分微分方程组控制，该方程组的全局时间经典解已经建立。针对非局部扩散生态流行病学模型推导了两种不同的无病同质稳态的基本繁殖数。相关的非空间模型经历超临界 Hopf 分岔，并具有从稳定的地方性平衡点分岔的稳定极限环。针对局域和非局域系统导出了地方性同质稳态的图灵不稳定性条件。对于局部模型和具有抛物线核函数的非局部模型，已经探索了一维空间域上的各种时空解。据观察，非局部疾病传播程度的增加增加了稳定空间均匀解的参数区域。另一方面，空间异质解的参数区域，表征相互作用群体的斑块分布，随着非局部疾病传播程度的增加而缩小。