Brucellosis has been increasingly concerned with the animal health and a huge loss of economics. Multiple transmission routes, seasonal pattern and spatial diffusion have been identified in brucellosis propagations. Meanwhile, infectious ability strongly depends on the distance of each adjacent infectious individual. Such property can be captured by a nonlocal infection with some integrable functions. In this paper, we first propose a seasonal brucellosis epidemic model with nonlocal transmissions and spatial diffusions. We calculate the next generation operator $\mathcal{R}\left(x\right)$ by a renewal process. The basic reproduction number ${\mathcal{R}}_0$ is defined as the spectral radius of $\mathcal{R}\left(x\right),$ which plays an equivalent role in a principal eigenvalue of a linear operator. It is shown that the proposed model exhibits the threshold dynamics in terms of ${\mathcal{R}}_0,$ i.e, if ${\mathcal{R}}_0<1,$ then the brucella-free steady state is globally asymptotically stable; otherwise, the model admits at least one positively periodic steady state. Numerical simulations elucidate that time heterogeneity enhances magnitudes of oscillations of animal population and brucella. Moreover, enlarging effective infection radii increases the risk of brucellosis propagations. As a result, we suggest that herdsmen should improve the sanitation of animals’ environment and isolate infected animals instantly to control brucellosis prevalence.

布鲁氏菌病日益关注动物健康和经济损失。在布鲁氏菌病传播中已经确定了多种传播途径，季节性模式和空间扩散。同时，传染能力在很大程度上取决于每个相邻传染个体的距离。可以通过具有某些可整合功能的非局部感染来捕获此类属性。在本文中，我们首先提出了具有非本地传播和空间扩散的季节性布鲁氏菌病流行模型。我们计算下一代运算符$\mathcal{[R}（X）$通过续订过程。基本复制数${\mathcal{[R}}_0$ 定义为 $\mathcal{[R}（X），$在线性算子的本征值中起等效作用。结果表明，所提出的模型在以下方面表现出阈值动态：${\mathcal{[R}}_0，$ 即，如果 ${\mathcal{[R}}_0<\mathrm{1个}，$则无布鲁氏菌的稳态是全局渐近稳定的；否则，该模型允许至少一个正周期稳态。数值模拟表明时间异质性增加了动物种群和布鲁氏菌振荡的幅度。此外，扩大有效感染半径会增加布鲁氏菌病传播的风险。因此，我们建议牧民应改善动物环境的卫生状况，并立即隔离受感染的动物，以控制布鲁氏菌病的流行。