Real epidemic spreading networks are often composed of several kinds of complex networks interconnected with each other, such as Lyme disease, and the interrelated networks may have different topologies and epidemic dynamics. Moreover, most human infectious diseases are derived from animals, and zoonotic infections always spread on directed interconnected networks. So, in this article, we consider the epidemic dynamics of zoonotic infections on a unidirectional circular-coupled network. Here, we construct two unidirectional three-layer circular interactive networks, one model has direct contact between interactive networks, the other model describes diseases transmitted through vectors between interactive networks, which are established by introducing the heterogeneous mean-field approach method. Then we obtain the basic reproduction numbers and stability of equilibria of the two models. Through mathematical analysis and numerical simulations, it is found that basic reproduction numbers of the models depend on the infection rates, infection periods, average degrees, and degree ratios. Numerical simulations illustrate and expand these theoretical results very well. theory [5,6], complex networks have become a powerful tool in studying epidemiology models [7][8][9][10][11]. Especially, a population can be viewed as a complex network, in the sense that a node denotes an individual and a link (edge) denotes the correlation between two individuals, then the disease can spread along edges of the network. In an epidemiology model, because the complexity of different contact types between individuals, it is unreasonable to simplify the complex network to a homogeneous network [12]. And, in order to study the effect of network structures on epidemic spread, many heterogeneous epidemic models have been established [13][14][15].Many previous studies focus on a single network, however, real networks are usually large and complex, such as social networks, neural networks, information networks and transportation networks [16][17][18][19][20][21][22][23], and many diseases spread among different populations with various contact patterns. Therefore, it is essential to study epidemic transmission on multiplex networks and coupled networks. Recently, some researchers have achieved important results, which lead to a deeper study on epidemiology [24][25][26][27][28][29][30]. For instance, Granell [24] studied a coupled multiplex network embed individual awareness and infection. In [25], the authors discussed the epidemic dynamics of infectious diseases on two interconnected complex networks. In [29], Wang compared network-based approach with homogeneous-mixing approach, then they showed the differences between two methods, and described individual behaviors of epidemic dynamics on complex networks.In multiplex networks, many studies are based on two-layer interdependent networks, which just contain two populations. In [31], the authors established a mathematical model in a one-way-coupled network with two subnetworks by mean-field a...
