Propagation dynamics of an epidemic model with infective media connecting two separated networks of populations

• An epidemic model based on two contact-networks is proposed, where cross network infection occurs via vectors.
• The basic reproduction number for this system is calculated and global stability is proven.
• The effect of animal–animal interactions and contact with vectors can induce endemic states for even low infection rates.
• Increased heterogeneity in either of the networks can exacerbate epidemic spreading.

Based on the fact that most human pathogens originate from animals, this paper attempts to illustrate the propagation dynamics of some zoonotic infections, which spread in two separated networks of populations (human network I and animal network II) and cross-species (vectors, or infective media). An epidemic time-evolution model is proposed via mean-field approximation and its global dynamics are investigated. It is found that the basic reproduction number in terms of epidemiological parameters and the network structure is the threshold condition determining the propagation dynamics. Further, the influences of various infection rates and contact patterns are verified. Numerical results show that the heterogeneity in connection patterns and inner infection in network I can easily trigger endemic dynamics, but when a pathogen, such as H7N9, has weak infectivity in humans, the effects of animal–animal interactions and the contacts with vectors tend to induce endemic states and enhance the prevalence in all the populations.