Complete global analysis of a two-scale network SIRS epidemic dynamic model with distributed delay and random perturbations

• The model validation results are established.
• The basic reproduction numbers at three human–vector contact levels are computed.
• The stochastic stability of equilibria is proven.
• Interplay between stability and human mobility are exhibited in real-life scenarios.

A stochastic SIRS epidemic dynamic model with distributed time delay for vector-borne diseases in two-scale network structured populations is presented. The distributed delay accounts for the varying incubation period of the disease. Furthermore, the disease dynamics is influenced by random environmental perturbations in the disease transmission process as well as the two-scale human mobility process. The basic reproduction numbers at three human–vector contact levels in the two-scale population are computed, and the results for the stochastic asymptotic stability of the equilibria are presented. Moreover, the asymptotic stability results are exhibited in several real life scenarios and the significance of the results are presented. Numerical simulation results are presented.