Dynamic analysis of a delayed model for vector-borne diseases on bipartite networks

In this paper, to study the spread of vector-borne diseases in human population, we build two coupled models for human population and vector population respectively on bipartite networks. By taking approximate expression for the density of infective vectors, we reduce the coupled models to a delayed SIS model describing the spread of diseases in human population. For the delayed dynamic model, we analyze its dynamic behavior. The basic reproduction number R0 is given. And based on the Lyapunov–LaSalle invariance principle, we prove the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium. Finally we carry out simulations to verify the conclusions and reveal the effect of the topology structure of networks and the time delay on the transmission process. Our results show that the basic reproduction number depends on the topology structure of bipartite networks and the time delay. It is also pointed out that the time delay can reduce the basic reproduction number. Furthermore, when the disease will disappear, the delay speeds up the disappearing process; when disease will become endemic, the delay slows the disease spreading down and reduces the density of infective humans.