Abstract
Multi-scale models provide a new insight into the interplays of the kinetics of within hosts and the transmission of between hosts. In this paper, we adopt the nested approach to get a linkage between the within- and between-host systems, and then propose a mean-field communicable disease model on complex networks. Then, we rigorously study the existence of the solution of the multi-scale epidemic model on complex networks and completely establish the stability of each feasible equilibrium of the within- and between-host subsystems. Numerical simulations suggest that the basic reproduction number of the between-host system R0B is an increasing function of the basic reproduction number of the within-host system R0T and the final epidemic size is an increasing function of R0B. Finally, we find that the topological structures of networks play a significant role in the transmission patterns of an infection.
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