Most of epidemic models assume that duration of the disease phase is distributed exponentially for the simplification of model formulation and analysis. Actually, the exponentially distributed assumption on the description of disease stages is hard to accurately approximate the interplay of drug concentration and viral load within host. In this article, we formulate an immuno-epidemiological epidemic model on complex networks, which is composed of ordinary differential equations and integral equations. The linkage of within- and between-host is connected by setting that the death caused by the disease is an increasing function in viral load within host. Mathematical analysis of the model includes the existence of the solution to the epidemiological model on complex networks, the existence and stability of equilibrium, which are completely determined by the basic reproduction number of the between-host system. Numerical analysis are shown that the non-exponentially distributions and the topology of networks have significant roles in the prediction of epidemic patterns.
