Epidemic dynamics of influenza-like diseases spreading in complex networks

Abstract

Population contact pattern plays an important role in the spread of an infectious disease. This can be described in the framework of a complex network approach. In this paper network epidemic models for influenza-like diseases that may have infectious force in incubative or asymptomatic stage are formulated and studied. Two general types of network models are considered: the annealed and the quenched networks. The next-generation matrix approach is employed to compute the basic reproduction number of our network-based models. The implicit equations for the final epidemic size are derived, and the existence and uniqueness of solutions for implicit equations are studied by rewriting implicit equations as suitable fixed-point problems. In particular, for networks with no degree correlation, low-dimensional systems of nonlinear ordinary differential model are derived by employing an edge-based compartmental approach. Due to their low dimension, a gap between the parameter identification problem for influenza-like diseases or network inference and network epidemic models may be built through our results. The analysis is applied to an example of influenza epidemic based on the final epidemic size, from which the transmission rate and the basic reproduction number can be estimated.