Differential equation and complex network approaches for epidemic modelling

Abstract

This study consists of three parts. The first part focuses on bifurcation analysis of epidemic models with sub-optimal immunity and saturated treatment/recovery rate as well as nonlinear incidence rate. The second part of the research focuses on estimating the domain of attraction for sub-optimal immunity epidemic models. In the third part of the research, we develop a bond percolation model for community clustered networks with an arbitrarily specified joint degree distribution.