We study the contact process on (dynamic) random graphs. The thesis is structured into four chapters, with the first three providing a survey of relevant literature. Chapter 1 covers the classic...Show moreWe study the contact process on (dynamic) random graphs. The thesis is structured into four chapters, with the first three providing a survey of relevant literature. Chapter 1 covers the classic theory of contact processes on lattices and regular trees, as well as recent research into contact processes on more general graphs. Chapter 2 introduces contact processes on configuration models and other random graphs, including Erdős–Rényi graphs, preferential attachment graphs and dynamic scale-free graphs. Chapter 3 provides an overview of results concerning contact processes in various random dynamic environments, where the recovery rate or the infection rate varies depending on the environment of the vertex or the edge, respectively. Chapter 4 focuses on two special dynamic random environments: one where vertices recover at rate \(0\) in environment \(0\), and the other where edges transfer infections at rate \(0\) in environment \(0\). Meanwhile, the environment of vertices or edges switches between \(0\) and \(1\) in a Markovian way. We establish monotonicity properties as underlying parameters are varied, by investigating the point process of valid infections in the graphical representation. The key idea is to couple two renewal processes via hazard rates such that the random set of epoch times of one renewal process is a subset of that of the other.Show less