An analysis of contact tracing protocol in an over-dispersed SEIQR Covid-like disease

The aim of this work is to study an over-dispersed SEIQR infectious disease and obtain optimal methods of contact tracing. A prototypical example of such a disease is that of the current SARS-CoV-2 pandemic. In consequence, this study is immediately applicable to the current health crisis. In this paper, we introduce both a discrete and continuous model for various modes of contact tracing. From the continuous model, we derive a basic reproductive number and study the stability of the equilibrium points. We also implement the continuous and discrete models numerically and further analyze the effectiveness of different types of contact tracing and their cost on society. Additionally, through these simulations, we also study the effect that various parameters of the disease have on its evolution.