A network theoretic method for the basic reproductive number for infectious diseases

Abstract

When an outbreak of an infectious disease occurs, whether it is COVID-19 in humans, pine wilt in trees or canine distemper in dogs, quick and decisive actions need to be taken to contain it. One tool that can help both the scientific and applied management communities understand the infection risk during an outbreak is the basic reproductive number, (Formula presented.). In this paper, we use a network method to calculate and analyse the basic reproductive number, specifically flow network theory. We convert traditional compartmental models to flow networks and then apply the fundamental Max-Flow Min-Cut Theorem to calculate the basic reproductive number. We show that this method is equivalent to the traditional next generation matrix method for the calculation of (Formula presented.), and thus a valid alternative. Then we provide step-by-step instructions and illustrate how to apply this method to epidemic models. The current methods available for calculating (Formula presented.) are complicated, requiring mathematical training. This can act as a barrier to understanding and cause delays in a real-time response. Our new approach drastically reduces the mathematical complexity of the calculation and is far more accessible to the broader scientific community. It also allows for novel insights and can be applied to models/situations where traditional methods fail.