A simple and intuitive method to calculate $R_0$ in complex epidemic models

TL;DR

This paper presents a straightforward method to compute the basic reproductive number, $R_0$, in complex epidemic models using fundamental Markov chain concepts, aiding in epidemic control strategies.

Contribution

It introduces a simple, intuitive approach to calculate $R_0$ in complex models, enhancing analytical tools for epidemic modeling.

Findings

Method based on Markov chains effectively computes $R_0$ in complex models.

Facilitates understanding of parameter effects on epidemic spread.

Supports decision-making to control outbreaks.

Abstract

Epidemic models are a valuable tool in the decision making process. Once a mathematical model for an epidemics has been established, the very next step is calculating a mathematical expression for the basic reproductive number, $R_0$, which is the average number of infections caused by an individual that is introduced in a population of susceptibles. Finding a mathematical expression for $R_0$ is important because it allows to analyze the effect of the different parameters in the model on $R_0$ so that we can act on them to keep $R_0 < 1$, so that the epidemic fades out. In this work we show how to calculate $R_0$ in complicated epidemic models by using only basic concepts of Markov chains.