How many can you infect? Simple (and naive) methods of estimating the reproduction number

TL;DR

This paper pedagogically explores simple methods to estimate the reproduction number during an epidemic, applying them to COVID-19 in Italy and discussing potential improvements over naive approaches.

Contribution

It introduces and compares three naive numerical methods for estimating reproduction numbers using the SIR model, with application to real COVID-19 data.

Findings

Lockdown effects observed two weeks after implementation

Simple methods can approximate reproduction numbers reasonably

Discussion of potential improvements to naive estimation methods

Abstract

This is a pedagogical paper on estimating the number of people that can be infected by one infectious person during an epidemic outbreak, known as the reproduction number. Knowing the number is crucial for developing policy responses. There are generally two types of such a number, i.e., basic and effective (or instantaneous). While basic reproduction number is the average expected number of cases directly generated by one case in a population where all individuals are susceptible, effective reproduction number is the number of cases generated in the current state of a population. In this paper, we exploit the deterministic susceptible-infected-removed (SIR) model to estimate them through three different numerical approximations. We apply the methods to the pandemic COVID-19 in Italy to provide insights into the spread of the disease in the country. We see that the effect of the national lockdown in slowing down the disease exponential growth appeared about two weeks after the implementation date. We also discuss available improvements to the simple (and naive) methods that have been made by researchers in the field. Authors of this paper are members of the SimcovID (Simulasi dan Pemodelan COVID-19 Indonesia) collaboration.