# How Many Can You Infect? Simple (and Naive) Methods of Estimating the Reproduction Number

## Authors

• H. Susanto 1) Department of Mathematics, College of Arts and Sciences, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates 2) Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom
• V.R. Tjahjono Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Sepuluh Nopember, Sukolilo, Surabaya 60111
• A. Hasan Center for Unmanned Aircraft Systems Mærsk McKinney Møller Institute, University of Southern Denmark, 5230 Odense
• M.F. Kasim Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, United Kingdom
• N. Nuraini Industrial and Financial Mathematics Research Group, Department of Mathematics, Institut Teknologi Bandung, Ganesha 10, Bandung, 40132
• E.R.M. Putri Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Sepuluh Nopember, Sukolilo, Surabaya 60111
• R. Kusdiantara Industrial and Financial Mathematics Research Group, Department of Mathematics, Institut Teknologi Bandung, Ganesha 10, Bandung, 40132
• H. Kurniawan Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Sepuluh Nopember, Sukolilo, Surabaya 60111,

## Keywords:

Reproduction number, infectious disease, compartment model, COVID-19

## 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 susceptibleinfected-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.

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2020-06-22

## How to Cite

Susanto, H., Tjahjono, V., Hasan, A., Kasim, M., Nuraini, N., Putri, E., Kusdiantara, R., & Kurniawan, H. (2020). How Many Can You Infect? Simple (and Naive) Methods of Estimating the Reproduction Number. Communication in Biomathematical Sciences, 3(1), 28-36. https://doi.org/10.5614/cbms.2020.3.1.4

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