  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.
