Abstract:
Mathematical modeling in epidemiology has a very important role in the study of the
dynamics of an epidemic. The outbreak of Covid-19, which is currently being spread widely
in the world requires indepth study, starting from the search for sources, prediction of spread
patterns, to strategies for handling this virus outbreak. Mathematical modeling can be applied
to support various fields of the study. In this paper, we discuss mathematical modeling of the
spread of Covid-19 by providing analysis and predictions based on data from the case of
Covid-19 in South Kalimantan Province. This study was conducted by estimating parameters
of the SIR Model, which is accommodates the death cases in the data, supported by several
methods, namely Runge Kutta Method and Nonlinear Least Squares Method. Our analysis to
the data and the model yields a Basic Reproduction Number R0 ≈ 3, which means that one
individual infected by Covid-19 can produce three new infected individuals. Whereas our
prediction shows that infected cases can reach to 37.82% and cases of death can reach to
0.49% of the population who remained in normal activities during the PSBB. The peaks of
this case are estimated to occur in the 2nd week of August to the 1st week of October 2020.
The fewer people who have normal activities, then the spread of Covid-19 is predicted to pass
faster with smaller cases of infection and death. Conversely, the more people who have
normal activities, then the spread of Covid-19 in South Kalimantan can take longer and take a
higher number of victims.
Keywords: Mathematical Modeling, Covid-19, South Kalimantan Province, Parameter
Estimation, SIR Model, Runge Kutta Method, Nonlinear Least Squares Method &
Basic Reproduction Number
