The daily computed weighted averaging basic reproduction number R 0 , k , ω n for MERS-CoV in South Korea

Abstract

In this paper, we propose the daily computed weighted averaging basic reproduction number $R_{0,k,\omega }^n$ for Middle East respiratory syndrome coronavirus (MERS-CoV) outbreak in South Korea, May to July 2015. We use an SIR model with piecewise constant parameters $\beta$ (contact rate) and $\gamma$ (removed rate). We use the explicit Euler's method for the solution of the SIR model and a nonlinear least-square fitting procedure for finding the best parameters. In $R_{0,k,\omega }^n$ , the parameters $n$ , $k$ , and $w$ denote days from a reference date, the number of days in averaging, and a weighting factor, respectively. We perform a series of numerical experiments and compare the results with the real-world data. In particular, using the predicted reproduction number based on the previous two consecutive reproduction numbers, we can predict the future behavior of the reproduction number.

Keywords: Explicit Euler’s method; MERS-CoV; Optimal parameter fitting; SIR model.