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All Journal Communication in Biomathematical Sciences Jambura Journal of Biomathematics (JJBM)
Arcede, Jayrold P.
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Computer Science & IT Decision Sciences, Operations Research & Management Mathematics Social Sciences

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Unveiling SIR Model Parameters: Empirical Parameter Approach for Explicit Estimation and Confidence Interval Construction Susyanto, Nanang; Arcede, Jayrold P.
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 1: June 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i1.26287

Abstract

We propose a simple parameter estimation method for the Susceptible-Infectious-Recovered (SIR) model. This method offers explicit estimates of parameters using second-order numerical derivatives to construct empirical parameters. In addition, the method constructs confidence intervals, providing a robust assessment of parameter uncertainty. To validate the accuracy of our method, we applied it to simulated data, in order to demonstrate its effectiveness in accurately estimating the true model parameters. Furthermore, we applied this method to actual COVID-19 case data from the USA, Indonesia, and the Philippines. This application enables the estimation of parameters and reproductive numbers, along with their confidence intervals, thus underscoring the efficacy of our technique. Notably, the parameter estimates obtained through our approach successfully predicted the case numbers in all three countries, confirming its predictive reliability. Our method offers significant advantages in terms of simplicity and accuracy, making it an invaluable tool for epidemiological modeling and public health planning.
Penyebaran Rumor dalam Masyarakat: Sebuah Pendekatan Pemodelan Matematika dalam Studi Kasus Pemilihan Umum Septyawan, Stefanus Raynaldo; Bunga, Esther Yolandyne; Nuraini, Nuning; Arcede, Jayrold P.
Communication in Biomathematical Sciences Vol. 7 No. 2 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2022.7.2.3

Abstract

Rumors can be defined as unverified information or statements shared by people that may be positive or negative and circulate without confirmation. Since humans naturally seek factual information for social and self-enhancement purposes, rumors become an inevitable aspect of human life, including in politics, such as elections. The complexity of the electoral process, with various factors such as individual candidates, social circumstances, and particularly the media, leads to the dynamic spread of rumors in society. Thus, it is both interesting and important to understand the dynamics of rumor spreading, particularly in the context of elections. In this article, we formulate a mathematical model of rumor spread dynamics based on different attitudes of people toward rumors. The model considers the spread of rumors about two candidates in the electoral context. From the model, we derived and investigated the basic reproductive number (R0) as a threshold for rumor spread and conducted a sensitivity analysis with respect to all the model parameters. Based on numerical experiments and simulations, it was revealed that the number of people resistant to or disbelieving in rumors increases significantly in the first ten days and remains higher than other subpopulations for at least after first seven days. Furthermore, we found that a high number of people directly affected by rumors, combined with the rumor transmission rate for both candidates being greater than each other, are necessary and sufficient conditions for rumors to circulate rapidly and remain stable in society. The results of this study can be interpreted and considered as a campaign strategy in an electoral context.
Co-Authors Bunga, Esther Yolandyne Nuning Nuraini Septyawan, Stefanus Raynaldo Susyanto, Nanang