# GLOBAL STABILITY OF DISEASE-FREE EQUILIBRIA IN COVID-19 SPREAD THROUGH LIVING AND INANIMATE OBJECTS MATHEMATICAL MODEL

• Ario Wiraya Mathematics Education Study Program, Faculty of Teacher Training and Education, Sebelas Maret University, Indonesia
• Yudi Ari Adi Mathematics Study Program, Faculty of Applied Science and Technology, Ahmad Dahlan University, Indonesia https://orcid.org/0000-0002-1831-9103
• Laila Fitriana Mathematics Education Study Program, Faculty of Teacher Training and Education, Sebelas Maret University, Indonesia https://orcid.org/0000-0002-1533-1617
• Triyanto Triyanto Mathematics Education Study Program, Faculty of Teacher Training and Education, Sebelas Maret University, Indonesia
• Amellia Putri Mathematics Education Study Program, Faculty of Teacher Training and Education, Sebelas Maret University, Indonesia
Keywords: Global Stability, Mathematical Model, Covid-19, Inanimate Objects

### Abstract

Covid-19 is a dangerous disease that is easily transmitted, both through living media in the form of interactions with infected human, as well as through inanimate objects in the form of surfaces contaminated with the Coronavirus. Various preventive and repressive efforts have been made to prevent the spread of this disease, such as isolating and recovering the infected human. In this study, the authors construct and analyze a new mathematical model in the form of a three-dimensional differential equations system that represent the interactions between subpopulations of coronavirus living on inanimate objects, susceptible human, and infected human within a population. The purpose of this study is to investigate the criteria that must be met in order to create a population free from Covid-19 by considering inanimate objects as a medium for its spread besides living objects. The model solution that represents the number of each subpopulation is non-negative and bounded, so it is in accordance with the biological condition that the number of subpopulations cannot be negative and there is always a limit for its value. The eradication rate of Coronavirus living on inanimate objects, the recovery rate of infected human, and the interaction rate between susceptible human and infected human such that the population is free from Covid-19 for any initial conditions of each subpopulation were investigated in this study through global stability analysis of the disease-free equilibrium point of the model.

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Published
2023-12-18
How to Cite
[1]
A. Wiraya, Y. Adi, L. Fitriana, T. Triyanto, and A. Putri, “GLOBAL STABILITY OF DISEASE-FREE EQUILIBRIA IN COVID-19 SPREAD THROUGH LIVING AND INANIMATE OBJECTS MATHEMATICAL MODEL”, BAREKENG: J. Math. & App., vol. 17, no. 4, pp. 1873-1884, Dec. 2023.
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Articles