An SIR epidemic model for COVID-19 spread with fuzzy parameter: the case of Indonesia

Muhammad Abdy; Syafruddin Side; Suwardi Annas; Wahyuddin Nur; Wahidah Sanusi

doi:10.1186/s13662-021-03263-6

An SIR epidemic model for COVID-19 spread with fuzzy parameter: the case of Indonesia

Adv Differ Equ. 2021;2021(1):105. doi: 10.1186/s13662-021-03263-6. Epub 2021 Feb 11.

Authors

Muhammad Abdy¹, Syafruddin Side¹, Suwardi Annas², Wahyuddin Nur³, Wahidah Sanusi¹

Affiliations

¹ Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Makassar, Makassar, Indonesia.
² Department of Statistics, Faculty of Mathematics and Natural Science, Universitas Negeri Makassar, Makassar, Indonesia.
³ Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Sulawesi Barat, Majene, Indonesia.

Abstract

The aim of this research is to construct an SIR model for COVID-19 with fuzzy parameters. The SIR model is constructed by considering the factors of vaccination, treatment, obedience in implementing health protocols, and the corona virus-load. Parameters of the infection rate, recovery rate, and death rate due to COVID-19 are constructed as a fuzzy number, and their membership functions are used in the model as fuzzy parameters. The model analysis uses the generation matrix method to obtain the basic reproduction number and the stability of the model's equilibrium points. Simulation results show that differences in corona virus-loads will also cause differences in the transmission of COVID-19. Likewise, the factors of vaccination and obedience in implementing health protocols have the same effect in slowing or stopping the transmission of COVID-19 in Indonesia.

Keywords: COVID-19; Fuzzy parameter; Health protocol; SIR model; Treatment; Vaccination.