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.
Highlights
A new virus that can cause an increase in pneumonia first appeared in Wuhan, China, at the beginning of December 2019
3 Results and discussion 3.1 SIR model of COVID-19 Consider an SIR model for COVID-19 that describes the dynamics of direct transmission of COVID-19 with interactions between suspected and infected, change from being infected to recovering, pure birth/death rates, vaccine effectiveness, treatment effectiveness, obedience in implementing health protocols, and deaths due to the COVID-19 infection
Dt where S is the proportion of susceptible individuals, I is the proportion of infected individuals, R is the proportion of recovered individuals, β is the infection rate parameter; γ is the recovery rate parameter; μ is the natural birth/death rate parameter, τ is the vaccine effectiveness parameter, θ is the treatment effectiveness parameter, π is the effectiveness of obedience in implementing health protocols, μC is the death rate parameter due to COVID-19
Summary
A new virus that can cause an increase in pneumonia first appeared in Wuhan, China, at the beginning of December 2019. The rapid spread of the disease throughout the world has made the World Health Organization declare the COVID-19 outbreak a global pandemic on March 12, 2020 [2]. According to the data collected by John Hopkins University, as of the beginning of November 2020, COVID-19 has spread to 219 countries in the world with the total number of cases infected with COVID-19 reaching 53,699,160, with 1,308,261 deaths, and 37,469,072 people have been declared cured. The spread of COVID-19 to Indonesia has been evident since the first confirmed case on March 2, 2020. COVID-19 is continuing to spread to all provinces, and as of the beginning of November 2020 it has reached a total of 457,735 infected cases, 15,037 deaths, and 385,094 people have been declared cured [3]
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