ANALISIS KESTABILAN DAN SENSITIVITAS MODEL KECANDUAN FILM KARTUN
Stability and Sensitivity Analysis of The Cartoon Addiction Model
DOI:
https://doi.org/10.59896/aqlu.v4i1.503Keywords:
Mathematical Models, Cartoon Addiction, Fixed Point Stability, Parameter SensitivityAbstract
This study aims to develop a model of cartoon addiction and analyze the stability of fixed points and parameter sensitivity. The novelty of this study lies in the mathematical model of cartoon addiction by dividing the population into four main classes, namely vulnerable individuals, occasional viewers, addicts, and those who have permanently stopped watching cartoons. The methods used include the formulation of a mathematical model based on a system of differential equations, the calculation of the basic reproduction number using the next generation matrix approach, the analysis of fixed point stability, and the evaluation of sensitivity indices to identify parameters that affect the basic reproduction number. The results of the analysis show that the fixed point without addiction is locally asymptotically stable when , while the endemic fixed point is locally asymptotically stable when . Sensitivity analysis shows that the parameters of the entry rate of susceptible individuals () and the effective contact rate () contribute positively to the increase in , while the parameters of the transition from susceptible to not interested in cartoons (), the recovery rate from addiction (), and natural mortality () contribute to the decrease in . In conclusion, this model provides a comprehensive overview of the dynamics of cartoon addiction and can be used to design more appropriate prevention and treatment strategies in society
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