Presentation Information
[N-2-05]Comparison of chaotic dynamics between an infectious disease model and a laser model
◎Ren Shimada1, Ryuki Ito1, Felix Koester1, Kazutaka Kanno1, Tomoki Yamagami1, Atsushi Uchida1 (1. Saitama Univ.)
Keywords:
Infectious diseases,Lasers,Chaos,Bifurcation,Lyapunov Exponent
Many mathematical models have been proposed to predict infectious disease outbreaks and laser output. Previous studies have shown that some infectious disease models and laser models have similar mathematical structures, allowing correspondences between them and reproduction of their dynamics. However, research on such correspondences remains limited. In this study, we construct an endemic SIR model with periodic modulation, representing seasonal variation in the infection rate, and a corresponding laser rate-equation model with gain modulation. The aim is to analyze complex dynamics, including transitions from stable states to chaotic behavior, and to investigate the relationship between the two models. The SIR model is extended by introducing birth and natural death rates, while the infection rate is expressed as a sinusoidal function. The corresponding laser model is derived from two-level rate equations. We confirm that two variables and four parameters correspond between the models. Numerical analyses of time waveforms, peak intensities, bifurcation structures, and Lyapunov exponents show that the two models exhibit similar behavior depending on the dynamical state and parameter range.