Brugnago Eduardo L, Gabrick Enrique C, Iarosz Kelly C, Szezech José D, Viana Ricardo L, Batista Antonio M, Caldas Iberê L
Physics Institute, University of São Paulo, 05508-090 São Paulo, SP, Brazil.
Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil.
Chaos. 2023 Dec 1;33(12). doi: 10.1063/5.0156452.
In this work, we study the dynamics of a susceptible-exposed-infectious-recovered-susceptible epidemic model with a periodic time-dependent transmission rate. Emphasizing the influence of the seasonality frequency on the system dynamics, we analyze the largest Lyapunov exponent along parameter planes finding large chaotic regions. Furthermore, in some ranges, there are shrimp-like periodic structures. We highlight the system multistability, identifying the coexistence of periodic orbits for the same parameter values, with the infections maximum distinguishing by up one order of magnitude, depending only on the initial conditions. In this case, the basins of attraction have self-similarity. Parametric configurations, for which both periodic and non-periodic orbits occur, cover 13.20% of the evaluated range. We also identified the coexistence of periodic and chaotic attractors with different maxima of infectious cases, where the periodic scenario peak reaches approximately 50% higher than the chaotic one.
在这项工作中，我们研究了一个具有周期性时间依赖传播率的易感-暴露-感染-康复-易感传染病模型的动力学。强调季节性频率对系统动力学的影响，我们沿着参数平面分析最大Lyapunov指数，发现了大的混沌区域。此外，在某些范围内，存在类似虾状的周期结构。我们突出了系统的多重稳定性，确定了相同参数值下周期轨道的共存，感染最大值相差一个数量级，仅取决于初始条件。在这种情况下，吸引盆具有自相似性。同时出现周期轨道和非周期轨道的参数配置覆盖了评估范围的13.20%。我们还确定了具有不同感染病例最大值的周期吸引子和混沌吸引子的共存，其中周期情况的峰值比混沌情况的峰值高出约50%。
