季節性流感模型的動態之模型生成與數值模擬

Dynamics of Seasonal Influenza Models: Modelling and Numerical Simulations

吳承翰(Cheng-Han Wu)

指導教授 ： 莊重

國立交通大學/理學院/應用數學系暨研究所/碩士(2020年)

摘要

我們提出並分析一個季節性流感模型的動態。這個模型結合了從症狀回復的兩種不同速率與免疫衰弱對於季節性流感的影響。 因此我們從原本的傳染病模型(SIR)建構出季節中與季節間的模型。具體來說，該模型由線性和非線性的動態所組成，取決於每個季節的起始點。季節間模型具有豐富的動態:固定點，週期解，混沌吸引子，或雙穩態。有趣的是，模型的動態有包含週期三與混沌吸引子的雙穩態但是沒有固定點與週期二的雙穩態。我們透過數值模擬的結果幫助我們觀察模型並提出理論分析。而本文著重在數值模擬的結果與理論計算的對應，並提供一些想法做為之後的研究方向。

關鍵字

季節性流感模型 ； 混和映射 ； 週期解 ； 混沌吸引子 ； 雙穩態

並列摘要

We propose and analyze the dynamics of a seasonal influenza model. This model combines the impact of two different rates of recovery from symptoms and immune
waning on seasonal influenza. Therefore, we construct the within and between season model from the Susceptible–Infectious–Recovered(SIR). Specifically, the map
consists of both linear and nonlinear dynamics depending on the starting point of each season is in the domain. So the between season model has rich dynamics: fixed points,
periodic solutions, chaotic attractors, or bistable state. Interestingly, the dynamics of the model have a bistable state with period three points and chaotic attractors but no bistable state with fixed point and period two points. Through the results of numerical simulation, it helps us observe the model and propose theoretical analysis. This thesis focuses on the correspondence between the results of numerical simulation and theoretical calculations and provides some ideas for future research directions.

並列關鍵字

Seasonal influenza model ； Hybird map ； Periodic solutions ； Chaotic attractor ； Bistable state

參考文獻

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