COVID-19疫情模型的最佳控制與成本效益分析

Abstract

數學模型常被用來描述疾病傳播的動態。在這篇論文中，試圖找出一個最佳控制的方法來抑制COVID-19疾病的傳播，且擁有最佳的成本效益。首先提出一個數學模型來描述COVID-19傳播的人口動態。接著對模型實施數學分析，利用靈敏度分析找出模型中哪些參數對模型的影響較大。用非線性最小平方法對台灣2022年4月至6月的確診資料做擬合，估計並找出合適的模型參數。接下來將模型延伸至最佳控制問題，含有三個控制變數：個人保護、疫苗接種、快篩檢測。然後使用電腦軟體對加進控制變數的模型進行數值模擬。最後使用ICER方法分析各種控制政策的成本效益並找出成本效益最高的控制方法。

Mathematical model is widely used to describe the dynamics of disease transmission. In this thesis, we aim to find an optimal control method that mitigate the spread of the COVID-19 pandemic with the best cost-effectiveness. First, we propose a mathematical model to describe the population dynamics of the COVID-19 spread. We conduct mathematical analysis on the proposed model. We do sensitivity analysis to find out the parameters with stronger influence on the model using nonlinear least-squares fitting method with the data of COVID-19 confirmed cases in Taiwan from April to June, 2022 to estimate and obtain appropriate fitting parameters and model. Next, we extend the model to an optimal control problem by adding three control variables: personal protection, vaccination, and rapid test detection. After that, we do numerical simulation for the model with the implementation of control variables with software tools. Lastly, we evaluate the cost-effectiveness of each control strategy and determine the one with the best cost-effectiveness with the ICER method.