新型冠状病毒肺炎（以下简称新冠病毒）在全球的大规模蔓延对世界经济造成了巨大损失，严重影响了各国的社会秩序。通过建立非线性动力学模型深入研究新冠病毒的传播规律和机理，探索有效的控制策略，不仅可以缓解当前危机，还能提高应对未来新发传染病的能力。目前，针对新冠病毒传播建模和控制策略的研究存在一些不足之处。在建模和分析方面，往往没有充分考虑到现实因素，如采取保护措施和接种疫苗的群体，也未使用真实疫情数据验证模型的有效性；在新冠病毒传播控制策略方面，大多数研究往往采用单一的控制策略，并且忽略了疫情防控所产生的经济成本。为此，本文根据新冠病毒传播特点，利用非线性动力学理论，建立不同时期的新冠病毒传播模型，对模型进行动力学性质分析，预测新冠病毒发展趋势，并探究有效抑制新冠病毒传播的最优混合控制策略。本文主要研究内容和创新点如下：

(1) 新冠病毒传播模型构建与分析。本文根据新冠病毒疫情传染性强、传播速度快、传播范围广等特点，考虑政府管控、个人防控、疫苗接种、医学隔离等情况，利用非线性动力学理论，建立适用于疫情不同发展阶段的新冠病毒传播动力学模型，为新冠病毒传播趋势预测奠定基础。根据新冠病毒疫情的真实感染数据，通过非线性最小二乘参数估计方法对模型进行参数估计，进一步预测新冠病毒传播趋势。预测结果表明，所提出的模型预测精度高，能够为探究新冠病毒传播趋势提供有效技术支撑。

(2) 新冠病毒传播控制策略研究。政府在制定新冠病毒疫情管控政策时，既要考虑政策有效性，即快速抑制疫情蔓延，又要考虑管控政策对社会经济发展和人们正常生活的影响，避免造成较大经济损失。本文在所建立的新冠病毒传播动力学模型基础上，考虑疫苗接种、医学隔离等管控措施，建立新冠病毒控制模型，提出混合控制策略，并以疫情管控措施所产生的经济成本和感染总人数最小化为目标，建立了最优控制模型。实验结果表明，最优控制策略的成本低于单一控制策略和混合控制策略，并且能够使病毒感染人数最小化，有效降低新冠病毒传播规模。

本文的研究成果既可以丰富新冠病毒等重大传染病科学防控与管理的理论体系，也可为新冠病毒等重大传染病疫情防控提供有效的技术支撑。

The widespread outbreak of COVID-19 has caused enormous losses to the world economy and seriously affected the social order of various countries. By establishing a nonlinear dynamical model to conduct in-depth research on the transmission patterns and mechanisms of the novel coronavirus, and exploring effective control strategies, we can not only alleviate the current crisis but also improve our ability to respond to future emerging infectious diseases. Currently, there are some shortcomings in the modeling and control strategies for the transmission of the novel coronavirus. Currently, there are still some shortcomings in the modeling and control strategies for the transmission of the novel coronavirus. In terms of modeling and analysis, real-life factors such as the group that takes protective measures and vaccine coverage are usually not fully considered, and the effectiveness of the model is not verified using practical epidemic data. As for the control strategies for the transmission of the novel coronavirus, most studies often adopt a single control strategy but ignore the economic costs associated with epidemic prevention and control. Therefore, this thesis uses nonlinear dynamical theory to establish models for the transmission of the virus at different stages, conducts dynamic property analysis of the models, predicts the development trends of the novel coronavirus, and explores the optimal mixed control strategy to effectively suppress the transmission of the virus. The main research contents and innovation points of this thesis are as follows:

(1) Construction and Analysis of the Transmission Model of COVID-19. This thesis uses the characteristics of the COVID-19 epidemic and the theory of nonlinear dynamics to establish a COVID-19 transmission dynamics model suitable for different stages of the epidemic, laying a foundation for predicting the transmission trend of COVID-19. Based on the practical infection data of the COVID-19 epidemic, the model is parameterized using the nonlinear least squares parameter estimation method to predict the transmission trend of COVID-19. The prediction results show that the proposed model has high prediction accuracy and can provide effective technical support for exploring the transmission trend of COVID-19.

(2) Research on the Control Strategy of COVID-19 Transmission. When formulating policies for controlling the COVID-19 epidemic, the government needs to consider both the effectiveness of the policies, which is to rapidly suppress the spread of the epidemic, and the impact of the control policies on social and economic development as well as people’s normal lives, in order to avoid causing significant economic losses. Based on the COVID-19 transmission dynamics model established in this article, this thesis considers control measures such as vaccination and isolation, and proposes a hybrid control strategy to establish an optimal control model that minimizes the economic costs and total number of infections generated by the epidemic control measures. The experimental results show that the cost of the optimal control strategy is lower than that of single and mixed control strategies, and it can minimize the number of virus infections, effectively reducing the scale of COVID-19 transmission.

The research findings of this thesis can not only enrich the theoretical system of scientific prevention and management of major infectious diseases such as COVID-19, but also provide effective technical support for epidemic prevention and control of major infectious diseases such as COVID-19.