肺癌中基因突变作用机制的数学建模研究

肺癌是世界上发病率和死亡率最高的一类癌症且患病人群呈年轻化趋势，研究肺癌的发病机制是一项非常迫切而具有重大社会意义的课题。传统的随机多阶段癌症模型都假设肿瘤是正常细胞经过多次突变转变为恶性肿瘤细胞的过程，它们并不能反映具体是哪些基因突变导致细胞的变异进而形成肿瘤，而基因突变选择关系可以为构建具有基因信息的肺癌数学模型提供依据。本项目旨在采用数学建模和统计推断的方法研究基因突变与肺癌风险的关系，进而揭示肺癌中基因突变的作用机制。其主要内容为：基于肿瘤异质性，分析肺癌基因突变的相关性，进而推断肺癌中基因突变的选择关系；根据基因突变选择关系和随机多阶段癌症模型建立基于基因突变的肺癌数学模型，并通过拟合肺癌流行病学数据验证模型的有效性，进一步分析模型的动力学特征；基于数学模型和流行病学数据研究基因突变对肺癌风险的影响。通过本项目的研究，深化癌症数学模型的理论研究，为肺癌的诊断和治疗提供理论指导。

Lung cancer is the most common type of cancer in the world with the highest incidence rate and mortality rate, and it shows a young trend. The research of cancer pathogenesis is very urgent and important social issues. Traditional stochastic multistage models of cancer assume that tumorigenesis is a process in which normal cells undergo multiple mutations to become malignant cells. These models do not reflect the specific genetic mutations that cause the healthy cells to become into tumor. However, the selection relationship of gene mutations can provide the basis for constructing the mathematical model with genetic information for lung cancer. This project mainly focuses on studying the relationship between gene mutations and lung cancer risk by mathematical modeling and statistical inference, which reveals the mechanism of gene mutations in lung cancer. There are three main contents in this project. First, the correlation significance analysis of gene mutations is analyzed by considering the heterogeneity of tumor, and then the selection relationship of gene mutations is inferred statistically for lung cancer. Then, the mathematical model with genetic information is constructed by the selection relationship of gene mutations and the traditional stochastic multistage model of cancer, and the rationality of the model is verified by fitting epidemiological data of lung cancer, and the dynamic characteristics of the model are further analyzed. Finally, the impact of gene mutations on lung cancer risk is studied by mathematical model and epidemiological data. Through the research of this project, the theoretical research of mathematical model of cancer is deepened, which provides theoretical guidance for the diagnosis and treatment of lung cancer.