一类具有疫苗接种行为决策函数的传染病模型的敏感性分析

Sensitivity Analysis of Infectious Disease Models with Vaccination Behavior Decision Functions

摘要: 文章构建了一个融合了疫苗决策功能的SEIRV动力学模型。考虑基本的疾病传播过程的同时，引入疫苗接种决策变量，计算了模型边界平衡点和内部平衡点以及基本再生数和控制再生数，验证了不同条件下边界平衡点的稳定性。利用拉丁超立方体抽样(LHS)与偏秩相关系数(PRCC)方法分析模型部分参数对疫情规模的影响程度，观察到提高疫苗有效性、延长疫苗保护时间以及采取更严格的措施可以有效抑制病毒的传播，并显著缩短其持续时间。

Abstract: This paper presents the construction of a SEIRV dynamical model that incorporates a vaccine decision-making functionality. In addition to considering the fundamental processes of disease transmission, the model introduces a vaccination decision variable. We compute the model boundary, internal equilibrium points, basic reproduction numbers, and control reproduction numbers. The stability of the boundary equilibrium points under various conditions is rigorously verified. Utilizing Latin Hypercube Sampling (LHS) in conjunction with the Partial Rank Correlation Coefficient (PRCC) method, we analyze the impact of certain model parameters on the scale of the epidemic. Our findings reveal that increasing vaccine efficacy, extending vaccine protection duration, and implementing stricter measures can effectively mitigate viral transmission and substantially reduce its duration.