The robustness of human social networks against epidemic propagation relies on the propensity for physical contact adaptation. During the early phase of infection, asymptomatic carriers exhibit the same activity level as susceptible individuals, which presents challenges for incorporating control measures in epidemic projection models. This paper focuses on modeling and cost-efficient activity control of susceptible and carrier individuals in the context of the susceptible-carrier-infected-removed (SCIR) epidemic model over a two-layer contact network. In this model, individuals switch from a static contact layer to create new links in a temporal layer based on state-dependent activation rates. We derive conditions for the infection to die out or persist in a homogeneous network. Considering the significant costs associated with reducing the activity of susceptible and carrier individuals, we formulate an optimization problem to minimize the disease decay rate while constrained by a limited budget. We propose the use of successive geometric programming (SGP) approximation for this optimization task. Through simulation experiments on Poisson random graphs, we assess the impact of different parameters on disease prevalence. The results demonstrate that our SGP framework achieves a cost reduction of nearly 33% compared to conventional methods based on degree and closeness centrality.

翻译：人类社会网络对抗流行病传播的稳健性依赖于身体接触适应性的倾向。在感染初期，无症状携带者表现出与易感个体相同的活动水平，这给在流行病预测模型中纳入控制措施带来了挑战。本文聚焦于在两层接触网络上的易感-携带者-感染-移除（SCIR）流行病模型中，对易感个体和携带者进行建模及成本效益活动控制。在该模型中，个体根据状态依赖的激活率，从静态接触层切换至时态层以创建新连接。我们推导了感染在同质网络中消失或持续存在的条件。考虑到降低易感个体和携带者活动水平的显著成本，我们构建了一个优化问题，旨在有限预算约束下最小化疾病衰减率。我们提出采用连续几何规划（SGP）逼近方法来解决该优化任务。通过在泊松随机图上进行仿真实验，我们评估了不同参数对疾病流行程度的影响。结果表明，与基于度和接近中心性的传统方法相比，我们的SGP框架实现了近33%的成本降低。