Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been used to understand and control both transient and steady-state behaviors. Typically it is assumed that after recovery from an infection, every agent will either return to its original susceptible state or acquire full immunity to reinfection. We study the network SIRI (Susceptible-Infected-Recovered-Infected) model, an epidemic model for the spread of contagious processes on a network of heterogeneous agents that can adapt their susceptibility to reinfection. The model generalizes existing models to accommodate realistic conditions in which agents acquire partial or compromised immunity after first exposure to an infection. We prove necessary and sufficient conditions on model parameters and network structure that distinguish four dynamic regimes: infection-free, epidemic, endemic, and bistable. For the bistable regime, which is not accounted for in traditional models, we show how there can be a rapid resurgent epidemic after what looks like convergence to an infection-free population. We use the model and its predictive capability to show how control strategies can be designed to mitigate problematic contagious behaviors.

中文翻译：

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网络传染模型中的自适应敏感性和异质性


传染病、社会行为或计算机病毒的传播等传染过程会影响生物、社会和技术系统。网络上大量人群和有限人群的流行病模型已被用来理解和控制瞬态和稳态行为。通常认为，从感染中恢复后，每种病原体都会恢复到原来的易感状态，或者获得对再感染的完全免疫力。我们研究网络 SIRI（易感-感染-恢复-感染）模型，这是一种流行病模型，用于在异质代理网络上传播传染过程，可以调整其对再次感染的易感性。该模型概括了现有模型，以适应现实条件，在这种条件下，病原体在首次接触感染后获得部分或受损的免疫力。我们证明了区分四种动态状态的模型参数和网络结构的充分必要条件：无感染、流行、地方性和双稳态。对于传统模型中没有考虑到的双稳态机制，我们展示了在看似趋于无感染的人群之后，流行病如何迅速复苏。我们使用该模型及其预测能力来展示如何设计控制策略来减轻有问题的传染行为。