标题： 一种考虑人类行为和随机效应的流行病学分室模型 显示英文标题

标题： A Compartmental Model for Epidemiology with Human Behavior and Stochastic Effects

摘要： 我们提出一个流行病学的分 compartment 模型，其中人口被划分为遵守或不遵守旨在减缓疾病传播的协议的群体。 与疾病传播并行，我们假设不遵守协议的行为作为一种社会传染而传播。 我们首先推导出该模型的确定性版本的繁殖率，并利用此来完全表征无病平衡点的局部稳定性。 然后，我们将确定性模型与随机效应相结合，具体假设疾病的传播率和社会传染的传播率是不确定的。 我们证明了我们的随机模型的全局存在性和非负性。 然后，使用适当构建的随机李雅普诺夫函数，我们分析了随机系统相对于某些无病状态的行为。 我们通过数值模拟展示了所有结果。 显示英文摘要

摘要： We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that noncompliance with protocols spreads as a social contagion. We begin by deriving the reproductive ratio for a deterministic version of the model, and use this to fully characterize the local stability of disease free equilibrium points. We then append the deterministic model with stochastic effects, specifically assuming that the transmission rate of the disease and the transmission rate of the social contagion are uncertain. We prove global existence and nonnegativity for our stochastic model. Then using suitably constructed stochastic Lyapunov functions, we analyze the behavior of the stochastic system with respect to certain disease free states. We demonstrate all of our results with numerical simulations.