离散时间分期进展流行病模型
Discrete-time staged progression epidemic models
AI总结：
本研究从方法论角度分析离散时间分期进展流行病模型，计算基本再生数，刻画感染类别的渐近与单调性行为，并纳入接触次数分布以研究其对疾病动态的影响。
摘要：
在分期进展（SP）流行病模型中，感染者被划分为适当数量的状态。这些模型的目标是尽可能准确地描述经历不同阶段的个体所表现出的传染性差异的影响。本研究的主要目标是从方法论的角度研究无再感染且具有一般发病率函数的离散时间SP模型解的行为。除了计算$\mathcal{R}_{0}$外，我们还找到了流行病最终规模的界限，刻画了感染类别的渐近行为，给出了关于感染类别最终单调性的结果，并获得了关于疾病患病率初始动态的结果。此外，我们将接触次数的概率分布纳入模型，以便研究其对疾病动态的影响。
英文摘要：
In the Staged Progression (SP) epidemic models, infected individuals are classified into a suitable number of states. The goal of these models is to describe as closely as possible the effect of differences in infectiousness exhibited by individuals going through the different stages. The main objective of this work is to study, from the methodological point of view, the behavior of solutions of the discrete time SP models without reinfection and with a general incidence function. Besides calculating $\mathcal{R}_{0}$, we find bounds for the epidemic final size, characterize the asymptotic behavior of the infected classes, give results about the final monotonicity of the infected classes, and obtain results regarding the initial dynamics of the prevalence of the disease. Moreover, we incorporate into the model the probability distribution of the number of contacts in order to make the model amenable to study its effect in the dynamics of the disease.
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