Investigating the seasonality of disease incidences is very important in disease surveillance in regions with periodical climatic patterns. In lieu of the paradigm about disease incidences varying seasonally in line with meteorology, this work seeks to determine how well standard epidemic models can capture such seasonality for better forecasts and optimal futuristic interventions. Once incidence data are assimilated by a periodic model, asymptotic analysis in relation to the long-term behavior of the disease occurrences can be performed using the classical Floquet theory, which explains the stability of the existing periodic solutions. For a test case, we employed an IR model to assimilate weekly dengue incidence data from the city of Jakarta, Indonesia, which we present in their raw and moving-average-filtered versions. To estimate a periodic parameter toward performing the asymptotic analysis, eight optimization schemes were assigned returning magnitudes of the parameter that vary insignificantly across schemes. Furthermore, the computation results combined with the analytical results indicate that if the disease surveillance in the city does not improve, then the incidence will raise to a certain positive orbit and remain cyclical.

中文翻译：

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从经验数据中学习疾病发生的季节性

调查疾病发生的季节性对于具有周期性气候模式的地区的疾病监测非常重要。代替关于疾病发生率随气象学季节性变化的范式，这项工作旨在确定标准流行病模型如何能够很好地捕捉这种季节性，以进行更好的预测和最佳的未来干预。一旦发病率数据被周期模型同化，就可以使用经典的 Floquet 理论对疾病发生的长期行为进行渐近分析，这解释了现有周期解的稳定性。对于测试案例，我们使用 IR 模型来同化来自印度尼西亚雅加达市的每周登革热发病率数据，我们以原始版本和移动平均过滤版本呈现这些数据。为了估计执行渐近分析的周期性参数，为八种优化方案分配了返回参数幅度，这些幅度在方案之间变化不大。此外，计算结果结合分析结果表明，如果城市疾病监测没有改善，那么发病率将上升到一定的正轨道并保持周期性。