佩特里网和普通微分方程SIR组件模型的数值比较
Trevor Reckell1, Bright Kwaku Manu2, Beckett Sterner3
1School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA.
IEEE access : practical innovations, open solutions
|February 26, 2026
概括
这项研究验证了使用彼得里网模拟疾病传播的离散事件模拟,比如易受感染复原 (SIR) 模型. 数字程序确保与传统的普通微分方程 (ODE) 模型的准确融合.
科学领域:
- 计算生物学 计算生物学
- 流行病学建模 流行病学建模
- 离散事件系统是离散事件系统.
背景情况:
- 培养网为疾病传播建模提供了一个离散事件模拟框架.
- 易感染-恢复 (SIR) 模型是流行病学研究的基石,通常使用普通微分方程 (ODE).
- 现有的SIR模型的Petri net实现缺乏与ODE对应的系统数值收分析.
研究的目的:
- 系统地研究SIRS分区模型对标准ODE表述的两个不同的Petri网实现的数值趋同.
- 为SIRS动态引入新的确定性和随机性彼得里网模型.
- 为准确的模拟结果确定关键的数值程序.
主要方法:
- 在GPenSIM中使用可变过渡权重开发了SIRS模型的新型确定性彼得里网实现.
- 使用Spike创建了用于SIRS模型的随机Petri网模型.
- 在培养网模拟中应用了特定的重新缩放和圆形化程序.
- 将模拟结果与已建立的基于ODE的SIRS模型进行比较.
主要成果:
- 在将Petri网模型与ODE模拟进行比较时,实现了1%以下的相对根平均平方误差.
- 证明了重新缩放和圆在实现数值收方面发挥的关键作用.
- 验证了SIR类型动态的决定性和随机离散时间彼得里网模型.
结论:
- 带有适当的数值程序的Petri网是模拟SIR型流行病动态的有效工具.
- 这项工作为在更复杂,更大规模的疾病传播模拟中使用培养网奠定了基础.
- 这些发现支持将离散事件模拟方法集成到计算流行病学中.
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