Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles
Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles
复制标题
DOI：
10.3390/ijerph17062014
复制
发表时间：
2020-03-02
影响因子：
--
通讯作者：
Oraby, Tamer
中科院分区：
文献类型：
--
作者：
Islam, Md Rafiul;Peace, Angela;Oraby, Tamer
在本文中，我们比较系统的普通和（Caputo）分数阶微分方程描述的疾病的易感染暴露-感染-恢复（SEIR）模型之间的性能。为了理解这两种方法的起源整数和分数随机过程的平均场近似，我们介绍了分数阶微分方程（FDES）作为某种类型的分数阶非线性生灭过程的近似。然后，我们研究的有效性，这两种方法对经验课程的流行病，我们适合他们的情况下，发生在接种疫苗前的时代，在三个不同的地点的三个麻疹疫情的计数。虽然常微分方程（ODE）通常用于流行病建模，但FDE在拟合经验数据方面更灵活，并且在理论上提供了改进的模型预测。问题是，在实践中，使用FDE的好处是否超过了ODE增加的计算复杂性。虽然观察到瞬态动力学的重要差异，FDE仅在三个数据集中的一个中优于ODE。一般来说，FDE建模方法在具有大型精细数据集和良好数值算法的情况下可能是值得的。
In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations (FDEs) as approximations of some type of fractional nonlinear birth and death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While ordinary differential equations (ODEs) are commonly used to model epidemics, FDEs are more flexible in fitting empirical data and theoretically offer improved model predictions. The question arises whether, in practice, the benefits of using FDEs over ODEs outweigh the added computational complexities. While important differences in transient dynamics were observed, the FDE only outperformed the ODE in one of out three data sets. In general, FDE modeling approaches may be worth it in situations with large refined data sets and good numerical algorithms.