基于分数阶微分方程的疟疾和霍乱共动力模型分析

Livinus L. Iwa, U. K. Nwajeri, A. O. Atede, A. B. Panle, K. U. Egeonu
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引用次数: 5

摘要

本文研究了疟疾和霍乱在分数阶系统的Caputo-Fabrizio阶导数$\alpha\in(0,1)$随一些显著参数变化下的共动力学。分数阶系统包括10个隔间,分为人类和向量类。人口暴露于疟疾和霍乱等令人讨厌的疾病,如果不采取适当的护理,可能导致过早死亡。因此,我们利用著名的Banach和Schauder不动点定理,定性地分析了分数阶系统解的存在唯一性。通过著名的迭代Atangana-Baleanu分数阶Adams-Bashforth格式实现了系统的数值解。利用该方案得到的数值算法对不同分数阶$\alpha\in(0,1)$进行图形模拟。使用各种分数阶产生的数字显示随着时间的增加,完全收敛和稳定。当分数阶趋于1时,稳定性和收敛性也很明显。在数值模拟中还建立了疾病的分数阶共动力系统的实际行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Malaria and cholera co-dynamic model analysis furnished with fractional-order differential equations
This paper presents malaria and cholera co-dynamics under Caputo-Fabrizio derivative of order $\alpha\in(0,1)$ varied with some notable parameters in the fractional system. The fractional order system comprises ten compartments divided into human and vector classes. The human population is exposed to obnoxious diseases such as malaria and cholera which can lead to an untimely death if proper care is not taken. As a result, we present the qualitative analysis of the fractional order system where the existence and uniqueness of the solution using the well-known Banach and Schauder fixed point theorems. The numerical solution of the system is achieved through the famous iterative Atangana-Baleanu fractional order Adams-Bashforth scheme. The numerical algorithm obtained from the scheme is used for graphic simulation for different fractional orders $\alpha\in (0,1)$. The figures produced using various fractional orders show total convergence and stability as time increases. It is also evident that stability and convergence are achieved as the fractional orders tend to 1. The actual behavior of the fractional co-dynamical system of the diseases is established also in the numerical simulation.
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