This study presents an innovative mathematical model denoted as the fractional SIP(H)–SI(M) model, which aims to analyze and understand the dynamics of malaria transmission and spread. This model is distinguished by incorporating memory effects through fractional differential equations, allowing for a more accurate and realistic analysis of disease spread compared to traditional models. The proposed model is applied to Algeria by estimating its parameters using recent health data (from 2000). The results revealed that the disease‐free equilibrium is stable only when the basic reproduction number is less than one, indicating that controlling the spread of malaria and possibly eradicating it can be achieved by implementing appropriate preventive measures. Simulations also demonstrated a direct correlation between the rate of infection transmission and an increase in the number of infected individuals, highlighting the need for swift action when signs of an outbreak emerge. Based on these findings, a set of preventive measures is recommended, including insecticide spraying programs, widespread distribution of insecticide‐treated bed nets, and implementation of effective treatment protocols for infected individuals. This study also emphasizes the importance of continuous monitoring of health data and updating model parameters to ensure the effectiveness and sustainability of preventive measures.

中文翻译：

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疟疾传播动力学的数学探索：分数模型和数值模拟的见解


本研究提出了一种创新的数学模型，称为分数 SIP（H）-SI（M） 模型，旨在分析和理解疟疾传播和传播的动态。该模型的特点是通过分数微分方程结合记忆效应，与传统模型相比，可以更准确、更真实地分析疾病传播。通过使用最近的健康数据（从 2000 年开始）估计其参数，所提出的模型应用于阿尔及利亚。结果显示，只有当基本繁殖数小于 1 时，无病平衡才稳定，这表明可以通过实施适当的预防措施来控制疟疾的传播并可能根除疟疾。模拟还表明，感染传播率与感染人数增加之间存在直接关联，这凸显了在出现疫情爆发迹象时迅速采取行动的必要性。基于这些发现，建议采取一系列预防措施，包括杀虫剂喷洒计划、广泛分发经杀虫剂处理的蚊帐以及为感染者实施有效的治疗方案。本研究还强调了持续监测健康数据和更新模型参数以确保预防措施的有效性和可持续性的重要性。