An age-structured mathematical model for studying Malaria transmission dynamics: Applications to some areas of Senegal

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2024-10-15 DOI:10.1016/j.matcom.2024.10.006

Rama Seck , Diene Ngom , Benjamin Ivorra , Angel M. Ramos

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Abstract

In this work, we formulate an age-structured model for studying the transmission of Malaria for both human and vector populations. First, we perform an analytical study of this model. To do so, we analyze the positivity and boundedness of solutions and study the stability of the Disease-Free Equilibrium (using a matrix-tree theorem). Then, we focus on the study of the Endemic Equilibrium. Applying a methodology grounded in graph theory, we prove that, under certain assumptions, the Endemic Equilibrium is both unique and globally asymptotically stable. We also conjecture that this result holds true even in cases where these assumptions are not met. While this conjecture remains unproven, it is supported by illustrative numerical experiments. Secondly, we illustrate the interest of our approach by considering real data from two specific areas in Senegal affected by Malaria, namely Dielmo and Ndiop. In particular, we estimate some of the model parameters for these zones and illustrate how the proposed model may help to estimate the behavior of Malaria outbreaks.

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研究疟疾传播动态的年龄结构数学模型：塞内加尔部分地区的应用

在这项工作中，我们建立了一个年龄结构模型，用于研究疟疾在人类和病媒种群中的传播。首先，我们对该模型进行了分析研究。为此，我们分析了解的实在性和有界性，并研究了无疾病均衡的稳定性（使用矩阵树定理）。然后，我们重点研究地方病均衡。我们运用以图论为基础的方法，证明在某些假设条件下，地方病均衡是唯一的，并且在全局上渐近稳定。我们还猜想，即使在不满足这些假设的情况下，这一结果也是成立的。虽然这一猜想仍未得到证实，但它得到了说明性数值实验的支持。其次，我们通过考虑塞内加尔受疟疾影响的两个特定地区（即 Dielmo 和 Ndiop）的真实数据来说明我们的方法的意义。特别是，我们估算了这些地区的一些模型参数，并说明了所提出的模型如何有助于估算疟疾爆发的行为。

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.