Souleiman Yahyeh, Ismail Liban, Eftimie Raluca
Centre de Recherche en Mathématiques et Numérique (CRMN), University of the Djibouti, Campus Balbala, Djibouti.
Laboratoire Mathématiques de Besançon (LMB), University of Bourgogne Franche-Comté, Besançon, France.
Infect Dis Model. 2024 Jun 16;9(4):1095-1116. doi: 10.1016/j.idm.2024.06.003. eCollection 2024 Dec.
Malaria is an infectious and communicable disease, caused by one or more species of Plasmodium parasites. There are five species of parasites responsible for malaria in humans, of which two, Plasmodium Falciparum and Plasmodium Vivax, are the most dangerous. In Djibouti, the two species of Plasmodium are present in different proportions in the infected population: 77% of P. Falciparum and 33% of P. Vivax. In this study we present a new mathematical model describing the temporal dynamics of Plasmodium Falciparum and Plasmodium Vivax co-infection. We focus briefly on the well posedness of this model and on the calculation of the basic reproductive numbers for the infections with each Plasmodium species that help us understand the long-term dynamics of this model (i.e., existence and stability of various eqiuilibria). Then we use computational approaches to: (a) identify model parameters using real data on malaria infections in Djibouti; (b) illustrate the influence of different estimated parameters on the basic reproduction numbers; (c) perform global sensitivity and uncertainty analysis for the impact of various model parameters on the transient dynamics of infectious mosquitoes and infected humans, for infections with each of the Plasmodium species. The originality of this research stems from employing the FAST method and the LHS method to identify the key factors influencing the progression of the disease within the population of Djibouti. In addition, sensitivity analysis identified the most influential parameter for Falciparium and Vivax reproduction rates. Finally, the uncertainty analysis enabled us to understand the variability of certain parameters on the infected compartments.
疟疾是一种由一种或多种疟原虫寄生虫引起的传染性疾病。有五种疟原虫会导致人类感染疟疾，其中两种，即恶性疟原虫和间日疟原虫，最为危险。在吉布提，这两种疟原虫在感染人群中的比例不同：恶性疟原虫占77%，间日疟原虫占33%。在本研究中，我们提出了一个新的数学模型，用于描述恶性疟原虫和间日疟原虫共同感染的时间动态。我们简要关注了该模型的适定性以及每种疟原虫感染的基本繁殖数的计算，这有助于我们理解该模型的长期动态（即各种平衡点的存在性和稳定性）。然后我们使用计算方法来：(a) 使用吉布提疟疾感染的实际数据确定模型参数；(b) 说明不同估计参数对基本繁殖数的影响；(c) 对每种疟原虫感染的感染性蚊子和受感染人类的瞬态动态，进行各种模型参数影响的全局敏感性和不确定性分析。这项研究的独特之处在于采用快速搜索法（FAST方法）和拉丁超立方抽样法（LHS方法）来确定影响吉布提人群中疾病进展的关键因素。此外，敏感性分析确定了对恶性疟原虫和间日疟原虫繁殖率最有影响的参数。最后，不确定性分析使我们能够了解某些参数对受感染区室的变异性。
