Asymptomatic individuals in the context of malarial disease are subjects who carry a parasite load, but do not show clinical symptoms. A correct understanding of the influence of asymptomatic individuals on transmission dynamics will provide a comprehensive description of the complex interplay between the definitive host (female Anopheles mosquito), intermediate host (human), and agent ( Plasmodium parasite). The goal of this article is to conduct a rigorous mathematical analysis of a new compartmentalized malaria model accounting for asymptomatic human hosts for the purpose of calculating the basic reproductive number ( $$\mathcal {R}_0$$ R 0 ) and determining the bifurcations that might occur at the onset of disease-free equilibrium. A point of departure of this model from others appearing in the literature is that the asymptomatic compartment is decomposed into two mutually disjoint sub-compartments by making use of the naturally acquired immunity of the population under consideration. After deriving the model, a qualitative analysis is carried out to classify the stability of the equilibria of the system. Our results show that the dynamical system is locally asymptotically stable provided that $$\mathcal {R}_0<1$$ R 0 < 1 . However, this stability is not global, owning to the occurrence of a sub-critical bifurcation in which additional non-trivial sub-threshold equilibrium solutions appear in response to a specified parameter being perturbed. To ensure that the model does not undergo a backward bifurcation, we demand an auxiliary parameter denoted $$\varLambda <1$$ Λ < 1 in addition to the threshold constraint $$\mathcal {R}_0<1$$ R 0 < 1 . The authors hope that this qualitative analysis will fill in the gaps of what is currently known about asymptomatic malaria and aid in designing strategies that assist the further development of malaria control and eradication efforts.

中文翻译：

---

无症状携带者的疟疾流行病学模型


疟疾疾病中的无症状个体是携带寄生虫但不表现出临床症状的受试者。正确理解无症状个体对传播动力学的影响将有助于全面描述终宿主（雌性按蚊）、中间宿主（人类）和媒介（疟原虫寄生虫）之间复杂的相互作用。本文的目标是对考虑无症状人类宿主的新的分区疟疾模型进行严格的数学分析，以计算基本再生数 ( $$\mathcal {R}_0$$ R 0 ) 并确定分叉这可能发生在无病平衡开始时。该模型与文献中出现的其他模型的不同之处在于，通过利用所考虑人群的自然获得免疫力，将无症状区室分解为两个相互不相交的子区室。推导模型后，进行定性分析，对系统平衡的稳定性进行分类。我们的结果表明，只要 $$\mathcal {R}_0<1$$ R 0 < 1 ，动力系统是局部渐近稳定的。然而，这种稳定性不是全局的，因为亚临界分岔的发生，其中响应于被扰动的指定参数而出现额外的非平凡的亚阈值平衡解。为了确保模型不会发生后向分叉，除了阈值约束 $$\mathcal {R}_0<1$$ R 0 < 之外，我们还需要一个表示为 $$\varLambda <1$$ Λ < 1 的辅助参数1. 作者希望这种定性分析将填补目前对无症状疟疾的了解空白，并有助于设计有助于进一步发展疟疾控制和根除工作的战略。