Centre for Cellular and Molecular Biology (CSIR), Uppal Road, Hyderabad, India.
Malar J. 2011 Jul 21;10:202. doi: 10.1186/1475-2875-10-202.
Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease.
数学模型被用于提供一个明确的框架，以理解人类种群中的疟疾传播动力学已有 100 多年的历史。由于环境和社会经济条件的变化，该疾病仍然肆虐，并有可能成为主要的死亡和残疾来源，因此有必要对现有的模型进行批判性评估，并研究它们在描述宿主-寄生虫生物学方面的演变和功效。在本文中，从基本的 Ross 模型出发，讨论了关键的数学模型及其基础特征，这些模型基于其在理解疟疾传播和传播方面的具体贡献。本文的第一个目的是从基本模型出发，建立一系列不同复杂程度的确定性模型的分层结构。第二个目标是使用一些有代表性的数学模型来说明建模策略的演变，以通过包含宿主-媒介-寄生虫相互作用的关键特征来描述疟疾的发病率。重点更多地放在基于确定性微分方程的流行病学房室模型的演变上，简要讨论了基于数据的统计模型。在这个全面的调查中，我们的方法是总结该领域的建模活动，以便帮助更多从事流行病学、传播和疟疾其他方面研究的研究人员了解相关知识。这可能有助于数学家进一步开发与当前情况相关的合适模型，并帮助生物学家和公共卫生人员更好地理解控制疾病的建模策略。
