Department of Mathematics, Millersville University of Pennsylvania, Millersville, PA 17551, USA.
Department of Mathematics, West Chester University of Pennsylvania, West Chester, PA 19382, USA.
Math Biosci. 2019 Apr;310:65-75. doi: 10.1016/j.mbs.2019.02.005. Epub 2019 Feb 13.
Malaria infection has posed a major health threat for hundreds of years in human history. Yet, due to the complex interactions between a host immune response and the parasite, no sophisticated mathematical models exist to study its dynamics. In this work, we propose a new system of structured partial differential equations that account for the dependence of red blood cell infectivity on maturation level. These equations are coupled with another set of differential equations for investigating the population dynamics of Plasmodium falciparum and its interaction with red blood cells and cells of the immune system. A finite difference scheme is developed to solve the system. Numerical simulations are applied to investigate the interplay between the host immune response and the parasite dynamics, the disease dynamics in acute infection, and treatment effectiveness with different drugs.
疟疾感染在人类历史上已经存在了数百年，构成了主要的健康威胁。然而，由于宿主免疫反应和寄生虫之间的复杂相互作用，目前还没有复杂的数学模型来研究其动态。在这项工作中，我们提出了一个新的结构偏微分方程组系统，该系统考虑了红细胞感染性对成熟度的依赖性。这些方程与另一组微分方程耦合，用于研究恶性疟原虫的种群动态及其与红细胞和免疫系统细胞的相互作用。开发了一个有限差分方案来求解该系统。数值模拟被应用于研究宿主免疫反应和寄生虫动态之间的相互作用、急性感染中的疾病动态以及不同药物的治疗效果。
