Mathematics Department, University of Louisiana at Lafayette, Lafayette, LA, USA.
J Math Biol. 2020 May;80(6):1803-1843. doi: 10.1007/s00285-020-01480-3. Epub 2020 Mar 10.
Infection by distinct Dengue virus serotypes and host immunity are intricately linked. In particular, certain levels of cross-reactive antibodies in the host may actually enhance infection severity leading to Dengue hemorrhagic fever (DHF). The coupled immunological and epidemiological dynamics of Dengue calls for a multi-scale modeling approach. In this work, we formulate a within-host model which mechanistically recapitulates characteristics of antibody dependent enhancement in Dengue infection. The within-host scale is then linked to epidemiological spread by a vector-host partial differential equation model structured by host antibody level. The coupling allows for dynamic population-wide antibody levels to be tracked through primary and secondary infections by distinct Dengue strains, along with waning of cross-protective immunity after primary infection. Analysis of both the within-host and between-host systems are conducted. Stability results in the epidemic model are formulated via basic and invasion reproduction numbers as a function of immunological variables. Additionally, we develop numerical methods in order to simulate the multi-scale model and assess the influence of parameters on disease spread and DHF prevalence in the population.
不同血清型登革热病毒的感染和宿主免疫之间存在着错综复杂的联系。特别是，宿主中一定水平的交叉反应性抗体实际上可能会加重感染的严重程度，导致登革出血热（DHF）。登革热的免疫和流行病学的耦合动力学要求采用多尺度建模方法。在这项工作中，我们构建了一个体内模型，该模型从机制上再现了登革热感染中抗体依赖性增强的特征。然后，通过宿主抗体水平的向量-宿主偏微分方程模型，将体内尺度与流行病学传播联系起来。这种耦合可以跟踪通过不同登革热株的初次和二次感染以及初次感染后交叉保护免疫的衰减，从而在人群中动态跟踪全人群的抗体水平。对体内和宿主间系统都进行了分析。通过基本和入侵繁殖数作为免疫变量的函数，给出了传染病模型中的稳定性结果。此外，我们还开发了数值方法，以便模拟多尺度模型，并评估参数对疾病传播和人群中 DHF 患病率的影响。
