Leon Cristina, Tokarev Alexey, Bouchnita Anass, Volpert Vitaly
Interdisciplinary Center for Mathematical Modelling in Biomedicine, S.M. Nikol'skii Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia.
M&S Decisions, 5 Naryshkinskaya Alley, 125167 Moscow, Russia.
Vaccines (Basel). 2023 Jan 4;11(1):127. doi: 10.3390/vaccines11010127.
In this work, we develop mathematical models of the immune response to respiratory viral infection, taking into account some particular properties of the SARS-CoV infections, cytokine storm and vaccination. Each model consists of a system of ordinary differential equations that describe the interactions of the virus, epithelial cells, immune cells, cytokines, and antibodies. Conventional analysis of the existence and stability of stationary points is completed by numerical simulations in order to study the dynamics of solutions. The behavior of the solutions is characterized by large peaks of virus concentration specific to acute respiratory viral infections. At the first stage, we study the innate immune response based on the protective properties of interferon secreted by virus-infected cells. Viral infection down-regulates interferon production. This competition can lead to the bistability of the system with different regimes of infection progression with high or low intensity. After that, we introduce the adaptive immune response with antigen-specific T- and B-lymphocytes. The resulting model shows how the incubation period and the maximal viral load depend on the initial viral load and the parameters of the immune response. In particular, an increase in the initial viral load leads to a shorter incubation period and higher maximal viral load. The model shows that a deficient production of antibodies leads to an increase in the incubation period and even higher maximum viral loads. In order to study the emergence and dynamics of cytokine storm, we consider proinflammatory cytokines produced by cells of the innate immune response. Depending on the parameters of the model, the system can remain in the normal inflammatory state specific for viral infections or, due to positive feedback between inflammation and immune cells, pass to cytokine storm characterized by the excessive production of proinflammatory cytokines. Finally, we study the production of antibodies due to vaccination. We determine the dose-response dependence and the optimal interval of vaccine dose. Assumptions of the model and obtained results correspond to the experimental and clinical data.
在这项工作中，我们考虑到严重急性呼吸综合征冠状病毒（SARS-CoV）感染、细胞因子风暴和疫苗接种的一些特殊性质，建立了针对呼吸道病毒感染的免疫反应数学模型。每个模型都由一个常微分方程组组成，该方程组描述了病毒、上皮细胞、免疫细胞、细胞因子和抗体之间的相互作用。为了研究解的动态变化，通过数值模拟完成了对驻点的存在性和稳定性的常规分析。解的行为特征是急性呼吸道病毒感染特有的病毒浓度大幅峰值。在第一阶段，我们基于病毒感染细胞分泌的干扰素的保护特性研究先天免疫反应。病毒感染会下调干扰素的产生。这种竞争可能导致系统出现双稳态，具有高强度或低强度的不同感染进展模式。之后，我们引入了具有抗原特异性T淋巴细胞和B淋巴细胞的适应性免疫反应。所得模型展示了潜伏期和最大病毒载量如何取决于初始病毒载量和免疫反应参数。特别是，初始病毒载量的增加会导致潜伏期缩短和最大病毒载量升高。该模型表明，抗体产生不足会导致潜伏期延长，甚至最大病毒载量更高。为了研究细胞因子风暴的出现和动态变化，我们考虑了先天免疫反应细胞产生的促炎细胞因子。根据模型参数，系统可以保持病毒感染特有的正常炎症状态，或者由于炎症与免疫细胞之间的正反馈，转变为以促炎细胞因子过度产生为特征的细胞因子风暴。最后，我们研究了疫苗接种导致的抗体产生。我们确定了剂量反应依赖性和疫苗剂量的最佳间隔。模型假设和所得结果与实验和临床数据相符。
