Title: A Study of Qualitative Correlations Between Crucial Bio-markers and the Optimal Drug Regimen of Type-I Lepra Reaction: A Deterministic Approach Show Chinese title

Title: I型麻风反应关键生物标志物与最佳药物方案之间的定性相关性研究

Abstract: Mycobacterium leprae is a bacteria that causes the disease Leprosy (Hansen's disease), which is a neglected tropical disease. More than 200000 cases are being reported per year world wide. This disease leads to a chronic stage known as Lepra reaction that majorly causes nerve damage of peripheral nervous system leading to loss of organs. The early detection of this Lepra reaction through the level of bio-markers can prevent this reaction occurring and the further disabilities. Motivated by this, we frame a mathematical model considering the pathogenesis of leprosy and the chemical pathways involved in Lepra reactions. The model incorporates the dynamics of the susceptible schwann cells, infected schwann cells and the bacterial load and the concentration levels of the bio markers $IFN-\gamma$, $TNF-\alpha$, $IL-10$, $IL-12$, $IL-15$ and $IL-17$. We consider a nine compartment optimal control problem considering the drugs used in Multi Drug Therapy (MDT) as controls. We validate the model using 2D - heat plots. We study the correlation between the bio-markers levels and drugs in MDT and propose an optimal drug regimen through these optimal control studies. We use the Newton's Gradient Method for the optimal control studies. Show Chinese abstract

Abstract: 麻风杆菌是一种引起麻风病（汉森病）的细菌，这是一种被忽视的热带疾病。 每年全球报告的病例超过200000例。 这种疾病会导致称为麻风反应的慢性阶段，主要导致周围神经系统神经损伤，进而导致器官丧失。 通过生物标志物水平早期检测这种麻风反应可以防止反应的发生和进一步的残疾。 受此启发，我们构建了一个数学模型，考虑麻风病的发病机制以及麻风反应中涉及的化学通路。 该模型包含了易感雪旺细胞、感染雪旺细胞以及细菌负荷和生物标志物 $IFN-\gamma$, $TNF-\alpha$, $IL-10$, $IL-12$, $IL-15$ 和 $IL-17$的浓度水平的动力学。 我们考虑了一个九个隔室的最优控制问题，将多药治疗（MDT）中使用的药物作为控制变量。 我们使用二维热图验证该模型。 我们研究了MDT中生物标志物水平与药物之间的相关性，并通过这些最优控制研究提出了一个最优药物方案。 我们在最优控制研究中使用了牛顿梯度法。