People afflicted with diseases such as retinitis pigmentosa and age-related macular degeneration experience a decline in vision due to photoreceptor degeneration, which is currently unstoppable and irreversible. Currently there is no cure for diseases linked to photoreceptor degeneration. Recent experimental work showed that mesencephalic astrocyte-derived neurotrophic factor (MANF) can reduce neuron death and, in particular, photoreceptor death by reducing the number of cells that undergo apoptosis. In this work, we build on an existing system of ordinary differential equations that represent photoreceptor interactions and incorporate MANF treatment for three experimental mouse models having undergone varying degrees of photoreceptor degeneration. Using MANF treatment levels as controls, we investigate optimal control results in the three mouse models. In addition, our numerical solutions match the experimentally observed surviving percentage of photoreceptors and our uncertainty and sensitivity analysis identifies significant parameters in the math model both with and without MANF treatment.

中文翻译：

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用MANF治疗感光细胞变性的最佳控制。

患色素性视网膜炎和与年龄相关的黄斑变性等疾病的人由于光感受器变性而导致视力下降，这是目前不可阻挡和不可逆的。目前尚无与光感受器变性有关的疾病的治疗方法。最近的实验工作表明，中脑星形胶质细胞衍生的神经营养因子（MANF）可以通过减少经历凋亡的细胞数量来减少神经元死亡，尤其是光感受器死亡。在这项工作中，我们建立在表示光感受器相互作用的现有常微分方程系统的基础上，并将MANF处理用于三种经历了不同程度的光感受器退化的实验小鼠模型。使用MANF治疗水平作为对照，我们研究了三种鼠标模型中的最佳控制结果。此外，我们的数值解决方案与实验观察到的感光体的存活百分比相匹配，并且我们的不确定性和灵敏度分析确定了经过或未经过MANF处理的数学模型中的重要参数。