Proposal for mathematical modelling of the interplay between reproduction and stress

妇女的性健康和生殖健康是一个对健康的生活方式和总体福祉具有重大影响的领域。压力是干扰内分泌系统的一个因素，干扰激素的产生。它可能会导致不规则的时期，影响生育能力。由于过去的社会偏见，这个问题没有得到广泛的研究，特别是从数学建模和分析的角度。这在科学文献中留下了空白。缩小这一差距有可能大大有助于改善妇女的整体健康状况。因此，本研究的目的是开发数学工具和技术来研究压力对女性生殖系统的影响，如月经周期的扰动以及不孕症。特别是，我们的最终目标是利用实验和临床知识和发现来建立一个数学模型，该模型考虑了压力因素（如剧烈运动和精神障碍）对周期的影响。理想情况下，我们希望同时考虑急性和慢性压力条件，并开发一个理论框架，该框架可以应用于整个生命周期，从初潮到更年期以及体外受精（IVF）治疗等生育治疗的情况。该模型将基于微分方程，描述了形成下丘脑-垂体-性腺（HPG）和（下丘脑-垂体-肾上腺）HPA轴的各种生理区室中的激素动力学。在治疗的情况下，如试管婴儿，我们将考虑药代动力学和药效学建模，以描述各种激素和神经肽的管理沿着他们的影响。我们将应用定性的理论，如分歧分析，以及定量研究模型中的参数敏感性。这种方法在以前的研究中没有采用过，将是完全新颖的。具体来说，在拟议的博士项目中，我们将建立在耦合振荡器模型来表示女性月经周期内的动态。研究计划如下：-从生物学角度检查HPA和HPG轴，以更好地了解它们在女性体内的控制机制，并将其纳入建模;-进行参数的分叉和敏感性分析。因此，修改模型并检查其可变性;-根据实验和临床数据测试模型的输出，以验证其有效性;-将不同压力水平和时间对生殖系统的影响关联起来。

Women's sexual and reproductive health is an area that has significant implications for healthy lifestyle and overall wellbeing. Stress is a factor that interfere with endocrine systems, disturbing hormone production. It may cause irregular periods and affect fertility. Due to societal prejudices in the past the subject has not been studied widely, especially from the perspective of mathematical modelling and analysis. This leaves a gap in the scientific literature. Bridging this gap has the potential to contribute greatly to improving women's health as a whole. Accordingly, the aim of this research is to develop mathematical tools and techniques to study the effects of stress on female reproductive system, such as perturbations to menstrual cycle as well as infertility. In particular, our ultimate aim is to use experimental and clinical knowledge and findings to inform a mathematical model that takes into account the effects of stress factors, such as strenuous exercise and mental disorders, on the cycle. Ideally, we would like to consider both, acute and chronic stress conditions, and develop a theoretical framework that could be applied across the life span, from menarche to menopause as well as in the case of fertility treatments such as In vitro fertilisation (IVF) treatments.The model will be based on differential equations, describing the hormones' dynamics in various physiological compartments forming the Hypothalamic-Pituitary-Gonadal (HPG) and (Hypothalamic-Pituitary-Adrenal) HPA axes. In the case of treatments, such as IVF, we will consider pharmacokinetic and pharmacodynamic modelling to describe the administration of various hormones and neuropeptides along with their effects. We will apply qualitative theory such as bifurcation analysis as well as study quantitatively parameter sensitivity in the model. Such approach has not been taken in previous research and will be completely novel. Specifically, in the proposed PhD project, we will build on the coupled oscillators model to represent the dynamics within women's menstrual cycle. The research plan is the following: - Examine the HPA and HPG axes from the biological perspective to better understand their governing mechanisms within female body and incorporate into the modelling;- Perform the bifurcation and sensitivity analysis of the parameters. Consequently, modifying the model and checking its variability;- Test the model's outputs against experimental and clinical data to verify its validity;- Correlate the effects of different stress levels and timings on the reproductive system.