Proposal for mathematical modelling of the interplay between reproduction and stress

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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.