“AI-MCMC” for the parametric analysis of the hormonal therapy of cancer

Over the past few decades, there have been significant advances in clinical, experimental, and theoretical frameworks for understanding cancer cells’ complexities and their interactions with the immune system. Breast cancer progression is associated with estrogen signalling and the estrogen receptor (ER), and the majority of human breast cancers originate as estrogen-dependent. Additionally, mounting data indicate that ER signalling is complicated, comprising both coregulatory proteins and extranuclear actions. This paper deals with a mathematical model of the tumour-immune response incorporating anti-tumour cytokines and estrogen. The designed model is formulated based on a detailed phenomenological description of the kinetic theory of tumour, immune system and estrogen. The experimental studies are used to estimate the model's parameters, and the Lyapunov approach is used to determine the stability of equilibrium points. Monte-Carlo-Markov-Chain (MCMC) methods have been used extensively to deal with the nonlinear fractals, and in the field of artificial intelligence for the evaluation of the parameters. In this manuscript, the sensitivity analysis is conducted to assess the parameters’ uncertainty with the aid of AI-MCMC toolbox. The numerical simulations of the model support the results of clinical studies. Furthermore, we discuss the pharmacokinetics and pharmacodynamics of chemotherapy and introduce cellular immunotherapy as treatments for boosting immune cells to fight against tumours. Our findings seem to indicate that the proposed model is a strong candidate for studying the dynamics of estrogen, and it helps in the provision of complex interactions of estrogen with breast tumours and immune cells.