Modelling the Effect of the Exposure to Perfluorooctanoate (PFOA) and Perfluorooctane Sulfonate (PFOS) on Thyroid Homeostasis

Thyroid homeostasis is crucial for the human body. The imbalance of thyroid homeostasis might cause diseases such as hypothyroidism. Humans are exposed to PFOS/PFOA frequently since they have been used in various industrial products. As reported that PFOS/PFOA increase the metabolic clearance rate of thyroid hormones, we then develop a mathematical model in terms of a system of differential equations to investigate thyroid homeostasis based on the changes in the levels of thyrotropin-releasing hormone, thyroid-stimulating hormone and thyroid hormones when the effect of the exposure to PFOS and PFOA is also incorporated as well. The geometric singular perturbation technique is then employed to identify the possible dynamic behaviours obtained from the model. Numerical investigations are also presented to illustrate the results from theoretical analysis. Both theoretical and numerical results imply that a periodic behaviour that has been observed clinically in the pulsatile secretions of thyroid hormones, thyroid-stimulating hormone and thyrotropin-releasing hormone could be obtained from our model. In addition, the numerical experiment also shows that the levels of thyroid hormones and thyroid-stimulating hormone for the case when there is the effect of exposure to PFOS and PROA are lower than those of the case when there is no effect of the exposure to PFOS and PFOA which might lead to the imbalance of thyroid homeostasis.