Mathematical Modeling and Stability Analysis of Population Dynamics

Abstract

This study provides a brief introduction of important terminologies and methodologies in the mathematical modelling and stability analysis of the population dynamics. As an example, a mathematical model of population dynamics for thyroid disorder during pregnancy is developed and analysed. The disorders are the second most common endocrine disorders among women in childbearing age, where inadequate or excessive amount of thyroid hormones are produced due to various causes. Thyroid disorders during pregnancy and postpartum can be divided into three types: hyperthyroidism, hypothyroidism and postpartum thyroiditis. They may lead to numerous complications to both mothers and foetuses, such as heart failure, pre-eclampsia, miscarriage, premature birth, and perinatal mortality. The model is described using a system of first order linear ordinary differential equations. Its stability is studied using Routh-Hurwitz criteria. It is found that the model has only one non-negative equilibrium, which is locally asymptotically stable.