# 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.

## Keywords

Mathematical model Thyroid disorders Equilibrium Stability analysis Routh Hurwitz criteria## Notes

### Acknowledgements

This research is funded by the Ministry of Higher Education, Government of Malaysia under the Research Acculturation Grant Scheme (RAGS 57108). The results of the study were partially presented during The 4th International Conference on Mathematical Sciences (ICMS4) on November 15–17, 2016 at Palm Garden Hotel, Putrajaya, Malaysia and the SEAMS School on Dynamical Systems and Bifurcation Analysis (DySBA)on August 6–13, 2018 at Universiti Sains Malaysia (USM), Penang, Malaysia.

Finally, I would like to express my gratitude to Salilah Saidun and Kritika Manimaran, who have contributed in this study.

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