Mathematical study of polycystic ovarian syndrome disease including medication treatment mechanism for infertility in women

Maryam Batool; Muhammad Farman; Aqeel Ahmad; Kottakkaran Sooppy Nisar; Maryam Batool; Muhammad Farman; Aqeel Ahmad; Kottakkaran Sooppy Nisar

doi:10.3934/publichealth.2024002

AIMS Public Health

2024, Volume 11, Issue 1: 19-35. doi: 10.3934/publichealth.2024002

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Research article

Mathematical study of polycystic ovarian syndrome disease including medication treatment mechanism for infertility in women

1.
Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan
2.
Department of Computer Science and Mathematics, Lebanese American University, 1107-2020, Beirut, Lebanon
3.
Faculty of Arts and science, Mathematical research center, Near East University, Northern Cyprus, Turkey
4.
Department of Mathematics, Ghazi University, DG Khan, Pakistan
5.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia

Received: 09 September 2023 Accepted: 16 November 2023 Published: 04 December 2023

Among women of reproductive age, PCOS (polycystic ovarian syndrome) is one of the most prevalent endocrine illnesses. In addition to decreasing female fertility, this condition raises the risk of cardiovascular disease, diabetes, dyslipidemia, obesity, psychiatric disorders and other illnesses. In this paper, we constructed a fractional order model for polycystic ovarian syndrome by using a novel approach with the memory effect of a fractional operator. The study population was divided into four groups for this reason: Women who are at risk for infertility, PCOS sufferers, infertile women receiving therapy (gonadotropin and clomiphene citrate), and improved infertile women. We derived the basic reproductive number, and by utilizing the Jacobian matrix and the Routh-Hurwitz stability criterion, it can be shown that the free and endemic equilibrium points are both locally stable. Using a two-step Lagrange polynomial, solutions were generated in the generalized form of the power law kernel in order to explore the influence of the fractional operator with numerical simulations, which shows the impact of the sickness on women due to the effect of different parameters involved.
- polycystic ovary syndrome,
- boundedness,
- uniqueness,
- reproductive number,
- stability
Citation: Maryam Batool, Muhammad Farman, Aqeel Ahmad, Kottakkaran Sooppy Nisar. Mathematical study of polycystic ovarian syndrome disease including medication treatment mechanism for infertility in women[J]. AIMS Public Health, 2024, 11(1): 19-35. doi: 10.3934/publichealth.2024002

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Abstract

Among women of reproductive age, PCOS (polycystic ovarian syndrome) is one of the most prevalent endocrine illnesses. In addition to decreasing female fertility, this condition raises the risk of cardiovascular disease, diabetes, dyslipidemia, obesity, psychiatric disorders and other illnesses. In this paper, we constructed a fractional order model for polycystic ovarian syndrome by using a novel approach with the memory effect of a fractional operator. The study population was divided into four groups for this reason: Women who are at risk for infertility, PCOS sufferers, infertile women receiving therapy (gonadotropin and clomiphene citrate), and improved infertile women. We derived the basic reproductive number, and by utilizing the Jacobian matrix and the Routh-Hurwitz stability criterion, it can be shown that the free and endemic equilibrium points are both locally stable. Using a two-step Lagrange polynomial, solutions were generated in the generalized form of the power law kernel in order to explore the influence of the fractional operator with numerical simulations, which shows the impact of the sickness on women due to the effect of different parameters involved.

Acknowledgments

This study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2023/R/1444).

Conflict of interest

The authors declare no conflict of interest.

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