Modeling the diagnosis and control infertility couples with different factors

Abstract

Background: There are different etiologies of infertility. Poly Cystic Ovarian Syndrome (PCOS) is a leading cause of infertility among women, and the male factor accounts for about 50 % of the total number of infertile couples. As with various etiologies, various treatments are required. Choosing the most suitable procedure of Assisted Reproductive Technology (ART) for individuals is of great importance. Therefore, mathematical models are needed to estimate the success rate of ART for every individual and to determine which treatment suits the best for each couple. Objective:In this study, we aim to present a new dynamic model that can predict the success rate of ART models for each base on the etiology of their infertility, lab tests, and clinical findings. Materials and Methods For this purpose, 502 participants were recruited and evaluated based on their BMI, AMH levels, the number of transferred embryos, and the etiology of infertility (PCOS, male factor, or both). For this purpose, the community is divided into eight classes: infertile susceptible couples, couples with the cause of infertility PCOS, male factor or both, couples with embryo quality A, B, and C, coupled with the positive βHCG test, couples with the positive result of clinical pregnancy and fertile couples. Results: Our dynamic models evaluate the success rate of ART in our subgroups considering all of the effective factors such as BMI, AMH level, number of transferred embryos, and the etiology of infertility. We have found that (BMI > 30 kg/m2) and low AMH levels (< 3.5ng/mL) indicate lower success rates. Moreover, ICSI was more promising for all the underlying etiologies of male factor, PCOS, or both. Conclusion: In conclusion, our new mathematical model is presented to investigate the dynamics and diagnose the cause of infertility in couples. It is shown that the equilibrium point free of disease is asymptotically stable. In this system, backward bifurcation occurs. When backward bifurcation occurs, we must reduce the primary reproduction number to less than one to eradicate the disease. In our system, we see that the factors that cause the reduction of the primary reproduction number are the factors used to eliminate infertility (the essential reproduction R0 depends on the recovery rate in infertile couples with positive clinical pregnancy (ξ). Therefore, backward bifurcation depends on the possibility of recovery. As the rate of recovery increases, the primary reproduction number R0 decrease and controls couple’s infertility. When male factors and treatment methods cause infertility are IVF and IV F&ICSI, we demonstrate that there is no Hopf bifurcation, i.e., no periodic orbit emerges or vanishes due to a change in the stability of a fixed point.