Analysis Of A Mathematical Model For The Population Dynamics Of Women With Gestational Diabetes

Gestational Diabetes Mellitus (GDM) is a condition that causes high blood sugar levels in pregnant women, with an observed increased risk of pregnancy complications and developing Diabetes Mellitus (DM) post-pregnancy. Approximately 10.5 pregnancies per 100 deliveries were affected by GDM in 2020, according to the CDC, representing an increase from 4.5 pregnancies per 100 deliveries in 2000. Overall, it affects 5-9% of pregnant women annually in the US. Despite its prevalence and increasing risk for DM, little mathematical modeling has been done to understand the population flow of women diagnosed with GDM into the diabetic population. Understanding the dynamics of a non-diabetic non-pregnant population into a newly diabetic population may serve as a foundation for researching effective interventions at the population level, before, during, and after pregnancy to reduce both the incidence of GDM and DM. We developed a model of pregnant women, focusing exclusively on women without diabetes who develop GDM. Using primarily CDC data to estimate initial parameter values, and assuming a fixed population growth rate, we observed the non-diabetic population converges to roughly 55.5 million and the diabetic population to approximately 470 thousand. The model also captures the dynamic of pregnant women who develop Gestational Diabetes-related complications, and the increased risk factor of developing DM from previous GDM. Equilibrium analysis was conducted to determine the steady state of the solution to the system of ODEs, and we were able to show the positivity and uniform boundedness of the solution. Additionally, sensitivity analysis was conducted on uncertain parameters.