Development and Analysis of a Mathematical Model for the Population Dynamics of Diabetes Mellitus During Pregnancy

Diabetes Mellitus (DM) during pregnancy is a major global public health burden with various adverse outcomes. In this paper, a mathematical model of the population dynamics of DM during pregnancy is developed and analyzed. Four independent variables have been considered, namely the numbers of nonpregnancy nondiabetic women, diabetic nonpregnant women, diabetic pregnant women and diabetic pregnant women with complication. The model is described by a system of ordinary differential equations. The stability of the equilibrium point is analyzed using Routh-Hurwitz criteria. The model is numerically simulated using MATLAB to verify the analytical results. The model has only one nonnegative equilibrium point which is asymptotically stable. The equilibrium solution is further investigated using simple sensitivity analysis. The results of simple sensitivity analysis of the equilibrium solution suggest the key parameters of the model. The equilibrium point of the model indicates the influential parameters that can be controlled to address the issue.