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

被引：19
作者：
Auni Aslah Mat Daud [1 ]
Toh C.Q. [1 ]
Saidun S. [2 ]
机构：
[1] School of Informatics and Applied Mathematics, University Malaysia Terengganu, Kuala Nerus, Terengganu
[2] Independent Researcher (MB BCh BAO LRCP&SI, M.Sc), Kuala Nerus, Terengganu
来源：
Mathematical Models and Computer Simulations | 2020年 / 12卷 / 4期
关键词：
diabetes mellitus; mathematical models; pregnancy; sensitivity analysis; stability analysis;
D O I：
10.1134/S2070048220040067
中图分类号：
学科分类号：
摘要：
Abstract: 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. © 2020, Pleiades Publishing, Ltd.
引用
收藏
页码：620 / 630
页数：10
相关论文
共 31 条
  • [1] Diagnostic Criteria and Classification of Hyperglycemia First Detected in Pregnancy, (2013)
  • [2] Umpierrez G.E., Murphy M.B., Kitabchi A.E., Diabetic ketoacidosis and the hyperglycemic hyperosmolar syndrome, Diabetes Spectr., 15, pp. 28-36, (2002)
  • [3] Fowler M.J., Microvascular and macrovascular complications of diabetes, Clin. Diabetes., 26, pp. 77-82, (2008)
  • [4] Negrato C.A., Mattar R., Gomes M.B., Adverse pregnancy outcomes in women with diabetes, Diabetol. Metab. Syndr., 4, (2012)
  • [5] Diabetes Atlas, (2009)
  • [6] Diabetes Atlas, (2015)
  • [7] Boutayeb A., Derouich M., Age structured models for diabetes in East Morocco, Math Comput Simul., 58, pp. 215-229, (2002)
  • [8] Boutayeb A., Achouayb K., Chetouani A., A mathematical model for the burden of diabetes and its complications, Biomed. Eng. Online, 3, pp. 1-8, (2004)
  • [9] Boutayeb A., Abdelaziz C., A nonlinear population model of diabetes mellitus, J. Appl. Math. Comput., 21, pp. 127-139, (2006)
  • [10] Boutayeb A., Chetouani A., A population model of diabetes and pre-diabetes, Int. J. Comput., 84, pp. 57-66, (2007)
1234