Diabetes is a chronic disease in which the body is unable to convert the excess sugar into a useable form. It is chronic disease that is fast becoming a menace in the Kenyan communities. In this study, the response of the complicated diabetic cases is examined under a constrained hospitalisation setting. The mathematical model is formulated by incorporating the carrying capacity and the per capita hospitalization rate. The models are numerically solved in MATLAB using the explicit Runge-Kutta (4, 5) technique, and the results are shown as graphs. The findings suggest that improving the quality of life in the susceptible class will result in an increase in the susceptible class and a decrease in diabetes cases. Increasing the proportion of diabetics who seek treatment each month leads to an increase in the number of people admitted to the hospital. Increasing carrying capacity reduces the number of hospitalized people.
Cite this paper
Andima, R. N. , Mutuku, W. N. , Farai, N. , Awuor, K. and Oke, A. S. (2022). Mathematical Modelling of Diabetes under a Constrained Hospitalisation Resources. Open Access Library Journal, 9, e9371. doi: http://dx.doi.org/10.4236/oalib.1109371.
Boutayeb, W., Lamlili, M.E.N., Boutayeb, A. and Derouich, M. (2014) Mathematical Modelling and Simulation of β-Cell Mass, Insulin and Glucose Dynamics: Effect of Genetic Predisposition to Diabetes. Journal of Biomedical Science and Engineering, 7, 330-342. https://doi.org/10.4236/jbise.2014.76035
Abdul Basith Khan, M., Hashim, M., Jawad, J.K.K., Devi Govender, R., Mustafa, H. and Al Kaabi, J. (2019) Epidemiology of Type 2 Diabetes—Global Burden of Disease and Forecasted Trends. Journal of Epidemiology and Global Health, 10, 107-111.
https://doi.org/10.2991/jegh.k.191028.001
Guariguata, L., Whiting, D.R., Hambleton, I., Beagley, J., Linnenkamp, U. and Shaw, J.E. (2014) Global Estimates of Diabetes Prevalence for 2013 and Projections for 2035. Diabetes Research and Clinical Practice, 103, 137-149.
https://doi.org/10.1016/j.diabres.2013.11.002
Ngugi, H.N., Mutuku, F.M., Ndenga, B.A., Musunzaji, P.S., Mbakaya, J.O., Aswani, P., Irungu, L.W., Mukoko, D., Vulule, J., Kitron, U. and LaBeaud, A.D. (2017) Characterization and Productivity Profiles of Aedes aegypti (L.) Breeding Habitats across Rural and Urban Landscapes in Western and Coastal Kenya. Parasites & Vectors, 10, Article No. 331. https://doi.org/10.1186/s13071-017-2271-9
Otieno, P.O., Kiroro, F., Runyenje, C. and Kamau, P. (2021) Unmet Need for Primary Healthcare and Associated Individual and Household-Level Factors in Kenya: Results from a National Survey. BMJ Open, 11, e041032.
https://doi.org/10.1136/bmjopen-2020-041032
Boutayeb, A., Twizell, E.H., Achouayb, K. and Chetouani, A. (2004) A Mathematical Model for the Burden of Diabetes and Its Complications. BioMedical Engineering Online, 3, Article No. 20. https://doi.org/10.1186/1475-925X-3-20
Li, J.X., Kuang, Y. and Mason, C.C. (2006) Modeling the Glucose-Insulin Regulatory System and Ultradian Insulin Secretory Oscillations with Two Explicit Time Delays. Journal of Theoretical Biology, 242, 722-735.
https://doi.org/10.1016/j.jtbi.2006.04.002
Zhang, J.H., Jia, J.W. and Song, X.Y. (2014) Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function. The Scientific World Journal, 2014, Article ID: 910421. https://doi.org/10.1155/2014/910421
Karachaliou, F., Simatos, G. and Simatou, A. (2020) The Challenges in the Development of Diabetes Prevention and Care Models in Low-Income Settings. Frontiers in Endocrinology, 11, Article No. 518. https://doi.org/10.3389/fendo.2020.00518
Demissie Regassa, L. and Assefa, T. (2021) Magnitude and Predictors of Hospital Admission, Readmission, and Length of Stay among Patients with Type 2 Diabetes at Public Hospitals of Eastern Ethiopia: A Retrospective Cohort Study. BMC Endocrine Disorders, 21, Article No. 74. https://doi.org/10.1186/s12902-021-00744-3
Olabanji Aye, P., Adefemi Adeyemo, K., Samuel Oke, A. and Evelyn Omotoye, A. (2021) Analysis of Mathematical Model for the Dynamics of Diabetes Mellitus and Its Complications. Applied Mathematics and Computational Intelligence, 10, 57-77.
Al Ali, H., Daneshkhah, A., Boutayeb, A. and Mukandavire, Z. (2022) Examining Type 1 Diabetes Mathematical Models Using Experimental Data. International Journal of Environmental Research and Public Health, 19, Article No. 737.
https://doi.org/10.3390/ijerph19020737
Nasir, H. and Daud, A.A.M. (2022) Population Models of Diabetes Mellitus by Ordinary Differential Equations: A Review. Mathematical Population Studies, 29, 95-127.
Jacqueline, H. (2013) Understanding the Social Factors That Contribute to Diabetes: A Means to Informing Health Care and Social Policies for the Chronically Ill. The Permanente Journal, 17, 67-72. https://doi.org/10.7812/TPP/12-099
Abdelrazec, A., Belair, J., Shan, C.H. and Zhu, H.P. (2016) Modeling the Spread and Control of Dengue with Limited Public Health Resources. Mathematical Biosciences, 271, 136-145. https://doi.org/10.1016/j.mbs.2015.11.004
Bada, O.I., Oke, A.S., Mutuku, W.N. and Aye, P.O. (2020) Analysis of the Dynamics of SI-SI-SEIR Avian Influenza A(H7N9) Epidemic Model with Re-Infection. Earthline Journal of Mathematical Sciences, 5, 43-73.
https://doi.org/10.34198/ejms.5121.4373
Oke, A.S., Bada, O.I., Rasaq, G. and Adodo, V. (2021) Mathematical Analysis of the Dynamics of COVID-19 in Africa under the Influence of Asymptomatic Cases and Re-Infection. Mathematical Methods in the Applied Sciences, 45, 137-149.
https://doi.org/10.1002/mma.7769
Ul Abadin Zafar, Z., Hussain, M.T., Inc, M., Baleanu, D., Almohsen, B., Oke, A.S. and Javeed, S. (2022) Fractional-Order Dynamics of Human Papillomavirus. Results in Physics, 34, Article ID: 105281. https://doi.org/10.1016/j.rinp.2022.105281
Oke, A.S. and Bada, O.I. (2019) Analysis of the Dynamics of Avian Influenza A(H7N9) Epidemic Model with Re-Infection. Open Journal of Mathematical Sciences, 3, 417-432.
https://doi.org/10.30538/oms2019.0084
Oke, A. (2017) Convergence of Differential Transform Method for Ordinary Differential Equations. Journal of Advances in Mathematics and Computer Science, 24, 1-17. https://doi.org/10.9734/JAMCS/2017/36489
Juma, B.A., Oke, A.S., Mutuku, W.N., Ariwayo, A.G. and Ouru, O.J. (2022) Dynamics of Williamson Fluid over an Inclined Surface Subject to Coriolis and Lorentz Forces. Engineering and Applied Science Letters, 5, 37-46.
Owuor, M.O., Otengah, W.A.P., Onyango, E.A. and Oure Oyoo, E. (2021) Patterns of Influence of Diabetics’ Integrating Healthcare-Seeking Behaviours on Diabetes Management in Rongo Sub County, Migori County, Kenya. African Journal of Health Sciences, 34, 498-511.
