© 2023 Department of Mathematics, Modibbo Adama University. All right reserved ∗ Corresponding author. Tel.: +2348061263095 E-mail addresses: lubem.kwaghkor@naub.edu.ng (Kwaghkor, L.M.) http://doi.org/10.62054/ijdm/0101.13 A Nonlinear Mathematical Model for the Effect of Diabetes Population on a Community Lubem M. Kwaghkor a* , Samuel Adamu a , Mohammed Abdullahi a and Suleiman Muhammad a a Department of Mathematics, Nigerian Army University Biu, Borno State, Nigeria 1. Introduction Excessive blood sugar causes Diabetes Mellitus (DM), a metabolic disease known as the "silent killer" in medical terminology (World Health Organization, 2023). Diabetes is a historical term from Greek that means "syphon." The word originally meant the act of passing water, or urine, via a syphon. The Latin term "mellitus" means "sweetened" or "like honey." When combined, the word "Diabetes Mellitus" literally referred to a medical condition where a person consistently passed sweetened urine (Kwaghkor and Luga, 2016). Polyurea (frequent urination), polydipsia (feeling thirstier), and polyphagia (feeling hungrier) are a few of the symptoms of diabetes that people may encounter. Many methods exist for diagnosing diabetes, but the most often used one is the glucose tolerance test (GTT), which measures the patient's blood glucose during a fast (World Health Organization, 1994). The three main types of diabetes are (1) Type 1 diabetes, which develops when your pancreas is unable to produce insulin, (2) type 2 diabetes, which develops when your pancreas doesn't produce enough insulin or when your body isn't using the insulin well and (3) gestational diabetes, which develops during pregnancy and typically goes away after the baby is delivered (Kwaghkor and Luga, 2016; Yadav & Maya, 2020; Kwaghkor et al., 2022). A bad lifestyle leads a susceptible individual to become a diabetic. Diabetes is primarily caused by unhealthy lifestyles, which include inactivity, inconsistent eating patterns, and other bad behaviours (Widyaningsih et al., 2018). Individuals with diabetes who have difficulties are typically already aware of how fragile their physical state is; in contrast, diabetics who do not experience complications have not been able to continue their lifestyle, particularly those who are undiagnosed. Diabetics without difficulties typically lead unhealthy lifestyles in day-to- day activities. Lifestyle "transmission" can occur when healthy people connect with diabetics who maintain unhealthy lifestyles. The effect of "transmission" of a lifestyle is occurrence. Diabetic prevalence rises with incidence (Hill et al., 2013; Widyaningsih et al., 2018; American Diabetes Association, 2018, 2020). In the field of natural sciences and engineering, mathematical models have been used for understanding complicated phenomena throughout time (Alkali et al., 2023; Kwaghkor et al., 2018; Kwaghkor et al., 2019; Kwaghkor et al., 2021; Orapine et al., 2023. Numerous studies have been conducted on the dynamics of diabetes. Diabetes Complication (DC) Model has provided a mathematical model to explain the prevalence of diabetics (Widyaningsih et al., 2018). The DC model was first introduced by Boutayeb et al. (2004) to find out how many changes of diabetics without complications (D) and diabetics with complications (C). The DC model was developed into a susceptible diabetes complication (SDC) model (Hill et al., 2013). As contained in Widyaningsih et al. (2018), the specific set of susceptible people led to this extension. In addition to the existing works, Modu et A R T I C L E I N F O Article history: Received 31 January 2024 Received in revised form 01 March 2024 Accepted 05 March 2024 Keywords: Diabetes, Mathematical Model, Simulation, Stability. MSC 2020 Subject classification: 34A34, 92B05, 92-10 A B S T R A C T This work presents a compartmental-based mathematical model of susceptible, diabetes without complications, diabetes with minor and major complications to study the effect of diabetes population on the population dynamics of a community. The model is a system of four nonlinear differential equations of first order. The solution of the model was found to exist and is positive by positivity analysis using a contradiction method. The diabetes-free and the diabetes-endemic equilibrium points were also found to be locally asymptotically stable using the Routh-Hurwitz Stability Criterion for a degree n-polynomial. The numerical simulation of the model was carried out using various scenarios and the results show that diabetes population in a community has great effect on the population dynamics of the community either positively or negatively. The results here represent a real-life scenario thereby making the proposed model realistic. INTERNATIONAL JOURNAL OF DEVELOPMENT MATHEMATICS journal homepage: https://ijdm.org.ng/index.php/Journals International Journal of Development Mathematics Vol 1 Issue 1 Page No. 172 - 185 ISSN: 3026-8656 (Print) | 3026-8699 (Online)