Mathematical Regression Models for Analyzing and Forecasting Diabetes prevalence in Oman

Diabetes mellitus has a significant impact on people's lives and drugs financial burden. On the other hand, diabetes also has substantial economic effects on countries and national health systems. Most countries spend between 5% and 20% of their total health expenditures on diabetes. This is due to the increased use of health services, lack of productivity, and the long-term demand for complications associated with diabetes, such as kidney failure, blindness, and heart problems. This is why diabetes poses a significant challenge to healthcare systems and hinders sustainable economic development. This work is concerned with proposing mathematical models characterized by accuracy and ease in predicting the number of diabetics type 2 in the Sultanate of Oman. By analyzing the proposed mathematical models of the current work (1, 2, and 3), it was found that the proposed mathematical model in Equation 6 can accurately predict the number of diabetics in Oman up to 2050. In order to test the model's accuracy and validity, we revised it with actual data. The results prove the accuracy of the proposed model in predicting future data of 99%. Lastly, several recommendations were recorded that could help to reduce the prevalence of diabetes type 2 in Oman. 5% with PDR. Besides, there no significant relationship between acquiring DR and the gender of the patient. Awad (Awad et al., 2020) proposed an age‐structured mathematical model to analyze and forecast type 2 diabetes mellitus risk factors and their cost in Oman between 1990 and 2050. The results show an increased prevalence rate from 15.2% in 2020 to 23.8% in 2050. Also, it showed a high health expenditure for Type 2 diabetes mellitus with 28.8% and the obesity cases with 71.4%.


Introduction
The most prevalent health problems, such as chronic diseases, especially cancer, diabetes, and cardiovascular diseases, are among the most significant challenges to modern societies regarding the high number of deaths and their economic cost . Chronic illness means persistent or recurrent disease, usually affecting a person for three months or more and can be prevented and reduced risk by following medical advice (CDC, 2015). The term chronic diseases apply to conditions that can be treated but may take a long time. Patients with chronic diseases need intensive care in health care clinics to teach patients to practice rehabilitation methods.
Patients with chronic diseases need to visit the doctor periodically for treatments and medical tests, which causes life-long discomfort. Therefore, health care homes offer different courses to reduce the effects of symptoms caused by chronic diseases, both healthily and psychologically (Alwan, 2014;Abusham & Zaabi, 2021).
Diabetes defines as a chronic disease that occurs when the body cannot use or produce enough insulin. The International Diabetes Federation (IDF) reports that diabetes will be the healthcare challenges in the 21st century as shown in Figure 1. The total losses gross domestic product (GDP) worldwide in the period 2011-2030 is 1.7 trillion US$. The highest rate was observed in high-income countries US$ 900 billion (WHO, 2016).
An estimated average cost of USD1,622 to USD2,886 per person with diabetes need for treating and managing the disease in 2015 as shown in Figure 2.
Diabetes affects individuals, families, businesses, and society as a whole. Among the world's 10 highest for the prevalence of diabetes, there are six Arabic countries named Egypt, United Arab Emirates (UAE), Bahrain, Kuwait, Oman and the Saudi Arabia. The annual mortality rate per 100,000 people from diabetes mellitus in Oman has increased by 21.3% since 1990, an average of 0.9% a year (IDF, 2019). The World Health Organization's current reports indicate that 60% of the number of deaths in the Arab Gulf countries results from chronic diseases, making it a large and growing problem and finding solutions quickly (IDF, 2020). Figure 3 displays the number of deaths due to non-communicable diseases in Gulf Cooperation Council in 2016. Figure   4 presents the comparison of prevalence of diabetes in Gulf Cooperation Council in 2015 and the predicted rate in 2040. The figure shows that Oman has the lowest prevalence rate of 9.9% and will be reached 17.2 % in 2040.
While LAS has the highest prevalence rate of 17.6 % and will be reached 22.9 % in 2040 Statista, (2021).

Diabetes Status in Oman
The  Figure 4 shows the annual mortality rate per 1000 people from diabetes mellitus in Oman in the period 2008-2018. Figure 4 illustrates that the rate of death related to diabetes is increased over time. Therefore, the government must to take series actions and do more research to specify the factors affecting the prevalence of diabetes.

Forecasting Models Techniques
Regression methods focus on extrapolating data, which describes annual changes in data. However, predicting such differences in diabetes, for example, is necessary for the decision-maker and medical institutions to take the measures The formula for a simple linear regression is: where y is the predicted value of the dependent variable (Y) and (x) is the value of the independent variable. B 0 is the intercept, and B 1 is the regression coefficient. And e is the error (differences between the experimental and estimated data).
Two main factors are used to validate the predicated results including the coefficient of determine (R-squared) and Adjusted R-squared (Yousif, 2011). R-squared (R 2 ) is a statistical pattern representing how the predicted data fits the experimental data in a regression model, which is computed as in equation 2. The preferred regression model that gets a value of R 2 closer to 1 (Yousif, 2015).
where yi is the actual output data, and fi is the expected (predicted) data, and ӯi is the arithmetic mean value of the real data targets.
Adjusted R-squared determines how many data sets befall within the regression line, which is computer as in where n is the number of data sets, and k is the number of independent variables in the regression model.

Results and Discussions
The experimental data that we used is presented in Figure 5. We notice a steady increase in the number of people with diabetes over the years. Then different linear and non-linear regression models were deployed for examine the expected number of diabetes prevalence in the next 30 years. This will help to accurately calculate the health expenses and the required equipment, medical personnel, including number of parents and nurses, and the volume of shipments of needed medicines.
The first model is implemented using a linear regression model, which is achieved a R-squared equal to (0.7934) and Adjusted R² equal to0.7851. This model is computed as in equation 4. X is the number of diabetes patient on yearly based.

Model-1 = -3686+1.86398*Year
(4) Figure 6 shows the regression of number of patients based on the model in equation 4. Through Figure 6, we notice that the predictive data line fits the actual data, which indicates that the used equation can accurately and efficiently simulate future data for predicting the number of diabetic patients.
The second model is deployed based on a polynomial regression model of third degree, which is obtained a Rsquared equal to (0.7089). This model is computed as in equation 5. X is the number of diabetes patient on yearly based.
Model-2 = 0.0068x 3 -0.1591x 2 + 1.5842x + 30 (5)  The third model is deployed based on non-linear polynomial regression model, which is obtained a R-squared equal to (0.9778). This model is computed as in equation 6. X is the number of diabetes patient on yearly based.

Conclusion & recommendations
Diabetes has a significant impact on people's lives and the financial burden of medication. On the other hand, diabetes has substantial economic effects on countries and national health systems. Most countries spend between 5% and 20% of their total health expenditures on diabetes. In addition to the significant physical burden that diabetes places on individuals and their families due to the cost of insulin and other essential drugs, diabetes also has substantial economic impacts on countries and national health systems. This is due to the increased use of health services, lack of productivity, and the long-term demand for complications associated with diabetes, such as kidney failure, blindness, and heart problems. This is why diabetes poses a significant challenge to healthcare systems and hinders sustainable economic development.
This work is concerned with proposing mathematical models characterized by accuracy and ease in predicting the number of diabetics in the Sultanate of Oman.
Review and analysis of previous research and studies showed that there is a forced increase in the number of diabetic patients due to several reasons, including the following: • Lack of interest in performing exercise and walking for specific periods during the week.
• Lack of interest in knowing or following up the sick family history and taking the necessary precautions.
• Lack of attention to the quality of healthy foods suitable for the body.
• Exercising harmful activities to the body, such as smoking, is a catalyst for increasing diabetes.
By analyzing the mathematical models of the current work (1, 2, and 3), the proposed mathematical model in Equation 6 can predict the number of diabetics in Oman up to 2050. In order to test the model's accuracy and validity, we revised it with actual data. The results prove the accuracy of the proposed model in predicting future data of 99%.
Among the recommendations for current work: a) The results of the current work show that there is an urgent need for more community education to diagnose and manage all types of diabetes efficiently. The social robot could be used in educating the diabetes patients (Yousif, 2021).
b) Interest in knowing and following up the family's history accurately and continuously. Early diagnosis of type 2 diabetes can prevent or delay the long-term health complications of affected people.
c) Encouraging lifestyle changes that slow the rise of type 2 diabetes, for example, exercise regularly. This reduces the risk of obesity, which contributes to increasing the number of type 2 diabetes. d) Promoting the necessary behavioral change to prevent disease through awareness of the dangers of smoking is a catalyst in increasing diabetes.