In this work, we predict the prevalence of type 2 diabetes among adult Rwandan people. We used the Metropolis-Hasting method that involved calculating the metropolis ratio. The data are those reported by World Health Organiation in 2015. Considering Suffering from diabetes, Overweight, Obesity, Dead and other subject as states of mathematical model, the transition matrix whose elements are probabilities is generated using Metropolis-Hasting sampling. The numerical results show that the prevalence of type 2 diabetes increases from 2.8% in 2015 to reach 12.65% in 2020 and to 22.59% in 2025. Therefore, this indicates the urgent need of prevention by Rwandan health decision makers who have to play their crucial role in encouraging for example physical activity, regular checkups and sensitization of the masses. Keywords: Non communicable diseases; type 2 diabetes; Markov Chain Monte Carlo method; Metropolis-Hasting method; Transition probabilities.rds:

In Rwanda, the prevalence of hypertension was 15.3% in 2015. At present, there are no accurate predictions of the prevalence of hypertension and its trend over time in Rwanda to assist decision makers in making plans for prevention and more effective interventions. This study used the Gibbs sampling method in combination with the Markov Chain Monte Carlo approach to predict the prevalence of hypertension and its associated risk factors in Rwanda over a period of ten years. The data were from World Health Organization (WHO) reports. The findings showed that the prevalence of hypertension is estimated to reach 17.82% in 2025, with tobacco use, being overweight or obese, and other risk factors having a respective prevalence of 26.26%, 17.13%, 4.80%, and 33.99%, which shows the increase and, therefore, measures for prevention to be taken. Therefore, to prevent and reduce the prevalence of this disease, the government of Rwanda should take appropriate measures to promote a balanced diet and physical exercise.

This study uses the Hamiltonian Monte Carlo (HMC) and Gibbs methods to predict of Hypertension, Tobacco use, Overweight and Obesity. The methods were applied on data from World Health Organization report 2015. Corresponding stochastic matrices were generated and utilized in the prediction and comparison of the two sampling methods. Using Python and the NumPy library, the state vectors for these conditions were predicted, with the results showing slight variations between the two methods. In the long term, both methods converged to stable probability distributions, indicating steady-state values for each condition. HMC predicted long-term prevalence of 17.48% for hypertension, 17.5% for tobacco use, 17.56% of Overweight, 14.36% of Obesity and 33.1% for "Other subjects, while Gibbs predicted 17.82%, 26.27%, 17.13%, 4.80% and 33.98%, respectively. Additionally, Gibbs was found to outperform HMC in terms of error metrics, with lower values for Mean Squared Error (MSE), Mean Absolute Error (MAE), indicating better prediction accuracy. This analysis aids practitioners in selecting the most suitable method based on specific problem characteristics and dataset complexities.