Detecting the spread of pandemics will greatly reduce human and economic loss. Existing Epidemiological models used for coronavirus disease 2019 (COVID-19) prediction models are too slow and fail to capture epidemic development thoroughly. This research presents a Physics-based Machine Learning Architecture (PMLA) to improve the processing speed and accuracy of epidemic forecasting governed by susceptible–exposed–infected–recovered–deceased (SEIRD) model equations. The dynamics of the epidemic were extracted using Convolutional Neural Networks (CNN) and Deep Reinforcement Learning (Deep RL) from data simulated with Partial Differential Equations (PDEs). The PMLA accuracy is measured using mean squared error. The PMLA prediction model enhances the ability of health authorities to predict the spread of COVID-19 in real time efficiently and effectively.

Keywords: COVID-19, Convolutional Neural Networks, Deep Reinforcement Learning, Partial Differential Equations, Machine learning, Finite Element Method.

Population demographics provides grounds for forecasting due to complex nature of various editions of population figures. The accurate prediction of population demographics is pivotal for urban planning, resource allocation, and the development of effective policies.  In this paper, we utilize historical demographic data collected over time to forecast future demographic trends, enabling informed decision-making by local authorities and urban planners. The study begins by gathering and preprocessing a comprehensive dataset that encompasses various demographic variables, such as age, gender, income, education level, and occupation, among others. We employ Prophet, a robust forecasting tool, with diverse time series analysis methods. It examines historical demographic data, refining models using Prophet’s flexibility and traditional time series techniques like ARIMA and exponential smoothing. By leveraging Prophet and time series analysis, this paper aims to offer accurate forecasts of population dynamics, age structures and migration trends, providing valuable insights for urban planning and policy formulation.

Keywords: population demographics, ARIMA, prophet, time series analysis.

The objective of this study was to investigate the empirical relationship between capital formation and saving in the case of Rwanda. The empirical literature review reveals that saving has a positive effect on capital formation. Results of the research obtained using the Ordinary Least Square method show that in Rwanda there is positive correlation between capital formation and saving. Saving is used to finance investments useful for the development of the country.

In the equation formulated, endogenous variable was capital formation while exogenous variables were saving, foreign direct investments and money supply. It has been demonstrated that coefficient of saving is positive. In Rwanda, an increase 1% of saving ends at an increase of gross capital formation of 1.271241%. Analyses done end at results that estimated coefficients are statistically significant at 5% margin of error i.e. 95% level of confidence. The relative probability for LSAV is less than 0.5. R-squared is 0.980003. This goes to mean that exogenous variables selected explain Gross Capital Formation at 98% and the model if fitted. Therefore, the government of Rwanda should make supplementary effort to encourage saving in the country so to boost the economy through more investment in order to meet its major objective, i.e the economic and social development.