A Comparative Analysis of Mathematical and Linear Regression Models to Predict the Outcomes of COVID-19 Pandemic in Rwanda

Abstract

The research objective was to investigate the level of COVID-19 outbreak in Rwanda using mathematical and linear models for future prediction of the disease. Both Mathematical model and linear model were used. A sequential mathematical preliminary of COVID-19 was considered to check how it grows within a large number of population. The model diagram was proposed with four compartmental model. The non-linear dynamical system of COVID-19 was derived from the model. The model was checked for positivity and boundedness in system. We found that it’s positively invariant in system. The results also showed that the disease is locally and globally unstable due to the fact that the basic reproduction number is greater than zero i.e., R0 > 0. The basic reproduction number was computed using the next generation Matrix and found that COVID-19 affects a very large population in the system. Method for real data: The study used a sample of 463 COVID-19 daily reports, that is, the available data by 9 April 2021. The data are analyzed using Statistical software (STATA version 13.1). The probability of skewness and kurtosis was P ≤ 0.0001 for New cases, and New deaths. Besides Chi-Square p ≤ 0.0001 for both New cases and New deaths was < 0.05 that means the significance at a 5% level. Results: By comparing the mean and standard deviation, the results show that the number of New cases is higher than that of New deaths, that is 50.00432 with high standard deviation 78.47841, and 0.6781857 with low standard deviation 1.474935; respectively. A spearman rank correlation shows strong correlation between New cases and New deaths. Linear regression analysis model shows that there is a linear relationship of New cases with New deaths. The findings show that the number of deaths will be higher than New cases. Conclusion: The statistics show that COVID-19 is still there within individuals and is moving around. The findings show that in future, the number of new deaths will be higher than that of new cases at a time t. We recommend the government of Rwanda to speed up the Vaccination to the total population to avoid more future deaths due to COVID-19 and to strictly tightening the preventive measures for both Rwandans and incoming travelers. With the above mentioned strategies and the measures, there is a hope that If the whole country is vaccinated, COVID-19 will vanish at time t.