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

Received: 30 August 2021     Accepted: 12 October 2021     Published: 28 October 2021
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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.

Published in Mathematics and Computer Science (Volume 6, Issue 5)
DOI 10.11648/j.mcs.20210605.12
Page(s) 77-82
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

COVID-19, Comparative Analysis, Mathematical Model, Regression Model, Outbreak Prediction

References
[1] Joab O Odhiambo, Philip Ngare, Patrick Weke, and Romanus Odhiambo Otieno. Modelling of COVID-19 transmission in kenya using compound poisson regression model. Journal of Advances in Mathematics and Computer Science, pages 101–111, 2020.
[2] World Health Organization et al. Modes of transmission of virus causing COVID-19: implications for ipc precaution recommendations: scientific brief, 27 march 2020. Technical report, World Health Organization, 2020.
[3] World Health Organization et al. COVID-19 weekly epidemiological update, 16 march 2021. 2021.
[4] Gianfranco Spiteri, James Fielding, Michaela Diercke, Christine Campese, Vincent Enouf, Alexandre Gaymard, Antonino Bella, Paola Sognamiglio, Maria Jose Sierra Moros, Antonio Nicolau Riutort, et al. First´ cases of coronavirus disease 2019 (COVID-19) in the who european region, 24 january to 21 february 2020. Eurosurveillance, 25 (9): 2000178, 2020.
[5] Shaheen Mehtar, Wolfgang Preiser, Ndeye Aissatou Lakhe, Abdoulaye Bousso, Jean-Jacques Muyembe` TamFum, Oscar Kallay, Moussa Seydi, Alimuddin Zumla, and Jean B Nachega. Limiting the spread of COVID-19 in africa: one size mitigation strategies do not fit all countries. The Lancet Global Health, 8 (7): e881–e883, 2020.
[6] World Health Organization et al. Coronavirus disease 2019 (COVID-19): situation report, 82. 2020.
[7] Alfred Bizoza and Simeon Sibomana. Indicative socio-economic impacts of the novel coronavirus (COVID-19) outbreak in eastern africa: Case of rwanda. Available at SSRN 3586622, 2020.
[8] Ebenezer Bonyah, Gratien Twagirumukiza, and Patience Pokuaa Gambrah. Mathematical analysis of diarrhoea model with saturated incidence rate. 2019.
[9] Odo Diekmann, Johan Andre Peter Heesterbeek, and Johan AJ Metz. On the definition and the computation of the basic reproduction ratio r 0 in models for infectious diseases in heterogeneous populations. Journal of mathematical biology, 28 (4): 365–382, 1990.
[10] Pauline Van den Driessche and James Watmough. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences, 180 (1-2): 29–48, 2002.
[11] Cumulative number in Rwanda. Update COVID-19 09 april 2021. WHO, https://www.afro.who.int/news/update-COVID-19-09-april-2021, Accessed April 2021.
[12] Total population, 2021. Rwanda population (live). worldometer, https://www.worldometers.info/world-population/rwanda-population/, Ac-cessed April 2021.
[13] Gratien Twagirumukiza and Edouard Singirankabo. Mathematical analysis of a delayed hiv/aids model with treatment and vertical transmission. Open J. Math. Sci, 5: 128–146, 2021.
[14] Situation Report on COVID-19. Situation report on novel coronavirus. Rwanda Biomedical Centre, https://www.rbc.gov.rw/index.php?id=717, Accessed April 2021.
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  • APA Style

    Gratien Twagirumukiza, Edouard Singirankabo, Leopord Hakizimana. (2021). A Comparative Analysis of Mathematical and Linear Regression Models to Predict the Outcomes of COVID-19 Pandemic in Rwanda. Mathematics and Computer Science, 6(5), 77-82. https://doi.org/10.11648/j.mcs.20210605.12

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    ACS Style

    Gratien Twagirumukiza; Edouard Singirankabo; Leopord Hakizimana. A Comparative Analysis of Mathematical and Linear Regression Models to Predict the Outcomes of COVID-19 Pandemic in Rwanda. Math. Comput. Sci. 2021, 6(5), 77-82. doi: 10.11648/j.mcs.20210605.12

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    AMA Style

    Gratien Twagirumukiza, Edouard Singirankabo, Leopord Hakizimana. A Comparative Analysis of Mathematical and Linear Regression Models to Predict the Outcomes of COVID-19 Pandemic in Rwanda. Math Comput Sci. 2021;6(5):77-82. doi: 10.11648/j.mcs.20210605.12

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  • @article{10.11648/j.mcs.20210605.12,
      author = {Gratien Twagirumukiza and Edouard Singirankabo and Leopord Hakizimana},
      title = {A Comparative Analysis of Mathematical and Linear Regression Models to Predict the Outcomes of COVID-19 Pandemic in Rwanda},
      journal = {Mathematics and Computer Science},
      volume = {6},
      number = {5},
      pages = {77-82},
      doi = {10.11648/j.mcs.20210605.12},
      url = {https://doi.org/10.11648/j.mcs.20210605.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210605.12},
      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.},
     year = {2021}
    }
    

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    AU  - Gratien Twagirumukiza
    AU  - Edouard Singirankabo
    AU  - Leopord Hakizimana
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    AB  - 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.
    VL  - 6
    IS  - 5
    ER  - 

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Author Information
  • Faculty of Applied Fundamental Sciences, Institute of Applied Sciences, Musanze, Rwanda

  • School of Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • School of Computing and Information Technology, University of Kigali, Musanze, Rwanda

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