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Aims/ Objectives: To develop a compartment based mathematical model, fit daily quarantine data from Ministry of Health of Kenya, estimate individuals in latency and infected in general community and predict dynamics of quarantine for the next 90 days.
Study Design: Cross-sectional study.
Place and Duration of Study: 13thMarch 2020 to 30th June 2020.
Methodology: The population based model was developed using status and characteristic of COVID-19 infection. Quarantine data up to 30/6/2020 was fitted using integrating and differentiating theory of odes and numerical differentiation polynomials. Parameter and state estimates was approximated using least square. Simulations were carried out using ode Matlab solver. Daily community estimates of individuals in latency and infected were obtained together with daily estimate of rate of enlisting individual to quarantine center and their proportions were summarized.
Results: The results indicated that maximum infection rate was equal 0.892999 recorded on 28/6/2020, average infection rate was 0.019958 and minimum 0.00012 on 26/6/2020.
Conclusion: Predictions based on parameters and state averages indicated that the number of individuals in quarantine are expected to rise exponentially up to about 26,855 individuals by 130th day and remain constant up to 190th day.
World Health Organization. Coronavirus disease 2019 (COVID-19). Situation Report. 2020;79.
Guan, Wei-jie, Zheng-yi Ni, Hu Yu, Liang, Wen-hua, Ou, Chun-quan, 402He, Jianxing, Liu, Lei, Shan, Hong, Lei, Chun-liang,
Hui, David SC. Clinical characteristics of coronavirus disease 2019 in China. New England Journal of Medicine. Mass Medical Soc; 2020.
Bentout S, Chekroun A, Kuniya T. Parameter estimation and prediction for coronavirus disease outbreak 2019 (COVID-19) in Algeria. AIMS Public Health. 2020;7(2):306.
Das B, Chakrabarty D. Lagranges interpolation formula: Representation of numerical data by a polynomial curve. International Journal of Mathematics Trend and Technology. 2016;23-31.
Jain MK. Numerical methods for scientific and engineering computation. New Age International; 2003. 41Ngari et al.; ARRB, 35(10): 25-42, 2020; Article no.ARRB.60626
Herceq D, Herceq D. Arduino and numerical mathematics. In Proceedings of the 9th Balkan Conference on Informatics. 2019;1-
Berrut JP, Trefethen LN. Barycentric lagrange interpolation. SIAM Review. 2004;46(3):501-517.
Guo L, Liu Y, Zhou T. Data-driven polynomial chaos expansions: A weighted least-square approximation. Journal of Computational Physics. 2019;381:129-145.
Roddam AW. Mathematical epidemiology of infectious diseases: Model building, analysis and interpretation. Diekmann O, Heesterbeek JAP, 2000, Chichester: John Wiley. 2001;303. ISBN 0-471-49241-8
Vynnycky E, White R. An introduction to infectious disease modelling. OUP oxford; 2010.
Allen LJ, Brauer F, Van den Driessche P, Wu J. Mathematical epidemiology. Berlin: Springer. 2008;1945.
Murray JD. Mathematical biology: I. An introduction. Springer Science & Business Media; 2007;17.
Rodrigues HS, Monteiro MTT, Torres DF. Sensitivity analysis in a dengue epidemiological model. In Conference Papers in Science. Hindawi. 2013;2013.
Ndiaye BM, Tendeng L, Seck D. Comparative prediction of confirmed cases with COVID-19 pandemic by machine learning, deterministic and stochastic SIR models; 2020. arXiv preprint arXiv:2004.13489.
Castillo-Chavez, Carlos, Feng, Zhilan, Huang, Wenzhang. On the computation of ro and its role on. Mathematical approaches
for emerging and reemerging infectious diseases: An Introduction. Springer. 2002;229.
Van den Driessche, Pauline. Reproduction numbers of infectious disease models. Infectious Disease Modelling, Elsevier. ;2:288-303.
Kenya National Bureau of Statistics. 2019 Kenya population and housing census volume I: Population by county and subcounty; 2019.
Wordometer. Kenya coronavirus; 2020. Available:https://www.worldometers.info/- coronavirus/country/kenya/
Calculation of infection rates; 2020. Available:http://health.utah.gov/epi/diseases/HAI/resources/Cal Inf Rates.pdf