Isaac Scientific Publishing
Journal of Advances in Applied Mathematics
JAAM > Volume 5, Number 3, July 2020

Predictive Modelling of the COVID - 19 Epidemic in Cameroon with Innovative Models

DOI: 10.22606/jaam.2020.53003

Author(s)
Jimbo Henri Claver, Ngongo Isidore Séraphin, Fotso Simeon, Waffo Guy, Andjiga Gabriel Nicolas, Etoua Rémy Malgoire, Tchantcho Bertrand
Affiliation(s)
Department of Applied Mathematics and Statistics, RISE, Waseda University, Tokyo, Japan
Department of Mathematics, ENS, University of Yaoundé I, Cameroon
Department of Mathematics, University of Yaoundé 1, Cameroon
Department of Computer Engineering, ENSPY, Cameroon
Department of Mathematics, ENS, University of Yaoundé I, Cameroon
Department of Mathematics, ENSPY. Yaounde 1, Cameroon
Department of Mathematics, ENS, University of Yaoundé I, Cameroon
Abstract
The mathematical model was recently used for COVID-19 in Wuhan, the Chinese city where the disease first broke out. It helped to outline the interventions needed to reduce the number of people at risk of catching the virus. The SEIR models were also used to predict interventions during the 2009 influenza pandemic in the US. In this project we will develop new models that are able to capture more features that the previous ones. Based on the official data modeling, this research work will study the Corona Virus Disease 2019 (COVID-19) propagation dynamics in Cameroon. The error between the model and the official data curve will be estimated. At the same time, it will realize the forward prediction of the epidemic situation, and the relevant analysis will help Cameroon to make important decisions on the epidemic evolution over time.
Keywords
Covid 19 modelling, SIR, SSIR, SEIR, SSEIR, model loss, model selection,reproduction number, stability analysis.
References
• [1]  T. P. Velavan & C. G. MeyerTe COVID-19 epidemic. Trop. Med. Int. Health25, 278–280 (2020).
• [2]  Z. Wu, & J. M. McGoogan, Characteristics of and important lessons from the coronavirus disease 2019 (COVID-19) outbreak in China: summary of a report of 72,314 cases from the Chinese center for disease control and prevention. JAMA 323, 1239–1242 (2020).
• [3]  W.J. Guan,et al. Clinical characteristics of coronavirus disease 2019 in China.
• [4]  N. Engl. J. Med. https://doi.org/10.1056/NEJMoa2002032 (2020).
• [5]  WHO. Coronavirus Disease 2019 (COVID-19): Situation Report 76 (WHO, 2020).
• [6]  A. Remuzzi, & G.Remuzzi, COVID-19 and Italy: what next? Lancet Health.
• [7]  Policy 395, 1225–1228 (2020).
• [8]  A. Giufrida, & P. Beaumont, Coronavirus: inquiry opens into hospitals atentre of Italy outbreak. Te Guardian (26 February 2020).
• [9]  Ministero della Salute (Italian Ministry of Health). http://www.salute.gov.it/ imgs/C_17_notizie_4403_0_fle.pdf (5 April 2020).
• [10]  Y. Wang, Y. Chen, & Q. Quin, Unique epidemiological and clinical features of the emerging 2019 novel coronavirus pneumonia (COVID-19) implicate special control measures. J. Med. Virol. 92, 568–576 (2020).
• [11]  D. Fisman, C. Rivers, E. Lofgren & M. S. Majumder, Estimation of MERS-Coronavirus reproductive number and case fatality rate for the Spring 2014 Saudi Arabia outbreak: insights from publicly available data. PLoS Curr https://doi.org/10.1371/currents.outbreaks.98d2f8f3382d84f390736cd5f5fe133c (2014).
• [12]  S. Zhao, et al. Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: a data-driven analysis in the early phase of the outbreak. Int. J. Inf. Dis. 92, 214–217 (2020).
• [13]  J. Read, J.R. Bridgen, D. A. T. Cummings, A. Ho, & C. P. Jewell, Novel coronavirus 2019- nCoV: early estimation of epidemiological parameters and epidemic predictions. Preprint at medRxiv https://doi.org/10.1101/2020.01.23.20018549 (2020).
• [14]  H.C. Jimbo et al., Simulation and analysis of HIV-AIDS dynamics, International Journal of Healthcare and Computation vol 1, no 1, 2019.
• [15]  O.Diekmann, & J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation (Wiley, 2000).
• [16]  H. W. Hethcote, Te mathematics of infectious diseases. SIAM Rev. 42, 599–653 (2000).
• [17]  F. Brauer, & Castillo-Chavez, C. Mathematical Models in Population Biology and Epidemiology 2nd edn (Springer, 2012).
• [18]  W. O. Kermack, & A. G. McKendrick, A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. 115, 700–721 (1927).
• [19]  Q. Lin, et al. A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action. Int. J. Inf. Dis. 93, 211–216 (2020).
• [20]  C. Anastassopoulou, L.Russo, A. Tsakris, & C. Siettos, Data-based analysis, modelling and forecasting of the COVID-19 outbreak. PLoS One 15, e0230405 (2020).
• [21]  F. Casella, Can the COVID-19 epidemic be managed on the basis of daily data? Preprint at https://arxiv.org/abs/2003.06967 (2020)
• [22]  G.M.Nakamura, A.S. Martinez . Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations. Sci Rep. 2019;9(1):1-9. doi:10.1038/s41598-019-52351-x
• [23]  B. Li, Periodic orbits of autonomous ordinary differential equations: Theory and applications, Nonlinear Analysis, 5 (1981), 931–958.
• [24]  G. Li and J. Zhen, Global stability of an SEI epidemic model with general contact rate, Chaos Solitons Fractals, 23 (2005), 997–1004.
• [25]  M. Y. Li, J. R. Graef, L. Wang and J. Karsai, Global dynamics of a SEIR model with varying total population size, Mathematical Biosciences, 160 (1999), 191–213.
• [26]  M. Y. Li and J. S. Muldowney, Global stability for the SEIR model in epidemiology, Mathematical Biosciences, 125 (1995), 155–164
• [27]  H.C, Jimbo et al., Co-Evolutionary Algorithm for Analyzing Gene Expression Data, Advance in Computer Science Research, Editor A. Dadvaud , Atlantis Press, Pp 120 – 126, 2016
• [28]  H. C., Jimbo et al., Modelling Cancer Chemotherapy with Side-Effects, IASTED, Acta Press, 838-010, 2016 Canada
• [29]  T. Yamada, H. C. Jimbo, S. Ishii, M. Nishiyama, K. Hong and Y. Sakumura, Identification of a Molecular System that Regulates Growth Cone Membrane Potential during growth cone Guidance, BMC NEUROSCIENCE, 2011 12 (Suppl 1) P28.
• [30]  H.C. Jimbo et al., A Dynamical Model of Cancer Chemotherapy with Disturbance, GECCO Campagnon 12, ACM, New York, USA, GECCO12, Pp1417- 1418,