ASSESSMENT OF THE MATHEMATICAL MODEL FOR INVESTIGATING COVID-19 PEAK AS A GLOBAL EPIDEMIC IN IRAN

Document Type : Original Article

Authors
Hossein Taheri 1
Nasrin Eghbali 2
Masoumeh Pourabd 3
Huaiping Zhu 4
1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran.
2 Department of Mathematics, Facualty of Mathematical Sciences, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran
3 Department of Mathematics, University of Mazandaran, 47415-95447, Babolsar, Iran
4 LAMPS and Canadian Centre for Dsieases Modeling (CCDM), Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada
10.22034/maco.3.2.12
Abstract
. In this paper, we investigate the COVID-19 pandemic in Iran from a mathematical modeling perspective. By improving the well-known susceptible infected recovered (SIR) family of compartmental models and adding unreported cases obtain a local model for Iran. Since we only want infected cases, we have refused to add other classes which there are can be. We estimate the infected case by using the reported data of the first period of the outbreak and will apply the results to data of the provinces of Ardabil and Guilan which were available to us as well as published data from Iran. We show that, if some of the indexes are constant, the future infectious reported cases are predictable. Also, we show a good agreement between the reported data and the estimations given by the proposed model. We further demonstrate the importance of choosing this proposed model used to by finding the basic reproductive number. Also, we will estimate the probability distribution for the death rate. Our study can help the decision-making of public health.

Keywords

[1] Azar A., Control Applications for Biomedical Engineering Systems, Elsevier Science, 2020.
[2] Brauer F. and Castillo-Chavez C., Mathematical Models in Population Biology and Epidemiology, Springer, 2012.
[3] Chen T. M., Rui J., Wang Q. P., Zhao Z. Y., Cui J. A. and Yin L., A mathematical model for simulating the phase-based transmissibility of a novel coronavirus, Infectious Diseases of Poverty, 9 (1), (2020), 1-8, Doi: org/10.1186/s40249-020-00640-3.
[4] Haefner J., Modeling Biological Systems: Principles and Applications, Springer, 2005.
[5] Ivorra B. and Ramos A. M., Application of the Be-CoDis mathematical model to forecast the international spread of the 2019 Wuhan coronavirus outbreak, Technical Report, 9 February 2020, 1 13, DOI: 10.13140/RG.2.2.31460.94081.
[6] Ivorra B. and Ramos A. M. , Validation of the forecasts for the international spread of the coronavirus disease 2019 (COVID-19) done with the Be-CoDis mathematical model, Technical Report, 28 February 2020, 1–7, DOI: 10.13140/RG.2.2.34877.00485.
[7] Ivorra B. , Ramos A. M. and Ngom D., Be-CoDiS: A mathematical model to predict the risk of human diseases spread between countries-validation and application to the 2014-2015 Ebola Virus Disease epidemic, Bulletin of Mathematical Biology, 77 (9), (2015), 1668–1704, DOI: 10.1007/s11538-015-0100-x.
[8] Lin Q., Zhao S., Gao D., Lou Y., Yang S., Musa S. S., ... and He D., A conceptual model for the outbreak of Coronavirus disease 2019 (COVID-19) in Wuhan, China with individual reaction and governmental action, International Journal of Infectious Diseases, 93, (2020), 211-216, Doi: org/10.1016/j.ijid.2020.02.058.
[9] Liu Z., Magal P., Seydi O. and Webb G., Understanding unreported cases in the COVID-19 epidemic outbreak in Wuhan, China, and the importance of major public health interventions, Biology,9 (3), (2020), Doi: org/10.3390/biology9030050.
[10] Rohatgi V. K. and Saleh A. M., An Introduction to Probability and Statistics, John Wiley and Sons, 2015.
[11] Tang B., Wang X., Li Q., Bragazzi N. L., Tang S., Xiao Y. and Wu J., Estimation of the transmission risk of 2019-nCov and its implication for public health interventions, J. Clin. Med., 9 (2), (462)(2020), Doi: 10.3390/jcm9020462.
[12] Tang B., Bragazzi N. L., Li Q., Tang S., Xiao Y. and Wu J., An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov), Infectious Disease Modelling, 5, (2020), 248- 255, Doi: org/10.1016/j.idm.2020.02.001.
[13] Vries G. de , Hillen T., Lewis M., Schõnfisch B. and Muller J., A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Methods, ser. Monographs on Mathematical Modeling and Computation, Society for Industrial and Applied Mathematics, 2006.
[14] Wu J. T., Leung K. and Leung G. M., Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study,The Lancet, 395 (10225), (2020), 689-697, Doi: org/10.1016/S0140-6736(20)30260-9.
[15] Yang W., Karspeck A. and Shaman J., Comparison of filtering methods for the modeling and retrospective forecasting of influenza epidemics, PLOS Computational Biology, 10 (4), (2014), Doi: org/10.1371/journal.pcbi.1003583.
[16] Worldometer website: https://www.worldometers.info/coronavirus/country/iran/.
Mathematical Analysis and Convex Optimization
Volume 3, Issue 2
December 2022
Pages 129-142