Authors:
Asish Mitra,DOI NO:
https://doi.org/10.26782/jmcms.2021.02.00001Keywords:
COVID-19,Epidemic Disease,Modified SIRD Model,Parameter Estimation,Abstract
The present study shows that a simple epidemiological model can reproduce the real data accurately. It demonstrates indisputably that the dynamics of the COVID-19 outbreak can be explained by the modified version of the compartmental epidemiological framework Susceptible-Infected-Recovered-Dead (SIRD) model. The parameters of this model can be standardized using prior knowledge. However, out of several time-series data available on several websites, only the number of dead individuals (D(t)) can be regarded as a more reliable representation of the course of the epidemic. Therefore it is wise to convert all the equations of the SIRD Model into a single one in terms of D(t). This modified SIRD model is now able to give reliable forecasts and conveys relevant information compared to more complex models.Refference:
I. Anastassopoulou et al. Data-based analysis, modelling and forecasting of the covid-19 out-break. PLOS ONE, 2020. doi:10.1371/journal.pone.0230405.
II. Asish Mitra, Covid-19 in India and SIR Model, J. Mech.Cont. & Math. Sci., 15, 1-8, 2020.
III. Castilho et al. Assessing the efficiency of different control strategies for the coronavirus (covid-19) epidemic. ArXiv e-prints, 2020, 2004.03539.
IV. Chen et al. A time-dependent sir model for covid-19 with undetectable infected persons. ArXiv e-prints, 2020, 2003.00122.
V. D. J. Daley and J. Gani. Epidemic Modelling: An Introduction. Cambridge University Press, 2001.
VI. Duccio Fanelli and Francesco Piazza. Analysis and forecast of covid-19 spreading in China, Italy and France. Chaos, Solitons and Fractals, 134:109761, 2020, 2003.06031. doi:10.1016/j.chaos.2020.109761.
VII. Goncalo Oliveira. Refined compartmental models, asymptomatic carriers and covid-19. ArXiv e-prints, 2020, 2004.14780. doi:10.1101/2020.04.14.20065128.
VIII. Herbert W. Hethcote. The mathematics of infectious diseases. SIAM Review, 42(4):599-653, 2000.
IX. https://data.humdata.org/dataset/novel-coronavirus-2019-ncov-cases.
X. Julie Blackwood and Lauren M. Childs. An introduction to compartmental modeling for the budding infectious disease modeler. Letters in Biomathematics, 5:1:195-221, 2018. doi:10.1080/23737867.2018.1509026.
XI. Keeling Matt J. and Pejman Rohani. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, 2008.
XII. Lipsitch et al. Transmission dynamics and control of severe acute respiratory syndrome.Science, 300(5627):1966-1970, 2003. doi:10.1126/science.1086616.
XIII. Loli et al. Preliminary analysis of covid-19 spread in Italy with an adaptive SEIRD model. ArXiv e-prints, 2020, 2003.09909.
XIV. Md. Zaidur Rahman, Md. Abul Kalam Azad, Md. Nazmul Hasan, : MATHEMATICAL MODEL FOR THE SPREAD OF EPIDEMICS, J. Mech.Cont. & Math. Sci., Vol.-6, No.-2, January (2012) Pages 843-858.
XV. Michael Y Li. An Introduction to Mathematical Modeling of Infectious Diseases. Springer International Publishing, 2018.
XVI. Natalie M Linton et all. Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data. Journal of clinical medicine, 9(2):538, 2020.
XVII. Prem et al. The effect of control strategies to reduce social mixing on outcomes of the covid-19 epidemic in Wuhan, China: a modelling study. The Lancet, 5:261-270, 2020. doi:10.1016/S2468-2667(20)30073-6.
XVIII. S. Gupta, R. Shankar Estimating the number of COVID-19 infections in Indian hot-spots using fatality data, arXiv:2004.04025 [q-bio.PE]
XIX. Solving applied mathematical problems with MATLAB / Dingyu Xue, Chapman & Hall/CRC.
XX. Villaverde. Estimating and simulating a SIRD model of covid-19 for many countries, states, and cities.
https://cepr.org/active/publications/discussion_papers/dp.php?dpno=14711, 2020.
XXI. W. O. Kermack and A. G. McKendrick. A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A, 115(772):700–721, 1927.
View Download