The Origin, Diffusion and a Comparison of Ordinary Differential Equations Numerical Solutions Used by SIR Model in Order to Predict SARS-CoV-2 in Nordic Countries
SARS-CoV-2 virus is currently one of the most
infectious pathogens for humans. It started in China at the end of
2019 and now it is spread in all over the world. The origin and
diffusion of the SARS-CoV-2 epidemic, is analysed based on the
discussion of viral phylogeny theory. With the aim of understanding
the spread of infection in the affected countries, it is crucial to
modelize the spread of the virus and simulate its activity. In this
paper, the prediction of coronavirus outbreak is done by using SIR
model without vital dynamics, applying different numerical technique
solving ordinary differential equations (ODEs). We find out that ABM
and MRT methods perform better than other techniques and that the
activity of the virus will decrease in April but it never cease (for
some time the activity will remain low) and the next cycle will start
in the middle July 2020 for Norway and Denmark, and October 2020
for Sweden, and September for Finland.
[1] Bank, R. E., Coughran, W. M., Fichtner, W., Grosse, E. H., Rose, D.
J., & Smith, R. K. Transient simulation of silicon devices and circuits.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and
Systems; 1985. 4(4), 436–451.
[2] Boujakjian, H. Modeling the spread of Ebola with SEIR and optimal
control. SIAM Undergraduate Research Online; 2016. 9, 299–310.
[3] Chen, Y., Cheng, J., Jiang, Y., & Liu, K. A time delay dynamical model
for outbreak of 2019-nCoV and the parameter identification. Journal of
Inverse and Ill-posed Problems; 2020. 28(2), 243–250.
[4] Cristianini, N., & Hahn, M. W. Introduction to computational genomics:
a case studies approach. Cambridge University Press; 2006.
[5] Dormand, J. R., & Prince, P. J. A family of embedded Runge-Kutta
formulae. Journal of computational and applied mathematics; 1980. 6(1),
19–26.
[6] Hosea, M. E., & Shampine, L. F. Analysis and implementation of
TR-BDF2. Applied Numerical Mathematics; 1996. 20(1-2), 21–37.
[7] Guo, Z., Xiao, D., Li, D., Wang, X., Wang, Y., Yan, T., & Wang, Z.
Predicting and evaluating the epidemic trend of ebola virus disease in the
2014-2015 outbreak and the effects of intervention measures. PloS one;
2016. 11(4).
[8] Kermack, W. O., & McKendrick, A. G. A contribution to the
mathematical theory of epidemics.Proceedings of the royal society of
london. Series A, Containing papers of a mathematical and physical
character; 1927. 115(772), 700–721.
[9] Lai, D. Monitoring the SARS epidemic in China: a time series
analysis.Journal of Data Science; 2005. 3(3), 279-293.
[10] Lipsitch, M., Cohen, T., Cooper, B., Robins, J. M., Ma, S., James, L.,
... & Fisman, D. Transmission dynamics and control of severe acute
respiratory syndrome. Science; 2003. 300(5627), 1966–1970.
[11] Loper, M. L. (Ed.). Modeling and simulation in the systems engineering
life cycle: core concepts and accompanying lectures. Springer; 2015.
[12] Pandey, G., Chaudhary, P., Gupta, R., & Pal, S. SEIR and Regression
Model based COVID-19 outbreak predictions in India. arXiv preprint
arXiv:2004.00958; 2020.
[13] Poon, L. L. M., Chu, D. K. W., Chan, K. H., Wong, O. K., Ellis, T.
M., Leung, Y. H. C., & Guan, Y. Identification of a novel coronavirus in
bats. Journal of virology; 2005. 79(4), 2001–2009.
[14] Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P.
Numerical recipes 3rd edition: The art of scientific computing. Cambridge
university press; 2007.
[15] Rachah, A., & Torres, D. F. Predicting and controlling the Ebola
infection. Mathematical Methods in the Applied Sciences; 2017. 40(17),
6155–6164.
[16] Read, J. M., Bridgen, J. R., Cummings, D. A., Ho, A., & Jewell, C.
P. Novel coronavirus 2019-nCoV: early estimation of epidemiological
parameters and epidemic predictions. MedRxiv; 2020.
[17] Shampine, L. F. Computer solution of ordinary differential equations:
The Initial Value Problem. W.H. Freeman, San Francisco; 1975.
[18] Shampine, L. F., & Reichelt, M. W. The matlab ode suite. SIAM journal
on scientific computing; 1997. 18(1), 1–22.
[19] Shampine, L. F., Reichelt, M. W., & Kierzenka, J. A. Solving index-1
DAEs in MATLAB and Simulink. SIAM review; 1999. 41(3), 538–552.
[20] Tang, Z., Li, X., & Li, H. Prediction of New Coronavirus Infection
Based on a Modified SEIR Model. medRxiv; 2020.
[21] https://www.ncbi.nlm.nih.gov/nuccore?LinkName=genome_nuccore_
samespecies&from_uid=86693
[22] https://www.who.int/emergencies/diseases/
novel-coronavirus-2019/situation-reports/?gclid=
EAIaIQobChMIptrK657D6QIVxeAYCh2I6g4YEAAYASACEgIHlv_
D BwE
[1] Bank, R. E., Coughran, W. M., Fichtner, W., Grosse, E. H., Rose, D.
J., & Smith, R. K. Transient simulation of silicon devices and circuits.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and
Systems; 1985. 4(4), 436–451.
[2] Boujakjian, H. Modeling the spread of Ebola with SEIR and optimal
control. SIAM Undergraduate Research Online; 2016. 9, 299–310.
[3] Chen, Y., Cheng, J., Jiang, Y., & Liu, K. A time delay dynamical model
for outbreak of 2019-nCoV and the parameter identification. Journal of
Inverse and Ill-posed Problems; 2020. 28(2), 243–250.
[4] Cristianini, N., & Hahn, M. W. Introduction to computational genomics:
a case studies approach. Cambridge University Press; 2006.
[5] Dormand, J. R., & Prince, P. J. A family of embedded Runge-Kutta
formulae. Journal of computational and applied mathematics; 1980. 6(1),
19–26.
[6] Hosea, M. E., & Shampine, L. F. Analysis and implementation of
TR-BDF2. Applied Numerical Mathematics; 1996. 20(1-2), 21–37.
[7] Guo, Z., Xiao, D., Li, D., Wang, X., Wang, Y., Yan, T., & Wang, Z.
Predicting and evaluating the epidemic trend of ebola virus disease in the
2014-2015 outbreak and the effects of intervention measures. PloS one;
2016. 11(4).
[8] Kermack, W. O., & McKendrick, A. G. A contribution to the
mathematical theory of epidemics.Proceedings of the royal society of
london. Series A, Containing papers of a mathematical and physical
character; 1927. 115(772), 700–721.
[9] Lai, D. Monitoring the SARS epidemic in China: a time series
analysis.Journal of Data Science; 2005. 3(3), 279-293.
[10] Lipsitch, M., Cohen, T., Cooper, B., Robins, J. M., Ma, S., James, L.,
... & Fisman, D. Transmission dynamics and control of severe acute
respiratory syndrome. Science; 2003. 300(5627), 1966–1970.
[11] Loper, M. L. (Ed.). Modeling and simulation in the systems engineering
life cycle: core concepts and accompanying lectures. Springer; 2015.
[12] Pandey, G., Chaudhary, P., Gupta, R., & Pal, S. SEIR and Regression
Model based COVID-19 outbreak predictions in India. arXiv preprint
arXiv:2004.00958; 2020.
[13] Poon, L. L. M., Chu, D. K. W., Chan, K. H., Wong, O. K., Ellis, T.
M., Leung, Y. H. C., & Guan, Y. Identification of a novel coronavirus in
bats. Journal of virology; 2005. 79(4), 2001–2009.
[14] Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P.
Numerical recipes 3rd edition: The art of scientific computing. Cambridge
university press; 2007.
[15] Rachah, A., & Torres, D. F. Predicting and controlling the Ebola
infection. Mathematical Methods in the Applied Sciences; 2017. 40(17),
6155–6164.
[16] Read, J. M., Bridgen, J. R., Cummings, D. A., Ho, A., & Jewell, C.
P. Novel coronavirus 2019-nCoV: early estimation of epidemiological
parameters and epidemic predictions. MedRxiv; 2020.
[17] Shampine, L. F. Computer solution of ordinary differential equations:
The Initial Value Problem. W.H. Freeman, San Francisco; 1975.
[18] Shampine, L. F., & Reichelt, M. W. The matlab ode suite. SIAM journal
on scientific computing; 1997. 18(1), 1–22.
[19] Shampine, L. F., Reichelt, M. W., & Kierzenka, J. A. Solving index-1
DAEs in MATLAB and Simulink. SIAM review; 1999. 41(3), 538–552.
[20] Tang, Z., Li, X., & Li, H. Prediction of New Coronavirus Infection
Based on a Modified SEIR Model. medRxiv; 2020.
[21] https://www.ncbi.nlm.nih.gov/nuccore?LinkName=genome_nuccore_
samespecies&from_uid=86693
[22] https://www.who.int/emergencies/diseases/
novel-coronavirus-2019/situation-reports/?gclid=
EAIaIQobChMIptrK657D6QIVxeAYCh2I6g4YEAAYASACEgIHlv_
D BwE
@article{"International Journal of Medical, Medicine and Health Sciences:80148", author = "Gleda Kutrolli and Maksi Kutrolli and Etjon Meco", title = "The Origin, Diffusion and a Comparison of Ordinary Differential Equations Numerical Solutions Used by SIR Model in Order to Predict SARS-CoV-2 in Nordic Countries", abstract = "SARS-CoV-2 virus is currently one of the most
infectious pathogens for humans. It started in China at the end of
2019 and now it is spread in all over the world. The origin and
diffusion of the SARS-CoV-2 epidemic, is analysed based on the
discussion of viral phylogeny theory. With the aim of understanding
the spread of infection in the affected countries, it is crucial to
modelize the spread of the virus and simulate its activity. In this
paper, the prediction of coronavirus outbreak is done by using SIR
model without vital dynamics, applying different numerical technique
solving ordinary differential equations (ODEs). We find out that ABM
and MRT methods perform better than other techniques and that the
activity of the virus will decrease in April but it never cease (for
some time the activity will remain low) and the next cycle will start
in the middle July 2020 for Norway and Denmark, and October 2020
for Sweden, and September for Finland.", keywords = "Forecasting, ordinary differential equations,
SARS-CoV-2 epidemic, SIR model.", volume = "15", number = "1", pages = "33-30", }
