Gülnur ÇELİK KIZILKAN, Ahmet DUMAN, Kemal AYDIN

Bazı SIR Salgın Hastalık Modellerinin Değişken Adım Genişliği Stratejisi ile Analizi

Bu çalışmada, bazı SIR salgın hastalık modelleri için değişken adım genişliği stratejisinin etkinliğini incelemeyi amaçladık. SIR modeli ve onun modifikasyonlarına gerçek veriler kullanarak değişken adım genişliği stratejisini uyguladık

Anahtar Kelimeler:

Salgın hastalık modeli, SIR modeli, Adım genişliği stratejisi, Lineer olmayan diferensiyel denklem sistemi, Değişken adım genişliği

Analysis with Variable Step Size Strategy of Some SIR Epidemic Models

In scientific studies involving norm calculations, the choice of the norm affects the obtained results. We have aimed to examine the behavior of the step sizes using different norms and norm inequalities in step size strategy for linear Cauchy problems obtained by Çelik Kızılkan and Aydın 2011 .

Keywords:

Epidemic model, SIR model, Step size strategy, System of non-linear differential equations, Variable step size,

PDF

___

bastin, G., 17 February 2012. Lectures on mathematical modelling of biological systems. http://perso.uclouvain.be/ georges.bastin/lectures-bio.pdf (Access date: 08.04.2016).
Centers for Disease Control and Prevation, 2016.
http://wwwnc.cdc.gov/travel/yellowbook/2016/infectious-diseases- related-to-travel/measles-rubeola. (Access date: 12.04.2016)
Chauhan, S., Misra, OP., Dhar, J. 2014. Stability analysis of SIR model with vaccination, Am. J. Comput. Appl. Math., 4(1):17- 23.
Chinviriyasit, S., Chinviriyasit, W. 2010. Numerical modelling of on SIR epidemic model with diﬀusion, Appl. Math. Comput., 216: 395-409.
Correia, AM., Mena, FC., Soares, AJ. 2011. An application of the SIR model to epidemics in Portugal. https://repositorium. sdum.uminho.pt/bitstream/1822/15211/1/CorrMenSoar2011. pdf (Access date: 08.04.2016).
Cui, Q., Yang, X., Zhang, Q. 2014. An NSFD scheme for a class of SIR epidemic models with vaccination and treatment, J. Differ. Equ. Appl., 20 (3): 416-422.
Çelik Kızılkan, G. 2004. On the finding of step size in the numerical integration of initial value problem, Master Thesis, Selcuk University Graduate Natural and Applied Sciences, Konya, (in Turkish).
Çelik Kızılkan, G. 2009. Step size strategies on the numerical integration of the systems of diﬀerential equations. Ph.D. The- sis, Selcuk University Graduate Natural and Applied Sciences, Konya, (in Turkish).