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SOME MATHEMATICAL MODELS AND APPLICATIONS USED IN EPIDEMICS

Yıl 2019, Cilt: 37 Sayı: 1, 17 - 23, 01.03.2019

Öz

Tuberculosis (TB), AIDS (Acquired Immune Deficiency Syndrome), measles, malaria and CCHF (Crimean-Congo Hemorrhagic Fever) are the main epidemic diseases that persist as major global health problems. Estimating the number of affected people from epidemic diseases is of importance to reduce/minimize the probable negative outcomes. Therefore applicable and appropriate mathematical modelling is very useful and necessary to analyse, forecast and prevent the evolution of the diseases. A variety of mathematical models are used to detect losses from many epidemic diseases seen in the world. Some of these are SI, SIS, SIR, MSIRS, etc. Among the models, we studied SI (Susceptible-Infective) and SIS (Susceptible-Infective-Susceptible) models to decide the best appropriate/fitting model and to predict the effects of these epidemic diseases in some countries, namely, Norway for TB, malaria for Nigeria, HIV/AIDS for Ghana, CCHF for Bulgaria and measles for Afghanistan. We showed the relative predictive power of each model and in general models were found to confirm the reliability and robustness. After the analysis of the numerical results, we concluded that the SI and SIS models are very good at predicting the number of infected individuals, sensitive to fluctuations in real data and can follow the trend of exact data. Moreover, they give results in a short time.

Kaynakça

  • [1] Benedictow OJ., The Black Death 1346–1353: The Complete History. Boydell Press; 2004.
  • [2] Keeling MJ, Rohani P., Modeling Infectious Diseases in Humans and Animals. Princeton: Princeton University Press, 2007.
  • [3] Steere AC, (1989) Lyme disease. N Engl J Med 321: 586–596.
  • [4] Hilbi H, Jarraud S, Hartland E, Buchrieser C (2010) Update on Legionnaires’ disease: pathogenesis, epidemiology, detection and control. Mol. Microbiol. 76: 1–11.
  • [5] Taff ML, Siegal FP, Geller SA. Outbreak of an acquired immunodeficiency syndrome associated with opportunistic infections and Kaposi's sarcoma in male homosexuals: an epidemic with forensic implications., Am. J. Forensic.Med.Pathol.,1982 (3):259-264.
  • [6] Zuckerman AJ. The elusive hepatitis C virus. BMJ. 1989, 299(6704):871-3.
  • [7] Drosten C, Günther S, Preiser W, van der Werf S, Brodt HR, Becker S, Rabenau H, Panning M, Kolesnikova L, Fouchier RA, Berger A, Burguière AM, Cinatl J,Eickmann M, Escriou N, Grywna K, Kramme S, Manuguerra JC, Müller S, Rickerts V, Stürmer M, Vieth S, Klenk HD, Osterhaus AD, Schmitz H, Doerr HW. Identification of a Novel Coronavirus in Patients with Severe Acute Respiratory Syndrome, N. Engl.J.Med. 2003 348(20):1967-1976.
  • [8] Masuda N, Holme P. Predicting and controlling infectious disease epidemics using temporal networks. F1000 Prime Rep. 2013;5:6. doi: 10.12703/P5-6. Epub 2013.
  • [9] K Ergen, A Cilli , N Yahnioğlu, Predicting Epidemic Diseases Using Mathematical Modelling of SIR, Acta Physica Polonica A, Vol 127, page B-273-275, 2015. DOI:10.12693/APhysPolA.128.B-273
  • [10] Lih-Ing W. Roeger. Dynamically Consistent Discrete-Time SI and SIS Epidemic Models, Discrete and Continuous Dynamical systems, supplement, page 653-662, 2013.
  • [11] Kermack WO, McKendrick AG: A contribution to the mathematical theory of epidemics. P.R.Soc. Lond. A 1927, 115:700-721.
  • [12] Fact sheet on the World Malaria Report 2013
  • [13] MER_Crimean_Congo_Haemorragic_Fever_Prevention_and_Control.pdf
  • [14] World Health Organization. Afghanistan crisis health update 31 December 2001.
  • [15] World Health Statics 2015 Report, World Health organization.
  • [16] Weekly Epidemiological Monitor Volume 5, Issue 32, Regional office for the Eastern Mediterranean, WHO, 05 August 2012.
Yıl 2019, Cilt: 37 Sayı: 1, 17 - 23, 01.03.2019

Öz

Kaynakça

  • [1] Benedictow OJ., The Black Death 1346–1353: The Complete History. Boydell Press; 2004.
  • [2] Keeling MJ, Rohani P., Modeling Infectious Diseases in Humans and Animals. Princeton: Princeton University Press, 2007.
  • [3] Steere AC, (1989) Lyme disease. N Engl J Med 321: 586–596.
  • [4] Hilbi H, Jarraud S, Hartland E, Buchrieser C (2010) Update on Legionnaires’ disease: pathogenesis, epidemiology, detection and control. Mol. Microbiol. 76: 1–11.
  • [5] Taff ML, Siegal FP, Geller SA. Outbreak of an acquired immunodeficiency syndrome associated with opportunistic infections and Kaposi's sarcoma in male homosexuals: an epidemic with forensic implications., Am. J. Forensic.Med.Pathol.,1982 (3):259-264.
  • [6] Zuckerman AJ. The elusive hepatitis C virus. BMJ. 1989, 299(6704):871-3.
  • [7] Drosten C, Günther S, Preiser W, van der Werf S, Brodt HR, Becker S, Rabenau H, Panning M, Kolesnikova L, Fouchier RA, Berger A, Burguière AM, Cinatl J,Eickmann M, Escriou N, Grywna K, Kramme S, Manuguerra JC, Müller S, Rickerts V, Stürmer M, Vieth S, Klenk HD, Osterhaus AD, Schmitz H, Doerr HW. Identification of a Novel Coronavirus in Patients with Severe Acute Respiratory Syndrome, N. Engl.J.Med. 2003 348(20):1967-1976.
  • [8] Masuda N, Holme P. Predicting and controlling infectious disease epidemics using temporal networks. F1000 Prime Rep. 2013;5:6. doi: 10.12703/P5-6. Epub 2013.
  • [9] K Ergen, A Cilli , N Yahnioğlu, Predicting Epidemic Diseases Using Mathematical Modelling of SIR, Acta Physica Polonica A, Vol 127, page B-273-275, 2015. DOI:10.12693/APhysPolA.128.B-273
  • [10] Lih-Ing W. Roeger. Dynamically Consistent Discrete-Time SI and SIS Epidemic Models, Discrete and Continuous Dynamical systems, supplement, page 653-662, 2013.
  • [11] Kermack WO, McKendrick AG: A contribution to the mathematical theory of epidemics. P.R.Soc. Lond. A 1927, 115:700-721.
  • [12] Fact sheet on the World Malaria Report 2013
  • [13] MER_Crimean_Congo_Haemorragic_Fever_Prevention_and_Control.pdf
  • [14] World Health Organization. Afghanistan crisis health update 31 December 2001.
  • [15] World Health Statics 2015 Report, World Health organization.
  • [16] Weekly Epidemiological Monitor Volume 5, Issue 32, Regional office for the Eastern Mediterranean, WHO, 05 August 2012.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Articles
Yazarlar

Arzu Çilli Bu kişi benim 0000-0002-0596-3637

Kıvanç Ergen Bu kişi benim 0000-0002-5655-5975

Ercüment Akat Bu kişi benim 0000-0001-9267-1650

Yayımlanma Tarihi 1 Mart 2019
Gönderilme Tarihi 5 Şubat 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 37 Sayı: 1

Kaynak Göster

Vancouver Çilli A, Ergen K, Akat E. SOME MATHEMATICAL MODELS AND APPLICATIONS USED IN EPIDEMICS. SIGMA. 2019;37(1):17-23.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/