Investigation of Various Infectious Diseases in Turkey by Mathematical Models SI and SIS

Mathematical models can give us information on number of cases, deaths caused by infectious diseases. In this study, we aimed to predict the effects of Crimean-Congo Hemorrhagic Fever (CCHF), tuberculosis (TB), measles for Turkey and the efficiency of SI and SIS mathematical models were defined in the prediction of the number of infected people for these diseases. In CCHF, predictions for 2014 gave 0% error in both models. As for TB, SIS model predicted the exact number and SI model predicted a few more cases than that of SIS model. Again SI and SIS models gave the exact values for measles. According to these predictions it seems that CCHF and TB cases will continue to increase slightly while measles cases will approach zero. These models can predict exact numbers for each year, in a long term and in normal conditions (unless there are external parameters such as natural disaster, war, emigration and terrorism ) they can predict the trend for the diseases and can tell when to disappear. Therefore, updating data are of importance to achieve the powerful prediction.

Keywords:

Infectious Mathematical Model, Prediction,

PDF

___

[1] Steere AC (1989) Lyme disease. N Engl J Med 321: 586–596.
[2] Hilbi H, Jarraud S, Hartland E, Buchrieser C (2010) Update on Legionnaires’ disease: pathogenesis, epidemiology, detection and control. Mol Microbiol 76: 1–11.
[3] Taff ML, Siegal FP, Geller SA. Outbreak of an acquired immunodeficiency syndrome associated with opportunistic infections and Kaposi's sarcoma in male homosexuals. Am. J.Forensic Med.Pathol. 1982 Sep.3(3):259-64.
[4] Zuckerman AJ. The Elusive Hepatitis C Virus. BMJ. 1989 Oct 7;299(6704):871-3.
[5] 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 May 15;348(20):1967-76. Epub 2003 Apr 10.
[6] Masuda N, Holme P. Predicting and controlling infectious disease epidemics using temporal networks. F1000Prime Rep. 2013;5:6. doi: 10.12703/P5-6. Epub 2013 Mar 4.
[7] Lih-Ing W. Roeger. Dynamically Consistent Discrete-Time SI and SIS Epidemic Models, Discrete and Continuous Dynamical systems, supplement,653-662, 2013.
[8] Keeling MJ, Rohani P: Modeling Infectious Diseases in Humans and Animals. Princeton: Princeton University Press; 2007.
[9] www.thsk.gov.tr/component/k2/zoonotik-ve-vektorel-hastaliklar-daire-baskanligi-istatiksel- verileri.html
[10] www.thsk.gov.tr/component/k2/tuberkuloz-daire-baskanligi-istatiksel-verileri.html
[11] www.thsk.gov.tr/component/k2/asi-ile-onlenebilir-hastaliklar-daire-baskanligi-istatiksel-verileri.html
[12] Ergen K., Çilli A. and Yahnioğlu N., Predicting Epidemic Diseases using Mathematical Modelling of SIR,DOI:10.12693/APhysPolA.128.B-273.