Epidemiological modelling in infectious diseases: stages and classification

Öz

Modelling in infectious diseases has recently been an important field due to avian influenza, swine influenza, severe acute respiratory syndrome (SARS), Middle East respiratory syndrome-coronavirus (MERS-CoV), novel coronavirus (nCoV) and many other diseases. Epidemiological models are usually defined as mathematical and/or logical demonstrations of epidemiology of diseases and the related process. Concerning animal disease management, ‘models’ can be defined more widely in that they contain a range of statistical/mathematical tools regarding other aspects of the disease in addition to its spreading. Modelling might be useful when experimental or field studies are impossible or not practical or in retrospective analyzing of previous epidemics in order to search alternative control strategies. The aim of this study was to examine some of the modelling methods and determine what mathematical modelling meant in infectious diseases, its purpose of use, to classify the steps followed during modelling period and models used in the field of animal health.

Anahtar Kelimeler

• Infectious diseases
• epidemiological modelling
• modelling stages

Kaynakça

1. 1. Garner MG, Hamilton SA. Principles of epidemiological modelling. Rev Sci Tech Off Int Epiz. 2011;30 (2): 407-416.
2. 2. Dubé C, Garner G, Stevenson M, Sanson R, Estrada C, Willeberg P. The use of epidemiological models for the management of animal diseases, Conf. OIE. 2007a.p. 13- 23.
3. 3. Garner MG, Beckett SD. Modelling the spread of foot-and-mouth disease in Australia. Aust Vet J. 2005;83(12): 258-66.
4. 4. Mangen M, Jalvingh A, Nielen M, Mourits M, Dijkhuizen AA, Dijkhuizen A. Spatial and stochastic simulation to compare two emergency-vaccination strategies with a marker vaccine in the 1997/1998 Dutch classical swine fever epidemic. Prev Vet Med. 2001;48, 177-200.
5. 5. Zhou Y. Stability of periodic solutions for an SIS model with pulse vaccination, Mathematical and Computer Modelling. 2003;38: 299-308.
6. 6. Braur F. Basical ideal of mathematical epidemiology. In: Castillo-Chavez C, Blower S, editors. Mathematical Approaches for Emerging and Reemerging Infectious Diseases. Springer-Verlag, New York, 2002. p. 31-65.
7. 7. Gran JM. Infectious disease modelling and causal inference MSc, University of Oslo, Oslo, Norway. 2010.
8. 8. Yang Q, Jiang D, Shi N, Ji C. The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence. J Math Anal Appl. 2012;388 (1): 248-271.

9. 9. Wu J, Dhingra R, Gambhir M, Remais JV. Sensitivity analysis of infectious disease models: methods, advances and their application. J R Soc Interface. 2013;10: 20121018. http://dx.doi.org/10.1098/rsif.2012.1018
10. 10. Hethcote HW. Three basic epidemiological models. http://www.mtholyoke.edu/~ahoyerle/math333/ThreeBasicModels.pdf . Accessed: 12.12.2019.
11. 11. Can MF. Hayvan sağlığı ekonomisi alanında kullanılan modelleme teknikleri ve çeşitli modelleme çalışmaları. Vet Hekim Der Derg. 2009;80(3):7-12.
12. 12. Kelling MJ, Rohani P. Modeling infectious diseases in humans&animals, Clinical Infectious Diseases. 2008;47(6):864-865.
13. 13. Kelling MJ, Danon L. Mathematical modelling of infectious disease. British Medical Bulletin. 2009;92: 33–42.
14. 14. Anon2. Optimizasyon modelleri ve çözüm metodları. http://home.ku.edu.tr/~mturkay/indr501/Optimizasyon.pdf Accessed: 11.01.2020
15. 15. Eddymurphy UA. Discrete modeling and analysis of contact networks in epidemic models, Master’s Thesis, Lappeenranta University of Technology, Lappeenranta, Finland. 2018.
16. 16. Garner MG, Dubé C, Stevenson MA, Sanson RL, Estrada C, Griffin J. Evaluating alternative approaches to managing animal disease outbreaks - The role of modelling in policy formulation. Vet Ital. 2007;43 (2): 285-298.
17. 17. Green LE, Medley GF. Mathematical modelling of the foot and mouth disease epidemic of 2001: strengths and weaknesses. Res Vet Sci. 2002;73(3): 201-5.
18. 18. Law AM. How to build valid and credible simulation models. https://ieeexplore.ieee.org/abstract/document/1574236. Accessed: 09.01.2020.
19. 19. Taylor N. Review of the use of models in informing disease control policy development and adjustment. https://pdfs.semanticscholar.org/c8dc/8214ec760f8cd73f164e83aea403a98e54bb.pdf. Accessed: 17.01.2020.
20. 20. Sargent R. Verification and validation of simulation models. https://www.informs-sim.org/wsc11papers/016.pdf. Accessed: 12.01.2019.
21. 21. Dubé C, Stevenson MA, Garner MG, Sanson RL, Corso BA, Harvey N, Griffin J, Wilesmith JW, Estrada C. A comparison of predictions made by three simulation models of foot-and-mouth disease. NZ Vet J. 2007b;55 (6), 280-288.
22. 22. Frey HC, Patil R. Identification and review of sensitivity analysis methods. Risk Analysis. 2002;22 (3), 553-577.
23. 23. Chapagain P, van Kessel J, Karns J, Wolfgang D, Hovingh E, Nelen K, Schukken Y, Grohn Y. A mathematical model of the dynamics of Salmonella Cerro infection in a US dairy herd. Epidemiol Infect. 2008;136, 236-272.
24. 24. Gandolfi A. Percolation methods for SEIR epidemics on graphs. In: Rao VSH, Ravi D,editors. Dynamic Models of Infectious Diseases. 2013.p.31-58.
25. 25. Anon1. Deterministik ve stokastik modeller. http://ozgur aktekin.blogspot.com.tr/2015/09/deterministik-vs-stokastik-mode ller.html Accessed: 09.01.2020
26. 26. Ergönül Ö. Enfeksiyon hastalıkları epidemiyolojisi, Hastane enfeksiyonları: korunma ve kontrol sempozyum dizisi. 2008;80: 30-41.
27. 27. Gürsoy ŞT, Öcek ZA. Bağışıklamanın ekonomik analizi, İnfeksiyon Dergisi. 2007;21 (4): 217-223
28. 28. Choisy M, Guégan JF, Rohani P. Mathematical modeling of infectious diseases Dynamics. In: Michel T, editor. Encyclopedia of Infectious Diseases: Modern Methodologie, Wiley & Sons, Inc., Hoboken, New Jersey, USA. 2007.p.382-383.
29. 29. Becker NJ. Using data to ınform model choice, In: Chow SC, Jones B, Lıu J, Peace KE, Turnbull BW (ed) Modeling to inform infectious disease control, CRC Press Taylor & Francis Group. 2015. p 169.
30. 30. Yang B. Stochastic dynamics of an SEIS epidemic model, Advances in difference equations. 2016;226. doi: 10.1186/s13662-016-0914-3.
31. 31. Jenkins D. An examination of mathematical models for infectious disease, Honors research projects. 2015; projects 194.https://ideaexchange.uakron.edu/cgi/viewcontent.cgi?article=1195&context=honors_research_projects.
32. 32. Li MY, Muldowney JS. Global stability for the SEIR model in epidemiology. Mathematical Biosciences. 1995;125: 155-164.
33. 33. Hui J, Zhu DM. Dynamics of stochastic SEIS epidemic model with varying population size, Int J Bifurcation Chaos. 2007;17 (5): 1513- 1529.
34. 34. Chapman JD, Chappell MJ, Evans ND. The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies. Computer Methods and Programs in Biomedicine. 2011;104: 37- 49.
35. 35. Bichara D, Iggidr A, Sallet G. Global analysis of multi-strains SIS, SIR and MSIR epidemic models. J Appl Math Comput. 2013; 44(1-2):273-292.
36. 36. Hethcote HW. The mathematics of infectious diseases, SIAM Review. 2000;42 (4): 599–653.