Calibrating a stochastic SIR-model to simulated data using different calibration methods : a tutorial & comparison of methods

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dc.contributor.advisorHazelbag, Marijnen_ZA
dc.contributor.advisorDelva, Wimen_ZA
dc.contributor.authorVan Staden, Wynand-Junioren_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.en_ZA
dc.date.accessioned2020-02-28T17:20:23Z
dc.date.accessioned2020-04-28T12:24:14Z
dc.date.available2020-02-28T17:20:23Z
dc.date.available2020-04-28T12:24:14Z
dc.date.issued2020-04
dc.descriptionThesis (MSc)--Stellenbosch University, 2020.en_ZA
dc.description.abstractENGLISH ABSTRACT: Mathematical models have helped researchers identify and quantify trends in observed data, which is especially useful in the field of epidemiology. Fitting models to data enhances the credibility of model results, since the underlying framework of disease, is quantified and epidemiological drivers can be found. However, many calibration methods exist that quantify key parameters of a model, given observed data, and choosing which calibration method to use in a study needs justification. Also, understanding how different calibration methods work, can improve the quality and reduce uncertainty of estimated parameters. Four calibration methods (two optimization methods and two sampling methods) were reviewed and compared by calibrating a simple stochastic SIR model to model simulated data, with all four methods. With the target parameters known and by evaluating the performance of the calibration methods by using bias, accuracy and coverage measures, it was found that sampling methods (Bayesian Maximum Likelihood Estimation and the Approximate Bayesian Computation rejection algorithm) outperform optimization methods (Least Squares and Maximum Likelihood Estimation).en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: Wiskundige modelle help navorses om die neigings in waargeneemde data te identifiseer en te kwantifiseer, wat veral nuttig in die van epidemiologie is. Deur modelle aan data te kalibreer, word die geloofwaardigheid van model resultate verhoog, aangesien die onderliggende raamwerk van ’n siekte gekwantifiseer word en epidemiologiese drywers gevind kan word. Daar bestaan egter baie kalibrasiemetodes wat die sleutel parameters van ’n model kwantifiseer, gegewe waargenome data en die keuse van die kalibrasiemetode om in ’n studie te gebruik, moet gereverdig word. Deur om te verstaan hoe verskillende kalibrasiemetodes werk, kan dit die kwaliteit verbeter en onsekerheid van geskatte parameters verminder. Vier kalibrasiemetodes (twee optimeringsmetodes en twee steekproef metodes) is hersien en vergelyk deur ’n eenvoudige stogastiese SIR-model te kalibreer aan gesimuleerde data met al vier metodes te modelleer. Met die teikenparameters bekend en deur die werking van die kalibrasiemetodes te evalueer deur die berekening van vooroordeligheid, akkuraatheid en bedekking, is daar gevind dat steekproefmetodes (Bayesian Maximum Likelihood Estimation en die Approximate Bayesian Computation verwerpings algoritme) beter as optimeringsmetodes (Least Squares en Maximum Likelihood Estimation) vaar.af_ZA
dc.description.versionMastersen_ZA
dc.format.extentx, 57 pagesen_ZA
dc.identifier.urihttp://hdl.handle.net/10019.1/108187
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch University.en_ZA
dc.rights.holderStellenbosch University.en_ZA
dc.subjectCalibrationen_ZA
dc.subjectStochastic models -- Calibrationen_ZA
dc.subjectSIR modelen_ZA
dc.subjectEpidemiology -- Mathematical modelsen_ZA
dc.subjectBayesian statistical decision theoryen_ZA
dc.subjectSampling (Statistics)en_ZA
dc.subjectMathematical optimizationen_ZA
dc.subjectParameter estimationen_ZA
dc.subjectUCTD
dc.titleCalibrating a stochastic SIR-model to simulated data using different calibration methods : a tutorial & comparison of methodsen_ZA
dc.typeThesisen_ZA
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