A Sensitivity Analysis of Model Structure in Stochastic Differential Equation and Agent-Based Epidemiological Models

Bachelor Thesis


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University of Cape Town

The dynamics of infectious diseases have been modelled by several universally recognised procedures. The most common two modelling methods are differential equation models (DEM) and agent based models (ABM). These models have both been used through the late 20th and early 21st century to gain an understanding of prevalence levels and behaviour of infectious diseases; and subsequently to forecast potential impacts of a treatment. In the case of a life-threatening disease such as Malaria, it is problematic to be working with incorrect predictions and an epidemic may result from a misinformed judgement on the required treatment program. DEM and ABM have been documented to provide juxtapositioned results (and conclusions) in several cases, even whilst fitting identical data sets [Figueredo, et al. 2014]. Under the correct model, one would expect a fair representation of an infectious disease and hence an insightful conclusion. It is hence detrimental for the choice of treatment tactics to be dependent on the choice of model structure. This honours thesis has identified the necessity for caution on the model methodology and performs a sensitivity analysis on the incidence and prevalence of an infectious disease under varying levels of treatment. This thesis hones in on modelling methodology under various structures: the procedure is applicable to any infectious disease, and this thesis provides a case study on Malaria modelling with a later extension into Ebola. Beginning with a simple Susceptible-Infected-Recovered-Susceptible (SIRS) model: immediately obvious differences are examined to give an indication of the point at which the models lose integrity in direct comparability. The SIRS models are built up to include varying levels of exposure, treatment and movement dynamics and examining the nature of the differences in conclusions drawn from separate models.