Intervention evaluation and structural identifiability in compartmental models of infectious disease transmission

This thesis concerns the principled use of mathematical models for informing control interventions in the context of an infectious disease outbreak context. We address two main related questions. First, how can interventions be evaluated and compared in a principled manner using a dynamic (time-varying), mathematical model? The second question pertains to structural identifiability, a prerequisite for successful parameter inference in dynamic models: how does the type of model output influence the structural identifiability of dynamic, mathematical models for infectious disease transmission? We address the first question using two outbreaks of infectious disease - hepatitis A and African swine fever (ASF) - as illustrative examples, and the second question by conducting structural identifiability analysis of various ordinary differential equation (ODE) model versions. Links to all code and files needed to reproduce the results in this thesis have been provided. Our contributions are detailed in three papers: a published article and two manuscripts, now summarized. Chapter 3: Dankwa et al. (2021) developed a dynamic, deterministic model to explain transmission in the 2017-2019 hepatitis A virus (HAV) outbreak in Louisville, Kentucky, US, among persons experiencing homelessness or who use drugs, known to be at a high risk of HAV infection. With the model, alternative vaccination scenarios were examined for effectiveness and cost, and an estimate for the critical vaccination threshold required for herd immunity in this population was derived. Prior to this study, no such estimate had been obtained for this population anywhere in the US. Chapter 4: Dankwa et al. (2022b) developed a dynamic, stochastic, spatial model to explain ASF virus (ASFV) transmission among wild boar and domestic pig herds, and to evaluate alternative outbreak management measures. The model was developed such that it could be refined to account for more outbreak data and hence it is suitable for real- time outbreak analysis. This study is relevant, given the ongoing ASF epidemic in Europe, and the scarcity of ASFV transmission models which account for transmission at the wildlife-livestock interface, despite the evidence of such transmission in Europe. Chapter 5: Dankwa et al. (2022a) conducted structural identifiability analysis of unknown parameters, including initial conditions, of 26 ODE model versions to demonstrate the influence of the type of model output(s) on models' structural identifiability. Data types such as incidence and prevalence, typically encountered in disease surveillance, were studied as model outputs. This analysis emphasizes the importance of a careful consideration of model outputs prior to performing inference with transmission models.