Statistical methods for fitting dengue disease models, and related issues

Dengue is currently the world’s fastest growing vector-borne disease which causes fever, headache, muscle aches and other flu-like symptoms, affecting 50-100 million people worldwide yearly. Modeling dengue incidence over time is challenging because of multiple virus serotypes, high asymptomaticity, and the limited data availability. Different dengue modeling approaches have been explored in the public health literature such as economic models, agent-based (AB) models, and ordinary differential equation (ODE) models. ODE models are the standard to model dynamic systems involving interactions between various populations because of their solid mathematical/statistical foundation and ease of implementation in standard software packages. However, the homogeneous and perfectly mixing assumptions of the ODE model may not accurately represent the real world. On the other hand, AB models may lack the solid mathematical/statistical theory, but can model heterogeneity at the individual level. In the first part of this dissertation, we propose a simplified new ODE model (vSEIR) and compare this model with three existing ODE models. We also compare two discretization methods for initial value problems: derivative-free mesh adaptive direct search method with quadratic models (MADSQ) and derivative trust region (DTR) method. The simulation studies show that MADSQ can provide a better solution to the ODE compared to DTR when the parameter space has many local minima. We also demonstrate that the proposed vSEIR ODE model provides a better fit to the data than the other existing ODE models. In the second part of this dissertation, we validate a dengue ComputationaL ARthropod Agents (CLARA) AB model, by comparing with its corresponding ODE model and the real world data. We not only show the similarity between the two models, but also contrast them. Our future plan is to continue to improve dengue ODE models by providing a stochastic version. Improved dengue models will provide public health researchers tools to better understand dengue disease outbreaks