The Institute for Disease modeling is committed to fundamental research in Applied Math for computational epidemiology. These methods have the potential to dramatically increase computational efficiency, enable new forms of analysis, and gain a deep understanding of dynamical processes. Our research portfolio is diverse and ever evolving. Some areas of interest include rare event detection, parameter space exploration, model calibration, fractional diffusion, dynamic mode decomposition, Monte Carlo integration, and novel solvers for compartmental systems. Many of these methods can be applied directly to EMOD output, thereby facilitating baseline calibration, campaign planning, and more.
Dynamic Mode Decomposition
With the ever-expanding computational speed and storage capacity, high-dimensional, complex data-sets have become ubiquitous in traditional scientific and engineering applications. Many of these data-sets come from complex systems that either do not have a readily available set of governing equations or the equations are too computationally expensive to simulate. The necessity for data-driven, equation-free methods to analyze these types of complex systems is paramount. Dynamic Mode Decomposition (DMD) is one such method that is being utilized and further developed at IDM for use on spatial-temporal data for infectious disease spread. Despite the difficulty of high-dimensional data, DMD automatically reduces the dimension of the system, finds relevant modes of dynamic behavior, and allows for short time-prediction in the future. The application of data-driven methods such as DMD will only become increasingly more relevant for the study of infectious disease.
Stochastic simulations of reaction-diffusion processes are frequently used for modeling physical phenomena ranging from morphogenesis and pedestrian traffic to epitaxial growth and epidemics. The underlying spatial process for these models is often assumed to follow classical diffusion; however, this is not necessarily valid. There has been an increased interest in fractional diffusion processes owing to the observation that many physical processes deviate from classical diffusion, examples of which include but are not limited to diffusion in polymers, wool prices, and the circulation of bank notes used as a proxy for human travel. The latter example is especially important in disease modelling since the movement of people will dictate how fast an infection may spread. The application of heavy-tailed diffusion processes coupled to disease dynamics is the focus of this research.
Parameter Space Exploration using The Separatrix Algorithm
Put yourself in the shoes of a health minister faced with a challenge of eradicating Polio or achieving targets specified by the Millennium Development Goals. Which interventions would you use? How would your resource allocation vary as a function of the local environment? How confident would you be that your plan would work?
The Separatrix Algorithm was developed to leverage EMOD in answering these questions. The algorithm finds regions of parameter space in which the goal is expected to be achieved with high probability. The algorithm iteratively combines binomial kernel regression with Bayesian optimal experiment design to gain the most from each simulation realization. These novel techniques allow the algorithm to enjoy significant efficiency gains over more traditional approaches such as Latin Hypercube Sampling.
Stochastic Parameter Search for Events (SParSE)
Despite recent advancements in high-performance computing (HPC) and increased popularity of stochastic modeling, there is still a gap in methods for stochastic chemical kinetics that determine all parameter configurations which lead to an event of scientific interest. Such an event-based algorithm would answer many interesting questions related to projects at IDM. For example, it could be used to compute all intervention parameter combinations that achieve eradication of a given disease. This knowledge, with region-specific econometrics, could be used to compute optimally cost-effective eradication campaign strategies tailored to each region. This gap and the potential value of such a method motivated the development of a novel algorithm – Stochastic Parameter Search for Events (SParSE) – that automatically finds the unknown parametric hyperplane conferring an event of interest at a specific success probability and error tolerance. The current work focuses on applying SParSE to disease-specific scenarios as well as on improving its convergence rate and sampling strategies.