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System identification plays a crucial role in physics and machine learning for discovering governing equations directly from data. A powerful approach is the Sparse Identification of Nonlinear Dynamics (SINDy) method, which assumes that…
Disease forecasting models typically rely on a single data stream, making models brittle when histories are short or noisy. Recent top-performing models have shown that synthesizing multiple reporting systems for the same disease improves…
In this project, identifiability, observability and uncertainty properties of the deterministic and Chain Binomial stochastic SIR, SEIR and SEIAR epidemiological models are studied. Techniques for modeling overdispersion are investigated…
Analyzing data from multiple sources offers valuable opportunities to improve the estimation efficiency of causal estimands. However, this analysis also poses many challenges due to population heterogeneity and data privacy constraints.…
Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear…
Since the last century, deterministic compartmental models have emerged as powerful tools to predict and control epidemic outbreaks, in many cases helping to mitigate their impacts. A key quantity for these models is the so-called Basic…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
Capturing the structured mixing within a population is key to the reliable projection of infectious disease dynamics and hence informed control. Both heterogeneity in the number of contacts and age-structured mixing have been repeatedly…
The key issues pertaining to collection of epidemic disease data for our analysis purposes are that it is a labour intensive, time consuming and expensive process resulting in availability of sparse sample data which we use to develop…
Hysteresis-controlled devices are widely used in industrial applications. For example, cooling devices usually contain a two-point controller, resulting in a nonlinear hybrid system with two discrete states. Dynamic models of systems are…
Compartmental models, especially the Susceptible-Infected-Removed (SIR) model, have long been used to understand the behaviour of various diseases. Allowing parameters, such as the transmission rate, to be time-dependent functions makes it…
Insect species subject to infection, predation, and anisotropic environmental conditions may exhibit preferential movement patterns. Given the innate stochasticity of exogenous factors driving these patterns over short timescales,…
The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…
We compare the efficiency and ease-of-use of the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm and Sparse Physics-Informed Discovery of Empirical Relations (SPIDER) framework in recovering the relevant governing equations…
This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation…
Disease progression modeling provides a robust framework to identify long-term disease trajectories from short-term biomarker data. It is a valuable tool to gain a deeper understanding of diseases with a long disease trajectory, such as…
We consider epidemic and ecological models to investigate their coupled dynamics. Starting with the classical Susceptible-Infected-Recovered (SIR) model for basic epidemic behavior and the predator-prey (Lotka-Volterra, LV) system for…
Identifying areas in a landscape where individuals have a higher likelihood of disease infection is key to managing diseases. Unlike conventional methods relying on ecological assumptions, we perform a novel epidemiological tomography for…
Spatiotemporal dynamics pervade the natural sciences, from the morphogen dynamics underlying patterning in animal pigmentation to the protein waves controlling cell division. A central challenge lies in understanding how controllable…
People's personal hygiene habits speak volumes about the condition of taking care of their bodies and health in daily lifestyle. Maintaining good hygiene practices not only reduces the chances of contracting a disease but could also reduce…