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Rule-based models have been successfully used to represent different aspects of the COVID-19 pandemic, including age, testing, hospitalisation, lockdowns, immunity, infectivity, behaviour, mobility and vaccination of individuals. These…
Infectious diseases are among the most prominent threats to mankind. When preventive health care cannot be provided, a viable means of disease control is the isolation of individuals, who may be infected. To study the impact of isolation,…
Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…
The COVID-19 pandemic highlighted the limitations of existing epidemic simulation tools. These tools provide information that guides non-pharmaceutical interventions (NPIs), yet many struggle to capture complex dynamics while remaining…
The estimation of unknown parameters in simulations, also known as calibration, is crucial for practical management of epidemics and prediction of pandemic risk. A simple yet widely used approach is to estimate the parameters by minimizing…
This paper extends the canonical model of epidemiology, the SIRD model, to allow for time-varying parameters for real-time measurement and prediction of the trajectory of the Covid-19 pandemic. Time variation in model parameters is captured…
The role of epidemiological models is crucial for informing public health officials during a public health emergency, such as the COVID-19 pandemic. However, traditional epidemiological models fail to capture the time-varying effects of…
We present EPITIME (EPidemic Integral models TIMe profile Explorer), a computational framework for the simulation of two classes of integral epidemic models: an age of infection model and an information dependent behavioural model. The…
The COronaVIrus Disease 2019 (COVID-19) pandemic that has had the world in its grip from the beginning of 2020, has resulted in an unprecedented level of public interest and media attention on the field of mathematical epidemiology. Ever…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
Undulation of infection levels, usually called waves, are not well understood. In this paper we propose a mathematical model that exhibits undulation and decay towards a stable state. The model is a re-interpretation of the original…
In this work, we have described the mathematical modeling of COVID-19 transmission using fractional differential equations. The mathematical modeling of infectious disease goes back to the 1760s when the famous mathematician Daniel…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Differentiable programming has recently received much interest as a paradigm that facilitates taking gradients of computer programs. While the corresponding flexible gradient-based optimization approaches so far have been used predominantly…
Across the world, scholars are racing to predict the spread of the novel coronavirus, COVID-19. Such predictions are often pursued by numerically simulating epidemics with a large number of plausible combinations of relevant parameters. It…
Traditionally, the identification of parameters in the formulation and solution of inverse problems considers that models, variables and mathematical parameters are free of uncertainties. This aspect simplifies the estimation process, but…
The fast transmission rate of COVID-19 worldwide has made this virus the most important challenge of year 2020. Many mitigation policies have been imposed by the governments at different regional levels (country, state, county, and city) to…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex…
Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results…