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We introduce a Bayesian sequential data assimilation method for COVID-19 forecasting. It is assumed that suitable transmission, epidemic and observation models are available and previously validated and the transmission and epidemic models…
We make a retrospective review on various control measures taken by 127 countries/territories during the first wave of COVID-19 pandemic until July 7, 2020, and evaluate their impacts on the epidemic dynamics quantitatively. The SEIR-QD…
Epidemiological delays, such as incubation periods, serial intervals, and hospital lengths of stay, are among key quantities in infectious disease epidemiology that inform public health policy and clinical practice. This information is used…
We study the reported data from the COVID-19 pandemic outbreak in January - May 2020 in 119 countries. We observe that the time series of active cases in individual countries (the difference of the total number of confirmed infections and…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
We analyze the dynamics of the COVID-19 epidemic taking into account the role of the unreported cases. After a first section in which we deal with a framework of very slow test capacity, we turn to the model recently introduced/implemented…
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…
Classical epidemiological models assume homogeneous populations. There have been important extensions to model heterogeneous populations, when the identity of the sub-populations is known, such as age group or geographical location. Here,…
Understanding infectious disease spread remains a critical public health challenge, particularly given the interplay between household dynamics and community transmission patterns. Traditional epidemiological models often oversimplify these…
The evolution of epidemiological parameters, such as instantaneous reproduction number Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often…
This paper introduces a nonstandard finite difference (NSFD) approach to a reaction-diffusion SEIQR epidemiological model, which captures the spatiotemporal dynamics of infectious disease transmission. Formulated as a system of semilinear…
Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…
A model of reactive social distancing in epidemics is proposed, in which the infection rate changes with the number infected. The final-size equation for the total number that the epidemic will infect can be derived analytically, as can the…
We propose a compartmental mathematical model for the spread of the COVID-19 disease, showing its usefulness with respect to the pandemic in Portugal, from the first recorded case in the country till the end of the three states of…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
New coronavirus disease (COVID-19) has constituted a global pandemic and has spread to most countries and regions in the world. By understanding the development trend of a regional epidemic, the epidemic can be controlled using the…
The spread of COVID-19 has been greatly impacted by regulatory policies and behavior patterns that vary across counties, states, and countries. Population-level dynamics of COVID-19 can generally be described using a set of ordinary…
We consider state-dependent delay equations (SDDE) obtained by adding delays to a planar ordinary differential equation with a limit cycle. These situations appear in models of several physical processes, where small delay effects are…
The COVID-19 pandemic has presented unprecedented challenges worldwide, necessitating effective modelling approaches to understand and control its transmission dynamics. In this study, we propose a novel approach that integrates…