Related papers: Delay differential equations for the spatially-res…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…
While COVID-19 is rapidly propagating around the globe, the need for providing real-time forecasts of the epidemics pushes fits of dynamical and statistical models to available data beyond their capabilities. Here we focus on statistical…
In this paper, we present the Partial Integral Equation (PIE) representation of linear Partial Differential Equations (PDEs) in one spatial dimension, where the PDE has spatial integral terms appearing in the dynamics and the boundary…
Epidemic models are invaluable tools to understand and implement strategies to control the spread of infectious diseases, as well as to inform public health policies and resource allocation. However, current modeling approaches have…
Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible $S$, infected $I$, removed $R$ and dead people $D$. In order to have…
During the ongoing COVID-19 pandemic, mathematical models of epidemic spreading have emerged as powerful tools to produce valuable predictions of the evolution of the pandemic, helping public health authorities decide which intervention…
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…
During 2020, the infection rate of COVID-19 has been investigated by many scholars from different research fields. In this context, reliable and interpretable forecasts of disease incidents are a vital tool for policymakers to manage…
Over a year after the start of the COVID-19 epidemics, we are still facing the virus and it is hard to correctly predict its future spread over weeks to come, as well as the impacts of potential political interventions. Current epidemic…
As global living standards improve and medical technology advances, many infectious diseases have been effectively controlled. However, certain diseases, such as the recent COVID-19 pandemic, continue to pose significant threats to public…
The coronavirus disease 2019 (COVID-19) pandemic radically impacts our lives, while the transmission/infection and recovery dynamics of COVID-19 remain obscure. A time-dependent Susceptible, Exposed, Infectious, and Recovered (SEIR) model…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
This work proposes a method to compute the maximum value obtained by a state function along trajectories of a Delay Differential Equation (DDE). An example of this task is finding the maximum number of infected people in an epidemic model…
Breaking a complex bio-social phenomenon (epidemic) into its components, considering the processes that determine its dynamics, formalizing the accepted hypotheses in mathematical equations, selecting appropriate experimental and…
In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…
Given the ongoing Covid-19 pandemic, it is of interest to understand how the infections spread as the combined result of measures taken by central planners (governments) and individual behavior. In this work, the spread of Covid-19 is…
How can we learn a dynamical system to make forecasts, when some variables are unobserved? For instance, in COVID-19, we want to forecast the number of infected and death cases but we do not know the count of susceptible and exposed people.…
The COVID-19 pandemic has posed a heavy burden to the healthcare system worldwide and caused huge social disruption and economic loss. Many deep learning models have been proposed to conduct clinical predictive tasks such as mortality…
The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted…
This paper extends the canonical model of epidemiology, SIRD model, to allow for time varying parameters for real-time measurement of the stance of the COVID-19 pandemic. Time variation in model parameters is captured using the generalized…