Related papers: Delay differential equations for the spatially-res…
The current global health emergency triggered by the pandemic COVID-19 is one of the greatest challenges mankind face in this generation. Computational simulations have played an important role to predict the development of the current…
To better predict the dynamics of epidemics such as COVID-19, it is important not only to investigate the network of local and long-range contagious contacts but also to understand the temporal dynamics of infectiousness and detectable…
Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind…
Delay-Differential Equations (DDEs) are the most common representation for systems with delay. However, the DDE representation is limited. In network models with delay, the delayed channels are low-dimensional and accounting for this…
Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system…
Spatiotemporal modelling of infectious diseases such as COVID-19 involves using a variety of epidemiological metrics such as regional proportion of cases or regional positivity rates. Although observing their changes over time is critical…
We analyze mathematical models for COVID-19 with discrete time delays and vaccination. Sufficient conditions for the local stability of the endemic and disease-free equilibrium points are proved for any positive time delay. The stability…
Ordinary differential equations (ODE) are a popular tool to model the spread of infectious diseases, yet they implicitly assume an exponential distribution to describe the flow from one infection state to another. However, scientific…
We present an approach to studying and predicting the spatio-temporal progression of infectious diseases. We treat the problem by adopting a partial differential equation (PDE) version of the Susceptible, Infected, Recovered, Deceased…
We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity…
We present an early version of a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread…
Epidemic forecasts are only as good as the accuracy of epidemic measurements. Is epidemic data, particularly COVID-19 epidemic data, clean and devoid of noise? Common sense implies the negative answer. While we cannot evaluate the…
In this research, we have derived a mathematical model for within human dynamics of COVID-19 infection using delay differential equations. The new model considers a 'latent period' and 'the time for immune response' as delay parameters,…
A novel predictive modeling framework for the spread of infectious diseases using high dimensional partial differential equations is developed and implemented. A scalar function representing the infected population is defined on a…
Predicting the evolution of diseases is challenging, especially when the data availability is scarce and incomplete. The most popular tools for modelling and predicting infectious disease epidemics are compartmental models. They stratify…
To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the…
Epidemiological models are best suitable to model an epidemic if the spread pattern is stationary. To deal with non-stationary patterns and multiple waves of an epidemic, we develop a hybrid model encompassing epidemic modeling, particle…
In this article a space-dependent epidemic model equipped with a constant latency period is examined. We construct a delay partial integro-differential equation and show that its solution possesses some biologically reasonable features. We…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
In this paper, we propose a new real-time differential virus transmission model, which can give more accurate and robust short-term predictions of COVID-19 transmitted infectious disease with benefits of near-term trend projection.…