Related papers: An age-structured diffusive model for epidemic mod…
Epidemiological models are an important tool in coping with epidemics, as they offer a forecast, even if often simplistic, of the behavior of the disease in the population. This allows responsible health agencies to organize themselves and…
Hybrid neural network models combine the advantages of a neural network's fitting functionality with differential equation models to reflect actual physical processes and are widely used in analyzing time-series data. Most related studies…
A configuration model for epidemic spread, based on a scale-free network, is introduced. We obtain the analytical solutions describing both unstable and stable dynamics of the epidemic spreading, and demonstrate how these regimes can…
Generative models have recently undergone significant advancement due to the diffusion models. The success of these models can be often attributed to their use of guidance techniques, such as classifier or classifier-free guidance, which…
Understanding the timing of the peak of a disease outbreak forms an important part of epidemic forecasting. In many cases, such information is essential for planning increased hospital bed demand and for designing of public health…
It is of vital importance to understand and track the dynamics of rapidly unfolding epidemics. The health and economic consequences of the current COVID-19 pandemic provide a poignant case. Here we point out that since they are based on…
Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the…
Predicting counterfactual distributions in complex dynamical systems is essential for scientific modeling and decision-making in domains such as public health and medicine. However, existing methods often rely on point estimates or purely…
We study the long-time behavior of solutions of the SIRS model, a reaction-diffusion system that appears in epidemiology to describe the spread of epidemics. We allow the system to be heterogeneous periodic. Under some hypotheses on the…
A symmetry group classification for fourth-order reaction-diffusion equations, allowing for both second-order and fourth-order diffusion terms, is carried out. The fourth order equations are treated, firstly, as systems of second-order…
We propose a versatile and computationally efficient estimating equation method for a class of hierarchical multiplicative generalized linear mixed models with additive dispersion components, based on explicit modelling of the covariance…
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…
Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…
This paper generalizes a previously published differential equation that describes the relation between the age-specific incidence, remission, and mortality of a disease with its prevalence. The underlying model is a simple compartment…
Much traditional statistical modelling assumes that the outcome variables of interest are independent of each other when conditioned on the explanatory variables. This assumption is strongly violated in the case of infectious diseases,…
This is work in progress. We make it accessible hoping that people might find the idea useful. We propose a discrete, recursive 5-compartment model for the spread of epidemics, which we call {\em SEPIR-model}. Under mild assumptions which…
The shape of an epidemic wave in simple epidemic models applies to a homogeneous distribution of infected people in the population. In large inhomogeneous systems, at country-scale for instance, the wave shape is similar except for the…
In this paper, we show that many structured epidemic models may be described using a straightforward product structure. Such products, derived from products of directed graphs, may represent useful refinements including geographic and…
In presence of long range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical…
Mathematical models of epidemics often use compartmental models dividing the population into several compartments. Based on a microscopic setting describing the temporal evolution of the subpopulation sizes in the compartments by stochastic…