Related papers: Survival Dynamical Systems for the Population-leve…
Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the…
Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior.…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…
In this paper, we show how a dynamic population game can model the strategic interaction and migration decisions made by a large population of agents in response to epidemic prevalence. Specifically, we consider a modified…
We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed by individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local…
We propose a novel multi-scale modeling framework for infectious disease spreading, borrowing ideas and modeling tools from the so-called Refractory Density (RD) approach. We introduce a microscopic model that describes the probability of…
Modeling and control of epidemics such as the novel Corona virus have assumed paramount importance at a global level. A natural and powerful dynamical modeling framework to use in this context is a continuous time Markov decision process…
This paper considers the classical SIR epidemic model driven by a multidimensional L\'evy jump process. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. Our method differs from…
Transportation networks play a critical part in the spread of infectious diseases between populations. In this work, we define a networked susceptible-exposed-infected-recovered epidemic process with loss of immunity over time (SEIRS) that…
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal…
In this work, we review the figures used to characterize an epidemic outbreak most. Particular attention is drawn to epidemic spreading at time-varying transition rates. A time-varying SIR-like model is used to describe the epidemic…
We propose a new stochastic epidemiological model defined in a continuous space of arbitrary dimension, based on SIS dynamics implemented in a spatial $\Lambda$-Fleming-Viot (SLFV) process. The model can be described by as little as three…
This paper presents a detailed mathematical investigation into the dynamics of COVID-19 infections through extended Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological models. By…
The Dynamical Survival Analysis (DSA) is a framework for modeling epidemics based on mean field dynamics applied to individual (agent) level history of infection and recovery. Recently, DSA has been shown to be an effective tool in…
We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious, and recovered individuals, under epidemic spreading driven…
Dynamic properties of spreading infection through a heterogeneous population are studied numerically and analytically using a dynamic variant of Watts and Strogatz Small World Network-based stochastic Susceptible-Exposed-Infectious-Removed…
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…
We introduce a mathematical description of the impact of sociality in the spread of infectious diseases by integrating an epidemiological dynamics with a kinetic modeling of population-based contacts. The kinetic description leads to study…
We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from…
Recently the A/H1N1-2009 virus pandemic appeared in Mexico and in other nations. We present a study of this pandemic in the Mexican case using the SIR model to describe epidemics. This model is one of the simplest models but it has been a…