Related papers: A multiscale approach for spatially inhomogeneous …
Complex networks with pairwise connections have been vastly used for the modeling of interactions within systems. Although these type of models are capable to capture rich structures and different phases within a great variety of…
An epidemic model where disease transmission can occur either through global contacts or through local, nearest neighbor interactions is considered. The classical SIR--model describing the global interactions is extended by adding…
To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a…
We investigate the use of hybrid techniques in complex processes of infectious diseases. Since predictive disease models in biomedicine require a multiscale approach for understanding the molecule-cell-tissue-organ-body interactions,…
We prove that, for Poisson transmission and recovery processes, the classic Susceptible $\to$ Infected $\to$ Recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time $t>0$, a strict lower bound on the expected…
Traditional studies about disease dynamics have focused on global stability issues, due to their epidemiological importance. We study a classical SIR-SI model for arboviruses in two different directions: we begin by describing an…
The results of Kermack-McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of epidemic, systematically. The basic goal is to capture the effects of…
Contact patterns in populations fundamentally influence the spread of infectious diseases. Current mathematical methods for epidemiological forecasting on networks largely assume that contacts between individuals are fixed, at least for the…
Disease transmission is studied through disciplines like epidemiology, applied mathematics, and statistics. Mathematical simulation models for transmission have implications in solving public and personal health challenges. The SIR model…
We study the qualitative properties of a spatial diffusive heterogeneous SIR model, that appears in mathematical epidemiology to describe the spread of an infectious disease in a population. The model we consider consists in a system of…
We present an epidemiological compartment model, SAIR(S), that explicitly captures the dynamics of asymptomatic infected individuals in an epidemic spread process. We first present a group model and then discuss networked versions. We…
Infection dynamics have been studied extensively on complex networks, yielding insight into the effects of heterogeneity in contact patterns on disease spread. Somewhat separately, metapopulations have provided a paradigm for modeling…
The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action Susceptible-Infected-Recovered model of Kermack and McKendrick. Its usefulness derives largely from its conceptual and mathematical…
Seasonal variations in the incidence of infectious diseases are a well-established phenomenon, driven by factors such as climate changes, social behaviors, and ecological interactions that influence host susceptibility and transmission…
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…
We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…
Using a probability of novel encounter derived from a physical model, we augment the SIR compartmental model for disease spread. Scenarios with the same initial trajectories and identical $R_0$ values can diverge greatly depending on the…
In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for…
An understanding of the disease spreading phenomenon based on a mathematical model is extremely needed for the implication of the correct policy measures to contain the disease propagation. Here, we report a new model namely the Ising-SIR…
The aim of this work was to show few examples and few perspective of modeling in epidemiology. We began with differential equations which were a first tool to describe and predict that phenomena. Wroclaw as a cite was very important,…