Related papers: Slow decay of infection in the inhomogeneous SIR m…
In this work, the spread of a contagious disease on a society where the individuals may take precautions is modeled. The primary assumption is that the infected individuals transmit the infection to the susceptible members of the community…
The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all…
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.…
Understanding the dynamics of the spread of diseases within populations is critical for effective public health interventions. We extend the classical SIR model by incorporating additional complexities such as the introduction of a cure and…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
Our study is based on an epidemiological compartmental model, the SIRS model. In the SIRS model, each individual is in one of the states susceptible (S), infected(I) or recovered (R), depending on its state of health. In compartment R, an…
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…
The study of epidemic models plays an important role in mathematical epidemiology. There are many researches on epidemic models using ordinary differential equations, partial differential equations or stochastic differential equations. In…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
In real social networks, person-to-person interactions are known to be heterogeneous, which can affect the way a disease spreads through a population, reaches a tipping point in the fraction of infected individuals, and becomes an epidemic.…
Two factors that are often ignored but could play a crucial role in the progression of an infectious disease are the distributions of inherent susceptibility ($\sigma_{inh}$) and external infectivity ($\iota_{ext}$), in a given population.…
We study a susceptible-vaccinated--infected--recovered (SVIR) epidemic-spreading model with diversity of infection rate of the individuals. By means of analytical arguments as well as extensive computer simulations, we demonstrate that the…
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
We study a multistage epidemic model which generalizes the SIR model and where infected individuals go through K>0 stages of the epidemic before being removed. An infected individual in stage k=1,...,K may infect a susceptible individual,…
Although viral spreading processes taking place in networks are often analyzed using Markovian models in which both the transmission and the recovery times follow exponential distributions, empirical studies show that, in many real…
We consider a spatial SIR epidemic model where the infectivity of infected individuals depends upon their age of infection, and infections are non local. The domain is an unbounded subset of $\R^d$,and the individuals do not move. We extend…
The viral load is known to be a chief predictor of the risk of transmission of infectious diseases. In this work, we investigate the role of the individuals' viral load in the disease transmission by proposing a new…
We propose a simple SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two…
In the Staged Progression (SP) epidemic models, infected individuals are classified into a suitable number of states. The goal of these models is to describe as closely as possible the effect of differences in infectiousness exhibited by…
In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated…