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We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…
Different countries -- and sometimes different regions within the same countries -- have adopted different strategies in trying to contain the ongoing COVID-19 epidemic; these mix in variable parts social confinement, early detection and…
We propose a new dynamic SIR model that, in contrast with the available model on time scales, is biological relevant. For the new SIR model we obtain an explicit solution, we prove the asymptotic stability of the extinction and disease-free…
The infection dynamics of a population under stationary isolation conditions is modeled. It is underlined that the stationary character of the isolation measures can be expected to imply that an effective SIR model with constant parameters…
We introduce a minimal multiscale framework that links within-host virus dynamics to population-level SIRS epidemiology through explicit, bidirectional coupling. At the microscopic layer, a two variant quasispecies (master and mutant…
Cities have long served as nucleating centers for human development and advancement. Cities have facilitated the spread of both human creativity and human disease, and at the same time, efforts to minimize the spread of disease have…
The dynamics of epidemics depend on how people's behavior changes during an outbreak. At the beginning of the epidemic, people do not know about the virus, then, after the outbreak of epidemics and alarm, they begin to comply with the…
Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a…
Most infectious diseases including more than half of known human pathogens are not restricted to just one host, yet much of the mathematical modeling of infections has been limited to a single species. We investigate consequences of a…
We study a susceptible-infected-recovered (SIR) epidemic model on a network of $n$ interacting subpopulations. We analyze the transient and asymptotic behavior of the infection dynamics in each node of the network. In contrast to the…
Many disease models focus on characterizing the underlying transmission mechanism but make simple, possibly naive assumptions about how infections are reported. In this note, we use a simple deterministic Susceptible-Infected-Removed (SIR)…
We investigate the SIR epidemic on a dynamic inhomogeneous Erd\H{o}s-R\'enyi random graph, in which vertices are of one of $k$ types and in which edges appear and disappear independently of each other. We establish a functional law of large…
Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks…
This paper proposes a novel discrete-time multi-virus susceptible-infected-recovered (SIR) model that captures the spread of competing epidemics over a population network. First, we provide sufficient conditions for the infection level of…
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…
We have designed a computational model of a virus spread near the outbreak threshold. Using computer simulation we studied the Susceptible - Infected - Recovered (SIR) process where in consequence of a force of habit that is manifested by…
A current challenge for disease modeling and public health is understanding pathogen dynamics across scales since their ecology and evolution ultimately operate on several coupled scales. This is particularly true for vector-borne diseases,…
Transmission dynamics of infectious diseases are often studied using compartmental mathematical models, which are commonly represented as systems of autonomous ordinary differential equations. A key step in the analysis of such models is to…
Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been…
This paper presents an SIR epidemic model with two different types of perturbations: white and L\'evy noises. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. We use the comparison…