Related papers: A multiscale approach for spatially inhomogeneous …
We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe…
We formulate a generalized susceptible exposed infectious recovered (SEIR) model on a graph, describing the population dynamics of an open crowded place with an arbitrary topology. As a sample calculation, we discuss three simple cases,…
We show that precise knowledge of epidemic transmission parameters is not required to build an informative model of the spread of disease. We propose a detailed model of the topology of the contact network under various external control…
We study the effect of external infection sources on phase transitions in epidemic processes. In particular, we consider an epidemic spreading on a network via the SIS/SIR dynamics, which in addition is aided by external agents - sources…
Modeling and simulation approaches for infectious disease dynamics have proven to be essential tools for effective control of the spread of epidemics in the population. Among these approaches, it is obvious that compartmental mathematical…
We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of…
An SIRS type model of disease transmission in an open environment is discussed. We use the Poincar\'{e} index together with a perturbation method to show that the endemic proportions need not be unique.
Compartmental equations are primary tools in disease spreading studies. Their predictions are accurate for large populations but disagree with empirical and simulated data for finite populations, where uncertainties become a relevant…
Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic…
The classic SIR model of epidemic dynamics is solved completely by quadratures, including a time integral transform expanded in a series of incomplete gamma functions. The model is also generalized to arbitrary time-dependent infection…
The SIR-compartment model is among the simplest models that describe the spread of a disease through a population. The model makes the unrealistic assumption that the population through which the disease is spreading is well-mixed. Although…
We propose a mathematical model to analyze the effects of anti-infection behavior on the equilibrium states of an infectious disease. The anti-infection behavior is incorporated into a classical epidemiological SIR model, by considering the…
This brief note highlights a largely overlooked similarity between the SIR ordinary differential equations used for epidemics on the configuration model of a Poisson network and the classical mass-action SIR equations introduced nearly a…
With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic…
Models of epidemics over networks have become popular, as they describe the impact of individual behavior on infection spread. However, they come with high computational complexity, which constitutes a problem in case large-scale scenarios…
We examine the spread of an infectious disease, such as one that is caused by a respiratory virus, with two distinct modes of transmission. To do this, we consider a susceptible--infected--susceptible (SIS) disease on a hypergraph, which…
To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the…
The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the…
We study extensions of the classical SIR model of epidemic spread. First, we consider a single population modified SIR epidemics model in which the contact rate is allowed to be an arbitrary function of the fraction of susceptible and…
We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria…