Related papers: Various Logistic Curves in SIS and SIR Models

The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…

We investigate what structural aspects of a collection of twelve empirical temporal networks of human contacts are important to disease spreading. We scan the entire parameter spaces of the two canonical models of infectious disease…

Within the likes of any highly contagious and unpredictable disease, lies a predictable and attainable growth rate that researchers can find in order to make logistical conclusions about that particular disease and its affected regions'…

Undulation of infection levels, usually called waves, are not well understood. In this paper we propose a mathematical model that exhibits undulation and decay towards a stable state. The model is a re-interpretation of the original…

Errors of approximations of the quasi-stationary distribution (the QSD) of the logistic SIS model are evaluated numerically. The results are used to derive asymptotic approximations of the approximation errors for large populations. We show…

Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…

In this manuscript, we develop a mobility-based Susceptible-Infectious-Recovered (SIR) model to elucidate the dynamics of pandemic propagation. While traditional SIR models within the field of epidemiology aptly characterize transitions…

We study a variant of the classical Markovian logistic SIS epidemic model on a complete graph, which has the additional feature that healthy individuals can become infected without contacting an infected member of the population. This…

In the performance analyses of wireless networks, asymptotic quantities and properties often pro- vide useful results and insights. The asymptotic analyses become especially important when complete analytical expressions of the performance…

The present article studies the extension of two deterministic models for describing the novel coronavirus pandemic crisis, the SIR model and the SEIR model. The models were studied and compared to real data in order to support the validity…

We define and study an open stochastic SIR (Susceptible -- Infected -- Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same…

In this paper we present the discrete-time networked SIR and SEIR models and present assumptions under which they are well defined. We analyze the limiting behavior of the models and present necessary and sufficient conditions for…

We numerically study the dynamics of the SIR disease model on small-world networks by using a large-deviation approach. This allows us to obtain the probability density function of the total fraction of infected nodes and of the maximum…

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…

We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main…

Predicting Pandemic evolution involves complex modeling challenges, often requiring detailed discrete mathematics executed on large volumes of epidemiological data. Differential equations have the advantage of offering smooth, well-behaved…

Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the…

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…

This paper introduces a popular dimension reduction method, sliced inverse regression (SIR), into multivariate statistical process monitoring. Provides an extension of SIR for the single-index model by adopting the idea from partial least…

A probabilistic approach to the epidemic evolution on realistic social-contact networks allows for characteristic differences among subjects, including the individual number and structure of social contacts, and the heterogeneity of the…