Related papers: Toward a comprehensive system for constructing com…
A network epidemic model is studied. The underlying social network has two different types of group structures, households and workplaces, such that each individual belongs to exactly one household and one workplace. The random network is…
We consider the edge-based compartmental models for epidemic spread developed in Part I. We show conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In…
Social networks are an important infrastructure for information, viruses and innovations propagation. Since users behavior has influenced by other users activity, some groups of people would be made regard to similarity of users interests.…
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…
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…
Modeling epidemic dynamics plays an important role in studying how diseases spread, predicting their future course, and designing strategies to control them. In this letter, we introduce a model of SIR (susceptible-infected-removed) type…
This article explores mathematical models for understanding the evolution of contagious diseases. The most widely known set of models are the compartmental ones, which are based on a set of differential equations. But these are not the only…
We study the spread of stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school…
We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. Though the described Bayesian computational framework is general, we look at a specific application to the…
The abrupt outbreak and transmission of biological diseases has always been a long-time concern of humankind. For long, mathematical modeling has served as a simple and yet efficient tool to investigate, predict, and control spread of…
Compartmental models are used in epidemiology to capture the evolution of infectious diseases such as COVID-19 in a population by assigning members of it to compartments with labels such as susceptible, infected, and recovered. In a…
If model identifiability is not confirmed, inferences from infectious disease transmission models may not be reliable, so they might lead to misleading recommendations. Structural identifiability analysis characterizes whether it is…
Contact (or mixing, or more generally connectivity) matrices are a fundamental component of modelling and inference for infectious disease epidemiology. Their structure and parametrisation directly accounts for the frequency of interactions…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…
Since 1927, until recently, models describing the spread of disease have mostly been of the SIR-compartmental type, based on the assumption that populations are homogeneous and well-mixed. The focus of these models have typically been on…
The ability to actually implement epidemic models is a crucial stake for public institutions, as they may be overtaken by the increasing complexity of current models and sometimes tend to revert to less elaborate models such as the SIR. In…
Infectious disease modeling is used to forecast epidemics and assess the effectiveness of intervention strategies. Although the core assumption of mass-action models of homogeneously mixed population is often implausible, they are…
The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…
Epidemic models are always simplifications of real world epidemics. Which real world features to include, and which simplifications to make, depend both on the disease of interest and on the purpose of the modelling. In the present paper we…
This is work in progress. We make it accessible hoping that people might find the idea useful. We propose a discrete, recursive 5-compartment model for the spread of epidemics, which we call {\em SEPIR-model}. Under mild assumptions which…