Related papers: Petri nets in epidemiology
We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals…
In order to simulate the spread of infectious diseases, many epidemiological models use systems of ordinary differential equations (ODEs) to describe the underlying dynamics. These models incorporate the implicit assumption, that the stay…
The interplay between disease spreading and personal risk perception is of key importance for modelling the spread of infectious diseases. We propose a planar system of ordinary differential equations (ODEs) to describe the co-evolution of…
Epidemiological processes are studied within a recently proposed hierarchical network model using the susceptible-infected-refractory dynamics of an epidemic. Within the network model, a population may be characterized by $H$ independent…
A generalization of the standard susceptible-infectious-removed (SIR) stochastic model for epidemics in sparse random networks is introduced which incorporates contact tracing in addition to random screening. We propose a deterministic…
In this paper we consider SIR epidemics on random graphs with clustering. To incorporate group structure of the underlying social network, we use a generalized version of the configuration model in which each node is a member of a specified…
A wide range of infectious diseases are both vertically and horizontally transmitted. Such diseases are spatially transmitted via multiple species in heterogeneous environments, typically described by complex meta-population models. The…
This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate $\omega$ (and reconnect to non-infectious individuals with probability…
In this paper, we propose an SIR spread model in a population network coupled with an infrastructure network that has a pathogen spreading in it. We develop a threshold condition to characterize the monotonicity and peak time of a weighted…
In this paper, we introduce a modified epidemic model on regular and scale-free networks respectively. We consider the birth rate $\delta$, cure rate $\gamma$, infection rate $\lambda$, $\alpha$ from the infectious disease, and death rate…
We consider the problem of identifying the source of an epidemic, spreading through a network, from a complete observation of the infected nodes in a snapshot of the network. Previous work on the problem has often employed geometric,…
We formulate a general SEIR epidemic model in a heterogenous population characterized by some trait in a discrete or continuous subset of a space R d. The incubation and recovery rates governing the evolution of each homogenous…
In this paper we study the household-structure SIS epidemic spreading on general complex networks. The household structure gives us the way to distinguish inner and the outer infection rate. Unlike household-structure models on homogenous…
The effective reproduction number, R(t), is a central point in the study of infectious diseases. It establishes in an explicit way the extent of an epidemic spread process in a population. The current estimation methods for the time…
Since social interactions have been shown to lead to symmetric clusters, we propose here that symmetries play a key role in epidemic modeling. Mathematical models on d-ary tree graphs were recently shown to be particularly effective for…
In this paper we make the first steps to bridge the gap between classic control theory and modern, network-based epidemic models. In particular, we apply nonlinear model predictive control (NMPC) to a pairwise ODE model which we use to…
In the framework of population dynamics, the basic reproduction number R_0 is, by definition, the expected number of offspring that an individual has during its lifetime. In constant and time periodic environments it is calculated as the…
In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly…
We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate and it is shown the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence.…
We propose a new network-based SIR epidemic model in which transmission is modulated by a curvature-weighted contact matrix that encodes structural and geometric features of the underlying graph. The formulation encompasses both…