Related papers: A useful relationship between epidemiology and que…
We consider a stochastic epidemic model with sideward contact tracing. We assume that infection is driven by interactions within mixing events (gatherings of two or more individuals). Once an infective is diagnosed, each individual who was…
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…
In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this model can capture the essence of the stochastic, often…
We study how international flights can facilitate the spread of an epidemic to a worldwide scale. We combine an infrastructure network of flight connections with a population density dataset to derive the mobility network, and then we…
Epidemic dynamics in a stochastic network of interacting epidemic centers is considered. The epidemic and migration processes are modelled by Markov's chains. Explicit formulas for probability distribution of the migration process are…
This paper investigates the dynamics of infectious diseases with a non-exponentially distributed infectious period. This is achieved by considering a multi-stage infection model on networks. Using pairwise approximation with a standard…
Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious…
This paper gives an introduction to rule-based modelling applied to topics in infectious diseases. Rule-based models generalise reaction-based models with reagents that have internal state and may be bound together to form complexes, as in…
Epidemic spreading of infectious diseases is ubiquitous and has often considerable impact on public health and economic wealth. The large variability in spatio-temporal patterns of epidemics prohibits simple interventions and demands for a…
Epidemic spread in single-host systems strongly depends on the population's contact network. However, little is known regarding the spread of epidemics across networks representing populations of multiple hosts. We explored cross-species…
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…
In this work, we use a new approach to study the spread of an infectious disease. Indeed, we study a SIR epidemic model with variable infectivity, where the individuals are distributed over a compact subset $D$ of $\R^d$. We define…
In this work, the spread of a contagious disease on a society where the individuals may take precautions is modeled. The primary assumption is that the infected individuals transmit the infection to the susceptible members of the community…
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…
Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place…
We study the spread of information on multi-type directed random graphs. In such graphs the vertices are partitioned into distinct types (communities) that have different transmission rates between themselves and with other types. We…
Infectious diseases, either emerging or long-lasting, place numerous people at risk and bring heavy public health burdens worldwide. In the process against infectious diseases, predicting the epidemic risk by modeling the disease…
We use scale-free networks to study properties of the infected mass $M$ of the network during a spreading process as a function of the infection probability $q$ and the structural scaling exponent $\gamma$. We use the standard SIR model and…
Nowadays, the emergence of online services provides various multi-relation information to support the comprehensive understanding of the epidemic spreading process. In this Letter, we consider the edge weights to represent such multi-role…
The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…