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We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws…

We consider the spread of a Susceptible-Infected-Recovered (SIR) disease through finite populations and derive an expression for the final size distribution. Our derivation allows arbitrary distributions of the number of transmissions…

Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…

A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such…

We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…

Classical disease models use a mass action term as the interaction between infected and susceptible people in separate patches. We derive the equations when this interaction is a migration of people between patches. The results model what…

The importation and subsequent establishment of novel pathogenic strains in a population is subject to a large degree of uncertainty due to the stochastic nature of the disease dynamics. Mathematical models need to take this stochasticity…

Infectious disease outbreaks recapitulate biology: they emerge from the multi-level interaction of hosts, pathogens, and their shared environment. As a result, predicting when, where, and how far diseases will spread requires a complex…

This paper introduces a new optimal control model to describe and control the dynamics of infectious diseases. In the present model, the average time of isolation (i.e. hospitalization) of infectious population is the main time-dependent…

Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…

A cellular automata model that describes as limit cases of his parameters the spread of contagious diseases modeled by systems of ordinary or partial differential equations is developed. Periodic features of the behavior of human settlement…

The spread of infectious disease and the evolution of antigenically distinct strains are often modeled separately, despite strong feedbacks mediated by host immune memory and heterogeneous contacts. To tackle this challenging problem, we…

Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission…

Infectious disease remains, despite centuries of work to control and mitigate its effects, a major problem facing humanity. This paper reviews the mathematical modelling of infectious disease epidemics on networks, starting from the…

In the study of infectious diseases on networks, researchers calculate epidemic thresholds to help forecast whether a disease will eventually infect a large fraction of a population. Because network structure typically changes in time,…

The study of epidemic spreading on populations of networked individuals has seen recently a great deal of significant progresses. A common point of all past studies is, however, that there is only one peak of infected density in each single…

Epidemic models often reflect characteristic features of infectious spreading processes by coupled non-linear differential equations considering different states of health (such as Susceptible, Infected, or Recovered). This compartmental…

We motivate and explore the basic features of generalized contagion, a model mechanism that unifies fundamental models of biological and social contagion. Generalized contagion builds on the elementary observation that spreading and…

We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the tree vertex degree tends to infinity. We obtain the…

Diffusion processes are governed by external triggers and internal dynamics in complex systems. Timely and cost-effective control of infectious disease spread critically relies on uncovering the underlying diffusion mechanisms, which is…