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Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the…

We consider the spread of infectious disease through contact networks of Configuration Model type. We assume that the disease spreads through contacts and infected individuals recover into an immune state. We discuss a number of existing…

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…

Compartmental epidemic models have been widely used for predicting the course of epidemics, from estimating the basic reproduction number to guiding intervention policies. Studies commonly acknowledge these models' assumptions but less…

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…

The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review…

Deterministic compartmental models have been used extensively in modeling epidemic propagation. These models are required to fit available data and numerical procedures are often implemented to this end. But not every model architecture is…

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…

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…

The contact structure between hosts has a critical influence on disease spread. However, most networkbased models used in epidemiology tend to ignore heterogeneity in the weighting of contacts. This assumption is known to be at odds with…

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…

Viruses constantly undergo mutations with genomic changes. The propagation of variants of viruses is an interesting problem. We perform numerical simulations of the microscopic epidemic model based on network theory for the spread of…

Compartmental models of epidemics are widely used to forecast the effects of communicable diseases such as COVID-19 and to guide policy. Although it has long been known that such processes take place on social networks, the assumption of…

Network epidemiology often assumes that the relationships defining the social network of a population are static. The dynamics of relationships is only taken indirectly into account, by assuming that the relevant information to study…

Since its first formulations almost a century ago, mathematical models for disease spreading contributed to understand, evaluate and control the epidemic processes.They promoted a dramatic change in how epidemiologists thought of the…

Network epidemiology has become a core framework for investigating the role of human contact patterns in the spreading of infectious diseases. In network epidemiology represents the contact structure as a network of nodes (individuals)…

Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by…

Despite centuries of work on containment and mitigation strategies, infectious diseases are still a major problem facing humanity. This work is concerned with simulating heterogeneous contact structures and understanding how the structure…

Many real networks are not isolated from each other but form networks of networks, often interrelated in non trivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop…

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach…