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We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that…
One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the…
Dynamical systems running on the top of complex networks has been extensively investigated for decades. But this topic still remains among the most relevant issues in complex network theory due to its range of applicability. The contact…
Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories…
We show how the standard field theoretical language based on creation and annihilation operators may be used for a straightforward derivation of closed master equations describing the population dynamics of multivariate stochastic epidemic…
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…
The contact process is an emblematic model of a non-equilibrium system, containing a phase transition between inactive and active dynamical regimes. In the epidemiological context, the model is known as the susceptible-infected-susceptible…
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…
Understanding the dynamics of the spread of diseases within populations is critical for effective public health interventions. We extend the classical SIR model by incorporating additional complexities such as the introduction of a cure and…
The paper describes and compares three approaches to modeling an epidemic spread. The first approach is a well-known system of SIR ordinary differential equations. The second is a mean-field model, in which an isolation strategy for each…
We present an exact analytical solution to a one-dimensional model of the Susceptible-Infected-Recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming…
The simplest epidemiologic model composed by mutually exclusive compartments SIR (susceptible-infected-susceptible) is presented to describe a reality. From health concerns to situations related with marketing, informatics or even…
Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading,…
Motivated by fundamental issues in non-equilibrium statistical mechanics (NESM), we study the venerable susceptible-infected (SIS) model of disease spreading in an idealized, simple setting. Using Monte Carlo and analytic techniques, we…
We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approximation for the rest of the network. We…
This paper investigates the spread of infectious diseases within a networked community by integrating epidemic transmission and public opinion dynamics. We propose a novel discrete-time networked SIS (Susceptible-Infectious-Susceptible)…
In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a…
We approach the development of models and control strategies of susceptible-infected-susceptible (SIS) epidemic processes from the perspective of marked temporal point processes and stochastic optimal control of stochastic differential…
Epidemic propagation on networks represents an important departure from traditional massaction models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…