Related papers: Exact epidemic models from a tensor product formul…
Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time…
We study the susceptible-infected-susceptible (SIS) model on directed complex networks within the quenched mean-field approximation. Combining results from random matrix theory with an analytic approach to the distribution of fixed-point…
It has been known that epidemic outbreaks in the SIR model on networks are described by phase transitions. Despite the similarity with percolation transitions, whether an epidemic outbreak occurs or not cannot be predicted with probability…
Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…
A continuous-time quantum walk on a graph $X$ is represented by the complex matrix $\exp (-\mathrm{i} t A)$, where $A$ is the adjacency matrix of $X$ and $t$ is a non-negative time. If the graph models a network of interacting qubits,…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
Epidemiological contact network models have emerged as an important tool in understanding and predicting the spread of infectious disease, due to their capacity to engage individual heterogeneity that may underlie essential dynamics of a…
In epidemiological modelings, the spectral radius of the next generation matrix evaluated at the trivial equilibrium was considered as the basic reproduction number. Also, the global stability of the trivial equilibrium point was determined…
We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo…
These notes describe stochastic epidemics in a homogenous community. Our main concern is stochastic compartmental models (i.e. models where each individual belongs to a compartment, which stands for its status regarding the epidemic under…
Infectious diseases are practically represented by models with multiple states and complex transition rules corresponding to, for example, birth, death, infection, recovery, disease progression, and quarantine. In addition, networks…
The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach -- essentially a fusion of the $G…
Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…
We introduce a general system of ordinary differential equations that includes some classical and recent models for the epidemic spread in a closed population without vital dynamic in a finite time horizon. The model is vectorial, in the…
This book handles the fatty liver disease from the bio-statistical point of view . It discusses the disease process in the simple general form of health-disease-death multi-states model . Continuous Time Markov Chains are used to estimate…
Tracking the spread of infectious disease during a pandemic has posed a great challenge to the governments and health sectors on a global scale. To facilitate informed public health decision-making, the concerned parties usually rely on…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
In this paper, we aim to understand the transient dynamics of a susceptible-infected (SI) epidemic spreading process on a large network. The SI model has been largely overlooked in the literature, while it is naturally a better fit for…
Epidemic models on complex networks have been widely used to study how the social structure of a population affect the spreading of epidemics. However, their numerical simulation can be computationally heavy, especially for large networks.…
We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as…