Related papers: Geometrization of Some Epidemic Models
We introduce a kinetic model that couples the movement of a population of individuals with the dynamics of a pathogen in the same population. We consider that transmission occurs when a susceptible and an infectious individual are…
This paper provides a comprehensive survey of recent advancements in leveraging machine learning techniques, particularly Transformer models, for predicting human mobility patterns during epidemics. Understanding how people move during…
We study the impact of contact heterogeneity on epidemic dynamics. A system characterized by multiple susceptible populations is considered. The description of the spread of an infectious disease is obtained through the study of a system of…
A novel scenario for the emergence of geometry in random multitrace matrix models of a single hermitian matrix $M$ with unitary $U(N) $ invariance, i.e. without a kinetic term, is presented. In particular, the dimension of the emergent…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
Human mobility forms the backbone of contact patterns through which infectious diseases propagate, fundamentally shaping the spatio-temporal dynamics of epidemics and pandemics. While traditional models are often based on the assumption…
Degree correlation plays a crucial role in studying network structures; however, its varied forms pose challenges to understanding its impact on network dynamics. This study devised a method that uses eigenvalue decomposition to…
Discrete and Continuous Dynamics is the first in a series of articles on Network Models for Epidemiology. This project began in the Fall quarter of 2014 in my continuous modeling course. Since then, it has taken off and turned into a series…
A primary difficulty with unsupervised discovery of structure in large data sets is a lack of quantitative evaluation criteria. In this work, we propose and investigate several metrics for evaluating and comparing generative models of…
Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak…
The current work deals with an epidemic model on the complete graph K_n on n vertices in a non-homogeneous setting, where the vertices may have distinct types. Different types differ in the probability of getting infected, and/or in the…
Mathematical modeling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact…
The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their…
Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. In…
Our results concern geometry of a manifold endowed with a pair of complementary orthogonal distributions (plane fields) and a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as…
Recently, motivated by the pioneer works that reveal the small-world effect and scale-free property of various real-life networks, many scientists devote themselves into studying complex networks. One of the ultimate goals is to understand…
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 focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of so called graphons we…
We show how one can trace in a systematic way the coarse-grained solutions of individual-based stochastic epidemic models evolving on heterogeneous complex networks with respect to their topological characteristics. In particular, we have…
Human interactions and mobility shape epidemic dynamics by facilitating disease outbreaks and their spatial spread across regions. Traditional models often isolate commuting and random mobility as separate behaviors, focusing either on…