|
Epidemic Models On Lattices
Classic epidemic models of disease transmission are described in Compartmental models in epidemiology. Here we discuss the behavior when such models are simulated on a lattice. Lattice models, which were first explored in the context of cellular automata, act as good first approximations of more complex spatial configurations, although they do not reflect the heterogeneity of space (e.g. population density differences, urban geography and topographical differentiations). Lattice-based epidemic models can also be implemented as fixed agent-based models. Introduction The mathematical modelling of epidemics was originally implemented in terms of differential equations, which effectively assumed that the various states of individuals were uniformly distributed throughout space. To take into account correlations and clustering, lattice-based models have been introduced. Grassberger considered synchronous (cellular automaton) versions of models, and showed how the epidemic growth go ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
SIR Model Simulated Using Python
''Sir'' is a formal honorific address in English for men, derived from Sire in the High Middle Ages. Both are derived from the old French "" (Lord), brought to England by the French-speaking Normans, and which now exist in French only as part of "", with the equivalent "My Lord" in English. Traditionally, as governed by law and custom, Sir is used for men who are knights and belong to certain orders of chivalry, as well as later applied to baronets and other offices. As the female equivalent for knighthood is damehood, the ''suo jure'' female equivalent term is typically Dame. The wife of a knight or baronet tends to be addressed as Lady, although a few exceptions and interchanges of these uses exist. Additionally, since the late modern period, Sir has been used as a respectful way to address a man of superior social status or military rank. Equivalent terms of address for women are Madam (shortened to Ma'am), in addition to social honorifics such as Mrs, Ms, or Miss. Etym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Compartmental Models In Epidemiology
Compartmental models are a mathematical framework used to simulate how populations move between different states or "compartments." While widely applied in various fields, they have become particularly fundamental to the mathematical modelling of infectious diseases. In these models, the population is divided into compartments labeled with shorthand notation – most commonly S, I, and R, representing Susceptible, Infectious, and Recovered individuals. The sequence of letters typically indicates the flow patterns between compartments; for example, an SEIS model represents progression from susceptible to exposed to infectious and then back to susceptible again. These models originated in the early 20th century through pioneering epidemiological work by several mathematicians. Key developments include Hamer's work in 1906, Ronald Ross, Ross's contributions in 1916, collaborative work by Ross and Hilda Phoebe Hudson, Hudson in 1917, the seminal Kermack–McKendrick theory, Kermack and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of ''State (computer science), states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that dete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Agent-based Model
An agent-based model (ABM) is a computational model for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) in order to understand the behavior of a system and what governs its outcomes. It combines elements of game theory, complex systems, emergence, computational sociology, multi-agent systems, and evolutionary programming. Monte Carlo methods are used to understand the stochasticity of these models. Particularly within ecology, ABMs are also called individual-based models (IBMs). A review of recent literature on individual-based models, agent-based models, and multiagent systems shows that ABMs are used in many scientific domains including biology, ecology and social science. Agent-based modeling is related to, but distinct from, the concept of multi-agent systems or multi-agent simulation in that the goal of ABM is to search for explanatory insight into the collective behavior of agents ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematical Modelling Of Infectious Disease
Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including Plant disease forecasting, in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc. History The modelling of infectious diseases is a tool that has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic. The first scientist who systematically tried to quantify causes of death was John Graunt in his book ''Natural and Political Observations made upon the Bills of Mortality'', in 1662. The bills he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
John Cardy
John Lawrence Cardy FRS (born 19 March 1947, England) is a British– American theoretical physicist. He is best known for his work in theoretical condensed matter physics and statistical mechanics, and in particular for research on critical phenomena and two-dimensional conformal field theory. He was an undergraduate and postgraduate student (now an Honorary Fellow) at Downing College, Cambridge, before moving to the University of California, Santa Barbara, where he joined the faculty in 1977. In 1993, he moved to the University of Oxford, where until 2014 he was a Fellow of All Souls College (now Emeritus) and a Professor of Physics in the Rudolf Peierls Centre for Theoretical Physics. He was a Visiting Professor and then a Research Physicist (2015–2023) at the University of California, Berkeley. His research prior to 1978 was in particle physics, in particular high energy scattering theory. After this, he applied methods of quantum field theory and the renormalization grou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Kinetic Monte Carlo
The kinetic Monte Carlo (KMC) method is a Monte Carlo method computer simulation intended to simulate the time evolution of some processes occurring in nature. Typically these are processes that occur with known transition rates among states. These rates are inputs to the KMC algorithm; the method itself cannot predict them. The KMC method is essentially the same as the dynamic Monte Carlo method and the Gillespie algorithm. Algorithms One possible classification of KMC algorithms is as rejection-KMC (rKMC) and rejection-free-KMC (rfKMC). Rejection-free KMC A rfKMC algorithm, often only called KMC, for simulating the time evolution of a system, where some processes can occur with known rates r, can be written for instance as follows: # Set the time t = 0. # Choose an initial state ''k''. # Form the list of all N_k possible transition rates in the system r_, from state ''k'' into a generic state ''i''. States that do not communicate with ''k'' will have r_=0. # Calculate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Epidemic Model
Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc. History The modelling of infectious diseases is a tool that has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic. The first scientist who systematically tried to quantify causes of death was John Graunt in his book ''Natural and Political Observations made upon the Bills of Mortality'', in 1662. The bills he studied were listings of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Percolation
In physics, chemistry, and materials science, percolation () refers to the movement and filtration, filtering of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation. Background During the last decades, percolation theory, the mathematical study of percolation, has brought new understanding and techniques to a broad range of topics in physics, materials science, complex networks, epidemiology, and other fields. For example, in geology, percolation refers to filtration of water through soil and permeable rocks. The water flows to groundwater recharge, recharge the groundwater in the water table and aquifers. In places where infiltration basins or septic drain fields are planned to dispose of substantial amounts of water, a percolation test ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Percolation Threshold
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in Randomness, random systems. Below the threshold a giant connected component (graph theory), connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified Lattice model (physics), lattice models of random systems or networks (Graph (discrete mathematics), graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation probability ''p'', or more generally a critical surface for a group of parameters ''p''1, ''p''2, ..., such that infinite connectivity (''percolation'') first occurs. Percolation models The most common percolation model is to take a regular lattice, like a squa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Percolation Theory
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger Glossary of graph theory, connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles Network theory and Percolation (cognitive psychology). Introduction A representative question (and the etymology, source of the name) is as follows. Assume that some liquid is poured on top of some porosity, porous material. Will the liquid be able to make its way from hole to hole and reach the bottom? This physical question is mathematical model, modelled mathematically as a Grid graph, three-dimensional network of graph (discrete mathematics), vertices, usually called "sites", in which the graph (dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
