The contact process is a stochastic process used to model population growth on the set of sites of a graph in which occupied sites become vacant at a constant rate, while vacant sites become occupied at a rate proportional to the number of occupied neighboring sites. Therefore, if we denote by the proportionality constant, each site remains occupied for a random time period which is exponentially distributed parameter 1 and places descendants at every vacant neighboring site at times of events of a Poisson process parameter during this period. All processes are independent of one another and of the random period of time sites remains occupied. The contact process can also be interpreted as a model for the spread of an infection by thinking of particles as a bacterium spreading over individuals that are positioned at the sites of , occupied sites correspond to infected individuals, whereas vacant correspond to healthy ones. The main quantity of interest is the number of particles in the process, say , in the first interpretation, which corresponds to the number of infected sites in the second one. Therefore, the process survives whenever the number of particles is positive for all times, which corresponds to the case that there are always infected individuals in the second one. For any infinite graph there exists a positive and finite critical value so that if then survival of the process starting from a finite number of particles occurs with positive probability, while if their extinction is almost certain. Note that by reductio ad absurdum and the infinite monkey theorem, survival of the process is equivalent to , as , whereas extinction is equivalent to , as , and therefore, it is natural to ask about the rate at which when the process survives. (Wikipedia).
How to solve differentiable equations with logarithms
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
A17 Deriving the equation for the particular solution
Finishing the derivation for the equation that is used to find the particular solution of a set of differential equations by means of the variation of parameters.
From playlist A Second Course in Differential Equations
Physics Students Need to Know These 5 Methods for Differential Equations
Differential equations are hard! But these 5 methods will enable you to solve all kinds of equations that you'll encounter throughout your physics studies. Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up Sign up for my newsletter for additional physics les
From playlist Physics Help Room
B01 An introduction to numerical methods
Most differential equations cannot be solved by the analytical techniques that we have learned up until now. I these cases, we can approximate a solution by a set of points, by using a variety of numerical methods. The first of these is Euler's method.
From playlist A Second Course in Differential Equations
Particular solution of differential equations
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
Solve the general solution for differentiable equation with trig
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
The method of determining eigenvalues as part of calculating the sets of solutions to a linear system of ordinary first-order differential equations.
From playlist A Second Course in Differential Equations
How to solve a separable differential equation
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
Find the particular solution given the conditions and second derivative
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
Emmanuel Schertzer: General epidemiological models: law of large numbers and contact tracing
CIRM HYBRID EVENT Recorded during the meeting "5th Workshop Probability and Evolution " the June 28, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIR
From playlist Probability and Statistics
Limitations of mathematical models; historical context of BGW process [PART III]
Part 3 of a series on a stochastic process approach to model the spread of coronavirus (COVID-19) as opposed to the compartmental deterministic SIR model. This model is generally known as branching process, but this video only focuses on the simplest type, called Bienaymé-Galton-Watson (BG
From playlist Mathematics of coronavirus
Michael Aizenman - Metric graph extensions of lattice models with applications in stat mech (...)
As a counterpoint to ``be wise and discretize’’, continuous extensions are relevant and provide useful perspective. They occasionally pose challenges but also yield new tools. Examples of both may be found in: the contact process as extension of discrete percolation, long-range 1D Isi
From playlist 100…(102!) Years of the Ising Model
A unified stochastic modelling framework for the spread of... by Martín López García
DISCUSSION MEETING : MATHEMATICAL AND STATISTICAL EXPLORATIONS IN DISEASE MODELLING AND PUBLIC HEALTH ORGANIZERS : Nagasuma Chandra, Martin Lopez-Garcia, Carmen Molina-Paris and Saumyadipta Pyne DATE & TIME : 01 July 2019 to 11 July 2019 VENUE : Madhava Lecture Hall, ICTS, Bangalore
From playlist Mathematical and statistical explorations in disease modelling and public health
A comparative analysis between two time-discretized versions of the... by Antonio Gómez Corral
DISCUSSION MEETING : MATHEMATICAL AND STATISTICAL EXPLORATIONS IN DISEASE MODELLING AND PUBLIC HEALTH ORGANIZERS : Nagasuma Chandra, Martin Lopez-Garcia, Carmen Molina-Paris and Saumyadipta Pyne DATE & TIME : 01 July 2019 to 11 July 2019 VENUE : Madhava Lecture Hall, ICTS, Bangalore
From playlist Mathematical and statistical explorations in disease modelling and public health
Etienne Pardoux: Modèles mathématiques des épidémies
"Modèles mathématiques des épidémies" par Etienne Pardoux (Professeur - Aix-Marseille Université) Il y a cent ans, Sir Ronald Ross tentait de convaincre ses collègues médecins que l'épidémiologie doit être étudiée avec l'aide des mathématiques. Le but de cet exposé est d'expliquer pourqu
From playlist OUTREACH - GRAND PUBLIC
M3 Challenge David Baraff Lunch Talk 2016
David Baraff, Principal Software Engineer from Pixar Animation Studios, joined us as the lunchtime speaker at the Moody's Mega Math Challenge Final Event on April 25, 2016 in NYC. During his talk, Baraff discussed ways in which Pixar is using math to create computer animated effects like c
From playlist M3 Challenge
Gianpaolo Scalia Tomba: Estimating parameters in the initial phase of an epidemic
In recent years, new pandemic threats have become more and more frequent (SARS, bird flu, swine flu, Ebola, MERS, nCoV...) and analyses of data from the early spread more and more common and rapid. Particular interest is usually focused on the estimation of $ R_{0}$ and various methods, es
From playlist Probability and Statistics
Mathematical Modeling of Epidemics. Lecture 1: basic SI/SIS/SIR models explained.
This lecture explains basic compartmental models in epidemiology -SI, SIS, SIR and exponential growth rate of infection. This lecture is a part of Network Science course at HSE. Lecture slides: http://www.leonidzhukov.net/hse/2020/networks/lectures/lecture9.pdf Course website: http://www.
From playlist COVID-19 Modeling
B01 An introduction to separable variables
In this first lecture I explain the concept of using the separation of variables to solve a differential equation.
From playlist Differential Equations