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Topic: Compartmental models in epidemiology

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Mathematical modelling in epidemiology

Infectious disease

Parameter

Epidemiology

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	Compartmental models in epidemiology - Wikipedia, the free encyclopedia
		In order to model the progress of an epidemic in such a population this diversity must be reduced to a few key characteristics which are relevant to the infection under consideration.
		This is a good, simple, model for many infectious diseases including measles, mumps and rubella.
		For many infections, including measles, babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the placenta or through colostrum).
	en.wikipedia.org /wiki/Compartmental_models_in_epidemiology (748 words)

	Continuous Compartmental Computer Models of Transmission Systems
		Compartmental models are good for such purposes because they are conceptually simple and can be readily solved using numerical methods.
		The next task in building our model is to establish the amount of "I" we start with, the amount of "R" we start with, the value of the recovery rate, and the mathematical relationships in the flow regulator between the various model entities that influence the flow.
		The SIS model we will construct assumes that differences in susceptibility between individuals who have never been infected and individuals who were infected but lost their immunity are unimportant.
	www.sph.umich.edu /~jkoopman/Web606/Ex1606/Ex1606.htm (9801 words)

	Untitled
		The model is simple enough so that there is a "closed form" solution to the differential equations behind it, allowing us to elaborate upon the relationships between closed form models of time effects and dynamic simulations.
		In the compartmental models of populations which we construct, the stocks or population compartments will always be variables.
		The flows in compartmental models are merely functions of the parameters and the compartments.
	www.sph.umich.edu /~jkoopman/802Web/Chap2/Chap2.htm (10094 words)

	An introduction to mathematical models in sexually transmitted disease epidemiology -- Garnett 78 (1): 7 -- Sexually ...
		One of the paradoxes in modelling infectious diseases is that,
		non-linear model of an infection in a homogeneous population
		Modelling the spread of HIV-1: the basis for the 2001 UNAIDS country—specific estimates and projections of adult HIV prevalence and AIDS mortality.
	sti.bmjjournals.com /cgi/content/full/78/1/7 (3838 words)

	Compartmental (Site not responding. Last check: 2007-11-03)
		Compartmentalizing is the act of splitting an idea or concept up into (sometimes more or less arbitrary) parts, and trying to enforce thought processes which are inhibiting attempts to allow these parts to mix together again in an attempt to oversimplify things.
		The reason for this attempt of thought control is often to make it more easy to single out certain individuals, or to inhibit certain ideas.
		The main significance of compartmentalization (separate various organelles by forming different compartments in the cell) is to enable the cell carry out different metabolic activities at the same time.
	www.wwwtln.com /finance/44/compartmental.html (483 words)

	The Incidence of Epidemics
		The basic model for studying epidemics was developed by Kermack and McKendrick in 1927 and it's well covered in such books as Models in Biology by D. Brown.
		The key to the model is the relation between the infection rate, b and the recovery rate (usually the Greek gamma) For example if there are 50 S and 50 I and 10% of the susceptibles get the disease then there will be 5 new infectives.
		This simple model leads like most of the chaos and catastrophe and predator prey models to fantastic mathematical properties as the assumptions change about the relation of b to gamma and the initial population size changes.
	www.dailyspeculations.com /vic/Epidemics.html (993 words)

	Dictionary of (Ecological) Epidemiology
		A (rather misleading name for a) type of compartmental model in which the force of infection is treated as a parameter to be estimated.
		Continuous models have the advantage over discrete time models in that they are more amenable to algebraic manipulation, although they are slightly harder to implement on a computer.
		Prevalence models are compartmental models dividing the host population into, for example, susceptible, latent, infectious and immune individuals.
	www.swintons.net /jonathan/Academic/glossary.html (4970 words)

	Epidemic Models -- Wednesday afternoon session
		Operator splitting methods for nonlinear models arising from population dynamics and epidemiology are described and analyzed.
		Our main approach in modelling Hib disease is an individual-based state-transition model where each individual is in one of the states S, I or R (S=susceptible for infection, I=infective carrier, R= temporarily resistant to infection).
		On this population model we have superimposed the Hib infection dynamics as an S-I-R-S model.
	www.math.vanderbilt.edu /meetings/97mmmhs/schedule/epidem1.html (1057 words)

	Epidemiology Simulations (Site not responding. Last check: 2007-11-03)
		The Merriam-Webster Online Dictionary, defines epidemiology as "a branch of medical science that deals with the incidence, distribution, and control of disease in a population." For obvious reasons, studies of the spread of a disease in human populations must be based upon data collected during prior outbreaks.
		The SEIR (Susceptible-Exposed-Infected-Recovered) model is used to model infectious diseases such as measles, mumps, chicken pox and rubella.
		The grid type model that we used for the population is called a Cellular Automata (CA).
	www.dickinson.edu /~cs131/Spring2006/Labs/Lab03/handout.html (3505 words)

	Measurement Issues in Environmental Epidemiology
		In either case, compartmental rate relationships are used in the model's equations to estimate concentrations at critical tissues.
		Pharmacokinetic modeling of exposure and dose may be viewed as a counterpart to biologically based disease models.
		To be useful in environmental epidemiology studies, a biologic exposure marker should be clearly better than anamnestic data or environmental measures; should allow for differentiation between exposure levels; should be applicable on a large scale; or if too costly for large-scale use, should at least be acceptable to subjects in a validation substudy.
	www.ehponline.org /members/1993/Suppl-4/hatch-full.html (9115 words)

	Mathematical modelling in epidemiology
		It is possible to model mathematically the progress of most infectious diseases to discover the likely outcome of an epidemic or to help manage them by vaccination.
		Whenever we are modelling anything mathematically, whether in epidemiology or otherwise, we would be wise to remember that a mathematical model is only as good as the assumptions on which it is based.
		If a model makes predictions which are out of line with observed results and the maths is correct, we must go back and change our initial assumptions in order to make the model useful.
	articles.gourt.com /?article=mathematical+modelling+in+epidemiology (1288 words)

	Equilibrium points for nonlinear compartmental models.
		Equilibrium points for nonlinear autonomous compartmental models with constant input are discussed.
		A recursive process is discussed that generates iterates that converge to steady states for certain types of models.
		An attempt is made to provide general qualitative theory for such nonlinear compartmental systems.
	www.aegis.com /aidsline/1992/jul/M9271017.html (320 words)

	COMPARTMENTAL MODELS OF GEOGRAPHIC SPREAD (Site not responding. Last check: 2007-11-03)
		That may be useful in some cases because poulation data are often available on that basis but in general, it is not an astute way to go about that.
		A useful compartmentation for spread of an infectious disease such as a respiratory tract infection might be to make the major part of the town one compartment and the suburb another.
		With the introduction of a disease, each population subgroup would then be divided into compartments for the stages of the disease process, e.g.
	www.nku.edu /~longa/classes/2001spring/mat370/days/day23/docjacquez/node20.html (387 words)

	Spatial Compartmental Models (Site not responding. Last check: 2007-11-03)
		In this module we introduce the basics of compartmental modeling, examine some simple models, and indicate how compartmental models may be used in spatial problems.
		Introduce compartmental models of epidemics, including epidemic models that explicitly include geographic spread.
		Know how to create simple models using Stella, and understand some of the limitations of Stella.
	zappa.nku.edu /~longa/geomed/modules/compart (75 words)

	GraduateProgram: Math, ASU (Site not responding. Last check: 2007-11-03)
		Probabilistic methods for the study of birth and death processes in population biology with applications to genetics, demography and epidemics.
		Brauer Fred and Carlos Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Texts in Applied Mathematics Volume 40, Springer Verlag 2001.
		Explicit and implicit methods for linear and nonlinear neuronal cable models: Crank-Nicolson Method, derivative boundary conditions, branching conditions, handling nonlinear terms, compartmental models of neurons.
	math.la.asu.edu /~grad/doc/syllabi.html (1380 words)

	UK NONLINEAR NEWS (May 1998): New Conferences
		Mathematical Models in Population Biology and Epidemiology: From Elementary to the Frontier, 6-17 July 1998.
		This will include both the formulation of models in population biology and epidemiology and the mathematical analysis of these models.
		Applications will include continuous and discrete populations for single and interacting species, general compartmental models in epidemiology, interaction of demographic and epidemiological effects, and behavioral effects in sexually transmitted diseases.
	www.amsta.leeds.ac.uk /applied/news.dir/issue12.dir/conf/new.html (2755 words)

	Epidemiology 802 Course Home Page (Site not responding. Last check: 2007-11-03)
		This course teaches compartmental model construction and analysis for the purpose of generating and evaluating theory regarding epidemiological systems.
		Chapter 2: Rates and Risks: Modeling a constant rate process in a fixed Population
		Chapter 7: The "All or None" model of vaccine effects
	www.sph.umich.edu /~jkoopman/802Web/Course.htm (128 words)

	WWWeb Epidemiology & EBM Sources for Veterinarians (Site not responding. Last check: 2007-11-03)
		This list is selected to provide veterinary students and practitioners useful epidemiology, evidence-based medicine and biostatistics resources on the Web.
		Principles of Epidemiology: An introduction to applied epidemiology, 2nd ed.
		Understanding the fundamentals of epidemiology: an evolving text.
	www.vetmed.wsu.edu /courses-jmgay/EpiLinks.htm (2855 words)

	Spatial Epidemiology Modules (Site not responding. Last check: 2007-11-03)
		Pattern and Process: Gaining insights from time-space characteristics of disease distribution
		These modules are the core of a course on Spatial Epidemiology, developed at the University of Michigan in the
		Ann Arbor software company BioMedware participated in the project, which included developing software (
	zappa.nku.edu /~longa/geomed/modules (66 words)

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