docs/org.eclipse.stem.doc/help/html/epidemiologicalmodeling/overview.html - stem/org.eclipse.stem - Git at Google


            
            <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">


            <html>

            
            <head>

            
            <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">

            
            <title>Epidemiological Modeling Overview</title>

            
            </head>


            <body>

            
            <h1>Epidemiological Modeling</h1>


            <img src="images/sis.gif" align=RIGHT HSPACE=10 VSPACE=10 width=25%>

            
            <p> Compartmental disease models are some of the most widely used

            
            models of infectious disease. In these models individuals (or portions of

            
            an individual) are considered to be in a compartments based on their

            
            disease status. By convention, commonly used compartmental models are

            
            designated by the first letters of the compartments and the order

            
            people move between them. So, the model for a disease where people

            
            start out Susceptible, become Infectious after catching the disease,

            
            and then after some time clear the disease and become Susceptible again

            
            would be an SIS model. The four most commonly used compartments

            
            are <u>S</u>usceptible, <u>E</u>xposed, <u>I</u>nfectious, and

            
            <u>R</u>emoved. <u>S</u>usceptible contains those individuals

            
            who can still be infected with disease. <u>E</u>xposed contains individuals

            
            who have been infected with the disease, but have not yet become

            
            infectious themselves. <u>I</u>nfectious contains those individuals who

            
            are infected and infectious. <u>R</u>emoved (sometimes called <u>R</u>ecovered)

            
            contains those individuals who have been removed from the system

            
            either through death or immunity. The disease state of a population

            
            is speccified by knowing the nuber of individuals (or proportion of

            
            the population) that is in each compartment.


             <p> There are two main types of compartmental models: deterministic

            
             and stochastic. In deterministic model, rates of movements between

            
             compartments are used to represent the processes by which individuals

            
             are infected, become ill and eventually recover from disease. These

            
             rates specify a set of differential or difference equations, which

            
             can be evaluated to give that state of the model at a future time

            
             point. In deterministic models compartments need not contain an

            
             integer number of individuals.


             <p>Deterministic models only give the <i>expected</i> behavior of

            
             the disease in a population under a set of assumptions about

            
             the natural history and epidemiology of the disease. Often

            
             we would also like to know how the disease behaves in more

            
             extreme cases, and what the distribution of this behavior

            
             is. Stochastic models provide a method for addressing this

            
             issue. In a stochastic model, whole individuals are moved

            
             between compartments based on a random draw from some specified

            
             distribution. To get informative results from a stochastic

            
             compartmental model it is necessary to do hundreds, or even

            
             thousands of experiments.


            <p>Compartamental models also may have "closed" or "open" populations.

            
            In closed populations the set of individuals represented by the model

            
            is static, no one comes in and no one comes out. It is of note that

            
            in such populations any disease that confers permanent immunity

            
            after infection will eventually become extinct. In an open

            
            population there is continuous immigration and emigration from

            
            the population, usually via birth and death.


            <p>STEM comes with deterministic implementations for three commonly used

            
            compartmental models: SI(S), SIR(S), and SIER(S). These models are

            
            implemented as having open populations, but closed populations can

            
            be easily simulated by setting the immigration/emigration rate to

            
            zero. Which model is appropriate for a modeling project depends

            
            on both the disease of interest and the timescale that we are

            
            interested in modeling our results.


            <h2>The SI(S) Model</h2>

            
            <a href="simath.html">

            
            <img src="images/sis.gif" align=CENTER HSPACE=10 VSPACE=10 width=24% border=0>

            
            </a>


            <p>SI(S) are useful for modeling diseases with a short latent period (the time

            
            between being infected and becoming infectious) that either confer no long term

            
            immunity (in the case of SIS models) or result in permanent infection (in the case

            
            of SI models). Diseases of this type include the common cold and many

            
            macro-parasite infections. Susceptible individuals are infected at the

            
            rate of <em>&beta;I</em>, at which time they lose infectiousness

            
            at the rate of <em>&gamma;</em>. Mathematical details of this model

            
            can be viewed <a href="simath.html">here</a>.


            <h2>The SIR(S) Model</h2>

            
            <a href="sirmath.html">

            
            <img src="images/sirs.gif" align=CENTER HSPACE=10 VSPACE=10 width=36% border=0>

            
            </a>


            <p> SIR(S) models are useful for modeling diseases with a short latent

            
            period that confer immunity after infection, whether permanently (an SIR

            
            model), or temporarily (an SIRS model). Such a model might be useful for

            
            modeling diseases such as influenza or chicken-pox. Susceptible individuals are infected

            
            at the rate of <em>&beta;I</em>. They then loose infectiousness at the rate of

            
            <em>&gamma;</em> and then become immune to further infection. Immunity is lost

            
            at the rate of <em>&sigma;</em>.  Mathematical details of this model can be

            
            viewed <a href="sirmath.html">here</a>.


            <h2>The SEIR(S) Model</h2>

            
            <a href="seirmath.html">

            
            <img src="images/seirs.gif" align=CENTER HSPACE=10 VSPACE=10 width=48% border=0>

            
            </a>


            <p> SEIR(S) models are useful for modeling diseases that have a long latent

            
            period in which infected individuals are not themselves infectious.  Measles,

            
            influenza and smallpox are all diseases that might be appropriately characterized

            
            by this model. Susceptible individuals are infected  at the rate of <em>&beta;I</em>.

            
            These individuals become infectious at the rate of <em>&epsilon;</em>, and

            
            then loose infectiousness at the rate of

            
            <em>&gamma;</em>, becoming immune to further infection. Immunity is lost

            
            at the rate of <em>&sigma;</em>. Mathematical details of this model can be

            
            viewed <a href="swirmath.html">here</a>.


            <h2>Further Reading</h2>

            
            <ol>

            
            	<li> Hethcote, H. W. 2000. The Mathematics of Infectious Diseases.

            
            	SIAM Rev. 42, 4 (Dec. 2000), 599-653. DOI= http://dx.doi.org/10.1137/S0036144500371907

            
            	<li>  Ford, D. A., Kaufman, J. H., Eiron, I.,2006. An extensible spatial

            
            		and temporal epidemiological modeling system.

            
            		Int J Health Geogr. 5, 4 (Jan. 2006). DOI=http://dx.doi.org/10.1186/1476-072X-5-4


            </ol>


            </body>

            
            </html>
	<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">

	<html>
	<head>
	<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
	<title>Epidemiological Modeling Overview</title>
	</head>

	<body>
	<h1>Epidemiological Modeling</h1>

	<img src="images/sis.gif" align=RIGHT HSPACE=10 VSPACE=10 width=25%>
	<p> Compartmental disease models are some of the most widely used
	models of infectious disease. In these models individuals (or portions of
	an individual) are considered to be in a compartments based on their
	disease status. By convention, commonly used compartmental models are
	designated by the first letters of the compartments and the order
	people move between them. So, the model for a disease where people
	start out Susceptible, become Infectious after catching the disease,
	and then after some time clear the disease and become Susceptible again
	would be an SIS model. The four most commonly used compartments
	are <u>S</u>usceptible, <u>E</u>xposed, <u>I</u>nfectious, and
	<u>R</u>emoved. <u>S</u>usceptible contains those individuals
	who can still be infected with disease. <u>E</u>xposed contains individuals
	who have been infected with the disease, but have not yet become
	infectious themselves. <u>I</u>nfectious contains those individuals who
	are infected and infectious. <u>R</u>emoved (sometimes called <u>R</u>ecovered)
	contains those individuals who have been removed from the system
	either through death or immunity. The disease state of a population
	is speccified by knowing the nuber of individuals (or proportion of
	the population) that is in each compartment.

	<p> There are two main types of compartmental models: deterministic
	and stochastic. In deterministic model, rates of movements between
	compartments are used to represent the processes by which individuals
	are infected, become ill and eventually recover from disease. These
	rates specify a set of differential or difference equations, which
	can be evaluated to give that state of the model at a future time
	point. In deterministic models compartments need not contain an
	integer number of individuals.

	<p>Deterministic models only give the <i>expected</i> behavior of
	the disease in a population under a set of assumptions about
	the natural history and epidemiology of the disease. Often
	we would also like to know how the disease behaves in more
	extreme cases, and what the distribution of this behavior
	is. Stochastic models provide a method for addressing this
	issue. In a stochastic model, whole individuals are moved
	between compartments based on a random draw from some specified
	distribution. To get informative results from a stochastic
	compartmental model it is necessary to do hundreds, or even
	thousands of experiments.

	<p>Compartamental models also may have "closed" or "open" populations.
	In closed populations the set of individuals represented by the model
	is static, no one comes in and no one comes out. It is of note that
	in such populations any disease that confers permanent immunity
	after infection will eventually become extinct. In an open
	population there is continuous immigration and emigration from
	the population, usually via birth and death.

	<p>STEM comes with deterministic implementations for three commonly used
	compartmental models: SI(S), SIR(S), and SIER(S). These models are
	implemented as having open populations, but closed populations can
	be easily simulated by setting the immigration/emigration rate to
	zero. Which model is appropriate for a modeling project depends
	on both the disease of interest and the timescale that we are
	interested in modeling our results.

	<h2>The SI(S) Model</h2>
	<a href="simath.html">
	<img src="images/sis.gif" align=CENTER HSPACE=10 VSPACE=10 width=24% border=0>
	</a>

	<p>SI(S) are useful for modeling diseases with a short latent period (the time
	between being infected and becoming infectious) that either confer no long term
	immunity (in the case of SIS models) or result in permanent infection (in the case
	of SI models). Diseases of this type include the common cold and many
	macro-parasite infections. Susceptible individuals are infected at the
	rate of <em>βI</em>, at which time they lose infectiousness
	at the rate of <em>γ</em>. Mathematical details of this model
	can be viewed <a href="simath.html">here</a>.


	<h2>The SIR(S) Model</h2>
	<a href="sirmath.html">
	<img src="images/sirs.gif" align=CENTER HSPACE=10 VSPACE=10 width=36% border=0>
	</a>

	<p> SIR(S) models are useful for modeling diseases with a short latent
	period that confer immunity after infection, whether permanently (an SIR
	model), or temporarily (an SIRS model). Such a model might be useful for
	modeling diseases such as influenza or chicken-pox. Susceptible individuals are infected
	at the rate of <em>βI</em>. They then loose infectiousness at the rate of
	<em>γ</em> and then become immune to further infection. Immunity is lost
	at the rate of <em>σ</em>. Mathematical details of this model can be
	viewed <a href="sirmath.html">here</a>.

	<h2>The SEIR(S) Model</h2>
	<a href="seirmath.html">
	<img src="images/seirs.gif" align=CENTER HSPACE=10 VSPACE=10 width=48% border=0>
	</a>

	<p> SEIR(S) models are useful for modeling diseases that have a long latent
	period in which infected individuals are not themselves infectious. Measles,
	influenza and smallpox are all diseases that might be appropriately characterized
	by this model. Susceptible individuals are infected at the rate of <em>βI</em>.
	These individuals become infectious at the rate of <em>ε</em>, and
	then loose infectiousness at the rate of
	<em>γ</em>, becoming immune to further infection. Immunity is lost
	at the rate of <em>σ</em>. Mathematical details of this model can be
	viewed <a href="swirmath.html">here</a>.


	<h2>Further Reading</h2>
	<ol>
	<li> Hethcote, H. W. 2000. The Mathematics of Infectious Diseases.
	SIAM Rev. 42, 4 (Dec. 2000), 599-653. DOI= http://dx.doi.org/10.1137/S0036144500371907
	<li> Ford, D. A., Kaufman, J. H., Eiron, I.,2006. An extensible spatial
	and temporal epidemiological modeling system.
	Int J Health Geogr. 5, 4 (Jan. 2006). DOI=http://dx.doi.org/10.1186/1476-072X-5-4

	</ol>

	</body>
	</html>