BME 210
Spring 2009
Modeling the Spread of Disease
BME 210
Biomedical Computer Simulation Methods
Modeling Spread of Disease
I
Introduction to the Spread of Disease
II.
Computer Simulation of Chance Events
III.
One Population Spread of Disease Problem Defined
IV.
Simulating the One Population Spread of Disease Problem
Study Problems
Study Problem Solutions
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View Full DocumentBME 210 Spring 2009
Modeling the Spread of Disease
2
Modeling the Spread of Disease
I.
Introduction to the Spread of Disease
In this section, we will be concerned with some aspects of the study of the spread of disease (i.e.,
epidemiology).
While much of the field of epidemiology deals with analysis of data
resulting from
studies on the incidence and spread of disease in a population, we will be concerned here with some
simple mathematical models for predicting
patterns in the spread of disease.
To do this we must
consider how we can use the computer to simulate the random or chance events, which are fundamental
to the spread of disease process.
Let us first, however, introduce some general ideas and concepts regarding the propagation of
disease in a population.
To do this, consider the following figure which divides a population into four
subpopulations depending on whether a subject has or has had a specific disease.
Healthy
→
Infected
→
Contagious
→ .
.
Healthy
not
immune
incubation
period
recuperation
period
immunity
period
From left to right, we have the following progress of disease.
A healthy
subject can contract the disease
if he or she has no immunity
to it and comes in contact with a person who is contagious, in which case
the subject becomes infected
.
The duration of time in which the subject is infected is termed the
incubation
period, the extent of which can differ somewhat from one subject to the next.
In the next
stage of the spread of a disease the infected subject becomes contagious,
during which time the disease
can be transmitted to another healthy nonimmune subject.
The duration of time the subject remains
contagious is referred to as the recuperation
period.
Finally, the subject will become healthy
again but
with an acquired immunity
, the duration of which depends on the disease.
II.
Computer Simulation of Chance Events
Certain types of physical systems and the models associated with these systems are said to be
deterministic
.
For such systems, the characteristics of the models (its parameters) and the selected
inputs completely determine the outputs.
For instance, when the resistance of air is neglected, the
movement of a ball is completely determined by its mass, its initial velocity, and the gravitational
constant.
The processes associated with the spread of disease, on the other hand, are said to be
stochastic
, because the results of the process are subject to uncertain and random events.
The tools we
need to simulate these stochastic processes are quite different from those we need to solve the equations
representing deterministic systems.
The class of techniques developed for computer simulation of
random or chance events are referred to as Monte Carlo methods.
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 Spring '07
 D'Argenio
 probability density function, Incubation period, The War of the Worlds

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