mathematical modeling: west nile virus richard allen and paula avery glorieta, 2002
TRANSCRIPT
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Mathematical Modeling:West Nile Virus
Richard Allen and Paula Avery
Glorieta, 2002
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Computational Science?
Computational science seeks to gain an understanding of science through the use of mathematical models on HP computers.
Computational Science involves teamwork
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Computational Science
Complements, but does not replace, theory and experimentation in scientific research.
Experiment
Computation
Theory
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Computational Science
Is often used in place of experiments when experiments are too large, too expensive, too dangerous, or too time consuming.
Can be useful in “what if” studies; e.g. to investigate the use of pathogens (viruses, bacteria, fungi) to control an insect population.
Is a modern tool for scientific investigation.
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Computational Science Process
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Mathematical Model
A mathematical formulation of some process in order to better understand it and to predict its future behavior.
The success of a mathematical model depends on its ease of use and its accuracy of prediction.
There are three simple rules for creating a model. Unfortunately, nobody knows what they are*.
You can’t “cook book” useful models
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Examples
Newton’s second law of motion: F = m*a
Radioactive decay: N(t) = N(0)*e-k*t
Compound interest: P(t) = P(0)(1 + r/n)nt
Bungee cord: m*g*(L + d) = k*d2/2
Golf ball trajectory: x(t) = (v0*cos )*t; y(t) = (v0*sin )*t - 0.5*g*t2
Population growth: Pn = Po + r*Po*(1 – Po/K)
0θ0θ
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Background: West Nile Virus Infection Cycle
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Background: West Nile Virus (Culex Tarsila Mosquito)
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Background: West Nile Virus (Culex Tarsila Mosquito)
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Background: NM County VBI Values