Mathematical Modeling: West Nile Virus Richard Allen and Paula Avery Glorieta, 2002

Computational Science? Computational science seeks to gain an understanding of science through the use of mathematical models on HP computers. Computational Science involves teamwork

Computational Science Complements, but does not replace, theory and experimentation in scientific research. Experiment Computation Theory

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.

Computational Science Process

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

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*d 2 /2 Golf ball trajectory: x(t) = (v 0 *cos )*t; y(t) = (v 0 *sin )*t - 0.5*g*t 2 Population growth: Pn = Po + r*Po*(1 – Po/K)

Background: West Nile Virus Infection Cycle

Background: West Nile Virus (Culex Tarsila Mosquito)

Background: NM County VBI Values