Introduction

12.1. Introduction#

The purpose of this chapter is to show how differential equations can be used to solve real world issues in both human disease tracking and natural phenomena.

  • Logistic Growth and COVID-19: This section shows how the logistic growth model can be useful in predicting the spread of a disease like COVID-19.

  • The Basic SIR Model: Introduces the SIR model, a system of three differential equations used to track the populations of infected, recovered, and susceptible individuals in an epidemic.

  • Cholera in Haiti: Uses the SIR model to track the spread of Cholera in Haiti during an outbreak.

  • CWS Model of Alzheimer’s Disease: Introduces the CWS model, a tool that can be useful in tracking the progression of Alzheimer’s Disease.

  • Gravity Fed Water Delivery: Analyzes an application of Newton’s 2nd law of motion (F=ma) on gravity-fed water delivery systems in the form of Bernoulli’s equation.

  • Earthquake Resistant Construction: Introduces the spring mass equation as it relates to structural dynamics, along with topics like resonance, damping, and forcing.