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.