User:Mayes-tang/sandbox

Calculus/Disease Models

Vocabulary and Notation

Given the variables S, I, and R, we are able to create three basic models for disease spread.

S = the number of susceptible, the people who are not sick but who could become sick

I = the number of people who are currently infected with the disease

R = the number of recovered or removed (have been sick and can no longer infect others)

The SI Model

The assumption behind this model is that people infected with the disease do not ever recover. This means that among the population there are only two type of people: people who are susceptible(S)and people who are currently infected with the disease(I).

 The relationship between S and I is: dI/dt=-dS/dt (i.e. when the rate of people getting the disease is increasing, the rate of people becoming susceptible will be decreasing.)

The SIS Model

The assumption behind this model is that people infected with the disease can recover but also can become susceptible again.

This assumption can be represented by the box model shown to the right:

SIS Box Model

In this visual, susceptible individuals are represented by S and infected individuals are represented by I.

The SIR Model

to be added

Example: 2020 Coronavirus

to be added