Epidemiology

Overview

Epidemiology is the study of the growth of infectious diseases. It draws on the common techniques of population modeling, but inlcudes models with characteristics specific to disease.

Periods

The following periods are commonly referred to in epidemiology models.

• pre-infectious - the point where an individual contracts a disease to when they are able to transmit the disease
• incubation period - is the time between infection to the onset of disease
• infectious period - the period when the host is able to transmit a disease.

Notice there can be overlap between incubation and the other periods.

SI Models

One of the key aspects of epidemiology is the fact that after an individual becomes infected, she may become immune (at least for a time) from becoming ill again. This aspect of infectious disease modeling is captured in SI models by modeling the population susceptible to disease.

SI models will typically define the following variables, and then add other variables as needed

• {% S(t) %} - is the number of susceptible individuals
• {% I(t) %} - the number of infected individuals

Models

• Susceptible Preinfection Infectious REmoved(SEIR) This type of model is used when individuals, once infected are always infected, such as with HIV.
• Susceptible Infectious Recovered(SIR) This type of model is used when individuals are immune to further infection after they have already been infected.