Disease epidemics

Definition

Disease epidemics are widespread occurrences of infectious diseases in a community at a particular time. They can be modeled mathematically to predict their spread and control.

5 Must Know Facts For Your Next Test

1. Differential equations are used to model the rate of change in the number of infected individuals over time.
2. The SIR model is commonly used in epidemiology, where S, I, and R represent susceptible, infected, and recovered individuals respectively.
3. Direction fields help visualize the behavior of solutions to differential equations representing disease spread.
4. Numerical methods like Euler's method can approximate solutions to differential equations when an analytic solution is difficult to find.
5. The basic reproduction number $R_0$ is a critical parameter indicating whether an epidemic will spread (if $R_0 > 1$) or die out (if $R_0 < 1$).

Review Questions

Related terms

Differential Equation:

An equation involving derivatives that represents how a quantity changes over time.

SIR Model: A compartmental model in epidemiology that divides the population into susceptible (S), infected (I), and recovered (R) individuals.

Euler's Method:

A numerical technique for solving ordinary differential equations using iterative steps.