SECTION 10.7: Modeling the spread of a disease

This section deals with the direct application of solving more than differential equation at the same time. It helps determine whether a disease is an epidemic or not and can help determined the level of vaccination necessary to prevent the disease.

Epidemics are studied based on an S-I-R model where S is the number of susceptible candidates for the sickness, I is the number of people already suffering from the disease and R is the number of people who have recovered from the disease. On the whole, in this model, it is assumed that the rate of change of susceptibles is related to th negative rate of change of the number of susceptibles who get sick. The rate of change of the number infected is the rate of change of susceptibles getting sick excluding the rate of change of those who have recovered.

( dS/dt= -aSI) and (dI/dt=aSI-bI) where a and b are constants. a measures how infectious the disease is and b represents the rate at which infected people are removed from infected population.

As a result of the above analysis, a threshold value is determined where the threshold population = b/a.

The section provides a very interesting study of exactly how calculus of this form can be directly applied in the field of science (especially biology). It could effectively help save lives when studied on a much larger scale.