Consider a system of differential equations describing the progress of a disease in a population, given by (xy)=F(x,y) for a vector-valued function FF. In our particular case, this is:

x=44xy2x

y=4xy2y

where x(t)x(t) is the number of susceptible individuals at time tt and y(t)y(t) is the number of infected individuals at time tt. The number of individuals is counted in units of 1,000 individuals.

The linearization of the system of differential equations at the equilibrium (x1,y1) gives a system of the form

(yx)=A(yx) Find A?

The linearization of the system of differential equations at the equilibrium (x1,y1) gives a system of the form

(yx)=B(yx) Find B?

Note: x1 < x2