Consider the SI model below. The meaning of the parameters is as follows: K is a constant recruitment rate (the number of susceptible entering the population), μ is the natural death rate and r is treatment rate which cures the disease but does not provide immunity.
{dS/dt =K−λSI+rI−μS,
{dI/dl =λSI−rI−μI.
Denoting the total population by N(t)=S(t)+I(t), obtain a single differential equation in N by adding the two equations of the model. What is the limit of N(t) as t→[infinity] ? (Note: you don't need to solve the ODE to answer this.)