An age-dependent population can be modeled by the differential equations p = + p(a bp),

An age-dependent population can be modeled by the differential equations p˙ = β + p(a − bp), β˙ = β(c + (a − bp)), where p is the population, β is the birth rate, and

a, b, and c are all positive constants. Find the critical points of this system and determine the long-term solution.