Determine the value of P for constant growth, increasing growth and declining growth.

Question

The population of Aedes mosquitoes which carry the Dengue virus can be modeled by a differential equation which describes the rate of growth of the population. The population growth rate dP/dt is given by dP/dt = rP(1-P/k) , where r is a positive constant and k is the carrying capacity.P0 is the initial population.

Answer 1

dP/dt<0 means declining growth, and this happens when 1-P/k<0, when P>k, the carrying capacity.

dP/dt=0, P=k and growth is state c or constant (no change).

dP/dt>0 means growth increases when P<k.