Consider the following three mathematical models for the spread of an epidemic:
a ) dx/dt = kx^2
b) dx/dt = kx(x-m)
dx/dt=k(m-x)^2
in all models,x(t) is the number of infected individuals at time t, k0 and M0.Draw the phase lines of the three models, and answer the follwing questions. justify your answer!
a) which models have the following property if x(0) =0 then x(t) =0 for all t?
b) whhich models have the follwing property if there are initialy any infected indivduals that is X00 then the number of infected individuals will always grow without bound.

Question

Consider the following three mathematical models for the spread of an epidemic:
a ) dx/dt = kx^2
b) dx/dt = kx(x-m)
dx/dt=k(m-x)^2
in all models,x(t) is the number of infected individuals at time t, k>0 and M>0.Draw the phase lines of the three models, and answer the follwing questions. justify your answer!
a) which models have the following property if x(0) =0 then x(t) =0 for all t?
b) whhich models have the follwing property if there are initialy any infected indivduals that is X0>0 then the number of infected individuals will always grow without bound.