non-linear model fit function not working

I have attempted to exercise a non-linear model fit to my data, dadtAbs, and got the following puzzle

nlm =    NonlinearModelFit[     Transpose[{Table[t, {t, 1, tmax}],dadtAbs}],      (1 - aaa)*bbb*NSPI[bbb, ddd, population, t] *        (1 - ddd)*(population - NSPI[bbb, ddd, population, t]),      {aaa, bbb, ddd},      t] 

where dadtAbs is a list, population is a known constant, aaa, bbb, ddd are the desired answers, and t is the variable.

When I queried nlm, I got

[0.] 

Here is the function NSPI:

NSPI[alpha_, delta_, population_, tt_] :=    population/(1 + (population - 1)*Exp[-alpha*population*(1 - delta)*tt]) 

population is a large constant, for example, 1000000