If this formula were valid, population densities like India and China wouldn't exist. Think how far the rest of the world has to go to reach their density. If the formula doesn't work in every setting, it's worthless. It's a theory that would make any mother proud, just so long as her son came up with it. But it doesn't stand up when exposed to reality.
The vital coefficients (a and b) that I provided were for the global population. If you wish to examine a particular population subset, then different parameters apply. For example, the United States has a=0.03134 and b=1.5887E-10. For the United States, zero population growth will be reached when the population reaches about 400 million.
You are partially right in mentioning China and India. Backwards countries that become industrialized have not fit this model very well because a more efficient use of resources will affect the parameters. However China has instituted severe population control policies that are offsetting the industrialization of these two countries; they probably wash each other out, and the global population prediction is still valid.