A plateauing of the Earth's population is better achieved through a decrease in birth rates than mass starvation, death and misery. Just saying.
Factors in reducing birth rates are a reduction in infant mortality (if you are confident that your children will reach adulthood you won't feel the need to have as many children) and female education. These are areas the Gates Foundation are working in.
Here in the 'developed world', it is likely that your grandmother had quite a few siblings and that it wouldn't be unusual had one died of whooping cough or an infection. Today, it would be a fair guess that your parents only had two or three children, with a good expectation that they would reach reproductive age.