A few more words about the relationship between poverty and health. First of all: both are human rights issues. Article 25 of the Universal Declaration states:
Everyone has the right to a standard of living adequate for the health and well-being of himself and of his family, including food, clothing, housing and medical care and necessary social services, and the right to security in the event of unemployment, sickness, disability, widowhood, old age or other lack of livelihood in circumstances beyond his control.
The concern is that people may find themselves in a trap. Their poverty causes ill health because healthcare costs money, because poverty leads to malnutrition etc. And their ill health leads to further poverty, because they aren’t as productive as healthy people.
The ill health of poor people isn’t a problem only for these poor people. If they were more healthy, they would be more productive and more creative, and the economy as a whole and the wellbeing of society as a whole would benefit. Healthy children are also likely to stay in school longer, and hence will be more valuable to society when they grow up.
There is, of course, some obscurity regarding the direction of the causation: rich countries may be more healthy on average mainly because they spend more on healthcare. But it may also be that they have become rich because their health was improved first. Impossible to disentangle all this, because the “wealth of nations” is the result of hugely complex processes of many forces and counter-forces.
For example, there were some developing countries that benefited from WHO assistance after World War II and from breakthroughs in medication (such as penicillin). These countries, therefore, didn’t improve their health through economic growth and increased wealth. Health improvements were caused by external forces. One result of these health improvements was increased life expectancy, but as a result of this increase, there was population growth that went beyond GDP growth, resulting in declining levels of income per head. After some decades, the economic benefits of having more people in the economy, and reduced birth rates caused by better healthcare (and access to contraceptives), reversed the trend. There’s an interesting study by Acemoglu and Johnson here.
Others, however, have pointed out that this is just a tiny piece of the puzzle, and other factors can push societies in other directions. An increase in the population doesn’t necessarily lead to Malthusian problems. International trade and cooperation for example, but also technological improvements have sharply reduced the possible impact on an economy of an increase in population levels.