Successful campaigns to eradicate malaria have been studied in a number of different countries. Each of these studies compares high-malaria-prevalence regions in the country with low-prevalence regions and checks what happens to children born in this areas before and after the campaign. They all find that life outcomes (such as education or earnings) of children born after the campaign in areas where malaria was once prevalent catch up with those of children born in low-incidence areas. This strongly suggests that eradicating malaria indeed results in a reduction in long-term poverty, although the effects are not nearly as large as those suggested by Jeffrey Sachs: One study on malaria eradication in the U.S. South (which had malaria until 1951) and several countries in Latin America suggests that a child who grew up malaria-free earns 50 percent more per year, for his entire adult life, compared to a child who got the disease. Qualitatively similar results were found in India, Paraguay, and Sri Lanka, although the magnitude of the gain varies from country to country.
Banerjee, Abhijit V. and Esther Duflo. Poor Economics: A Radical Rethinking of the Way to Fight Global Poverty. Hachette; New York. 2011. p. 45