What research would it be called where doctors study the economical influences on one's health and provide...?

value cures to such things as depression, heart disease, fatigue, and others by altering the economical and social structures to assist in the aid of one's health? It seems as most doctors only look at fixing the body, but would it also be worthwhile to fix one's environment to better conditions and patterns, to prevent further causes in the future?

Public Health professionals and epidemiologists study the causes and risk factors of disease.

Physicians treat the disease itself and advise on those causes and factors but rarely work directly in alleviating the causation factors.

Medical Social Workers concentrate on the socio-economic conditions that interfere with treatment and recovery or lead to increased risks.

Mental Health professionals concentrate on the personal and support group issues that interfere with treatment and recovery. In a medical scenario, the collaborate often with the Medical Social Worker.

Health Educators (often nurses but as often not) are interested in educating people about health risk factors in order to reduce the impact of those factors.

Environmental Health practitioners examine the physical/built conditions that may effect health and increase risk factors. They are interested in the human environment as it relates to health and includes health inspectors (for example).

There are other fields in public health as well, all working together to try and fix the conditions that promote disease. Just as your auto mechanic doesn't repair the potholes that damage your car; your physician leaves the specialized work of these other health professionals to them. But, there are many physicians who specialize in public health as well.

There are economists who study the effect of economic issues on health care at the individual and societal levels. They are called Health Economists.

There are also business professionals who specialize in the field of organizational development who look at ways to make the systems more effective and efficient. They generally specialize in Industrial/Organizational Psychology with a concentration in Health Care Administration.

There any number of types of scientist who study ways to cure and treat disease.

You've asked an interesting question and this is a very large and diverse field of study. It's so varied that no single profession can encompass the whole issue.

You find that kind of work going on in schools of public health. I'm not sure what it is specifically called other than public health research.