What was the social motivation that influenced european missionaries as they traveled to the rain forests of central africa?

The missionaries were motivated by belief that African natives needed the Christian message to be saved eternally, as well as feeling motivated to help the earthly well-being of the peoples in Africa as a Christian duty to help those in need.

Note that there is an implication in all of this that the European culture was superior to the African culture, and that the people of the central African rainforest were indeed in need.  Missionary endeavors set up medical clinics and schools and other facilities to aid the African natives.  There certainly was much good done in this way, but there also was a paternalistic attitude of the "white man's burden" to help seemingly lower human beings.   (Rudyard Kipling wrote the poem "White Man's Burden" in 1899 in reference to a different imperial venture, but the thought applies here as well.)

The constant presence of diseases or infectious agents within a given geographic area or population group. it may also refer to the usual prevalence of a given disease with such area or group. it includes holoendemic and hyperendemic diseases. a holoendemic disease is one for which a high prevalent level of infection begins early in life and affects most of the child population, leading to a state of equilibrium such that the adult population shows evidence of the disease much less commonly than do children (malaria in many communities is a holoendemic disease). a hyperendemic disease is one that is constantly present at a high incidence and/or prevalence rate and affects all groups equally. so probably family history.