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Fourth Law - Do the math

May 7, 2010 - 17:26 -- William Jobin

In many countries in Africa, sustained control efforts which had reduced the number of infected people in a population to near zero, were suddenly overcome by explosive epidemics. This happened in Garki Nigeria in the 1970's, and again in central Sudan in the 1980's.

We should not be mystified by this. The rapid recovery of malaria transmission after nearly successful control efforts was explained in clear, mathematical terms by Macdonald, back in 1956. He developed basic equations for malaria transmission which were later improved and written into computer simulations. These computer models were used in the Garki region of Nigeria and later in other places where malaria control was planned and analyzed with computer models. For those of you with a mathematical bent, this will be easy to understand.

Please see Macdonald 1956, Theory of the eradication of malaria, Bulletin WHO volume 15 page 369, and the book by Molineaux and Grammicia 1980 "The Garki Project", WHO, Geneva. An extensive treatment of the subject can be found in "A Realistic Strategy for Attacking Malaria in Africa" by Jobin, soon to be published as Blue Nile Monograph One by Boston Harbor Publishers.

MacDonald calculated that it is intrinsic in the nature of malaria transmission to quickly overcome incredible losses and setbacks. In fact temporarily successful control efforts shift parasite transmission into overdrive. When the parasite population nears extinction, it converts into a whirlwind which cannot be stopped. Thus has malaria survived in Africa through eons of droughts, floods, freezing and baking. Realistically, puny attacks by disorganized health agencies will be unable to overcome this relentless pressure from African malaria.

In Macdonald’s equations, the worst case showed that 50% of a nearly malaria-free population could be re-infected in about 40 days at the reproduction rate found in non-immune populations in Africa, where the mosquito vector is the most common and most dangerous species, Anopheles gambiae.

These theoretical predictions were born out by the well documented control attempts in Garki, Nigeria and also in the Blue Nile Health Project in Sudan.

Public health authorities in Africa who might initially experience delight when seeing rapid reductions in malaria prevalence due to their control programs, should thus be warned. The risk of complete failure of the control effort might be only a few months away, according to the computer simulations, and as verified by bitter experiences in two of the largest countries in Africa, Nigeria and Sudan.

Ignorance of this explosive ability to re-infect populations, along with several other factors, were key reasons for the failure of the global eradication program of 1956. Similar ignorance among the planners of current malaria control efforts in Africa will have the same results.

Do the math; eradication won’t happen in Africa

So from this, we conclude that we have to work on gradually reducing transmission to acceptable levels, mainly by adding permanent measures to the current unsustainable strategies which rely on drugs, insecticicides and treated bednets.