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Abstract / Synopsis

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain that the incidence of sickle cell within a given population is an example of an asymptotically stable equilibrium determined by the selective pressure of malaria. It summarizes the impact of malaria on human history in order to explain why this equilibrium has varied over time and space. Finally, the article summarizes how linkage analysis and other statistical modeling techniques are being used as an important step in developing genomic pharmaceuticals to combat such diseases.

DOI

10.5642/jhummath.201701.16

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