American Institute of Mathematical Sciences

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2006, 3(3): 467-483. doi: 10.3934/mbe.2006.3.467

The influence of infectious diseases on population genetics

Zhilan Feng 1, and  Carlos Castillo-Chavez 2,

1. 

Department of Mathematics, Purdue University, West Lafayette, IN 47907
2. 

Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287

Received  May 2005 Revised  January 2006 Published  May 2006

Malaria is the vector-transmitted disease that causes the highest morbidity and mortality in humans. Motivated by the known influence of sickle-cell anemia on the morbidity and mortality of malaria-infected humans, we study the effect of malaria on the genetic composition of a host (human) population where sickle-cell anemia is prevalent and malaria is endemic. The host subpopulations are therefore classified according to three genotypes, $A$$A$, $AS$, and $SS$. It is known that $A$$A$ malaria-infected individuals experience higher malaria-induced mortality than $AS$ or $SS$ individuals. However, individuals carrying the $S$ gene are known to experience a higher mortality rate in a malaria-free environment than those who lack such a gene. The tradeoffs between increased fitness for some types in the presence of disease (a population level process) and reduced fitness in a disease-free environment are explored in this manuscript. We start from the published results of an earlier model and proceed to remove some model restrictions in order to better understand the impact on the natural hosts' genetics in an environment where malaria is endemic.
Keywords: mathematical model, infectious diseases, population genetics, fast and slow dynamics..
Mathematics Subject Classification: 92D15, 92D25, 92D30, 34C60, 34D1.
Citation: Zhilan Feng, Carlos Castillo-Chavez. The influence of infectious diseases on population genetics. Mathematical Biosciences & Engineering, 2006, 3 (3) : 467-483. doi: 10.3934/mbe.2006.3.467
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