Malaria and Sickle Cell Anemia

Malaria is one of the most severe human diseases, causing more than 300–500 million cases today¹, leading to an estimated 2.7 million deaths worldwide with 80–90% of those occurring in the section of Africa below the Sahara Desert. Children ages one to four are most vulnerable to malaria due to their immature immune systems. Malaria is caused by a parasite transmitted to humans or animals by the Anopheles mosquito. The human parasite, Plasmodium falciparum, digests the hemoglobin found in red blood cells (RBCs) and breaks down the adhesive properties of the cells. Therefore the RBCs may become stuck to the walls of capillaries. When this occurs in the cerebral section of the brain, cerebral malaria develops, and blood clots in the brain occlude the vessels. Symptoms of malaria increase in severity each time an RBC bursts and releases more parasites. These symptoms can include high fever, chills, and uncontrollable shaking/shivering, also called rigors. Severe headache, vomiting, muscle pain, and extreme tiredness may accompany these symptoms as well. To combat the disease, many countries use an insecticide called DDT to control mosquito populations. Different medications have also been developed to treat and prevent malaria. These include chloroquine, doxycycline, and mefloquine.

Several variables are implicated in the epidemiology of this disease. In this chapter we develop a simplified model to investigate the dynamics of the spread of malaria in a closed ideal region without human immigration. We further assume that humans are the most important hosts and disregard other possible hosts aside from the mosquitoes, which pick up the malaria parasites when they feed on the blood of an infected human. Upon receipt of malaria parasites (Plasmodium sp.), the parasites reproduce in the gut of mosquitoes. Subsequently, malaria parasites are returned through the mosquitoes’ salivary glands to humans as the mosquitoes feed on red blood cells.