Malaria is the most lethal disease caused by parasites that transmitted to people through the bites of infected female mosquitoes. It is an estimated that 3.2 billion people, almost half of the world's population, are at risk of malaria. Most cases and deaths occur in sub-
Saharan Africa; Africa shares 89% of cases and 91% of deaths.
Malaria cases would be raised by the high levels of HIV infection, which weaken the immunity rendering people with HIV more susceptible to contracting the disease . It enhances the mortality rate for HIV patients about a factor of 25% in unstable malaria areas . Since malaria increases morbidity and mortality, it continues to inflict major public health and socioeconomic burdens in developing countries.…show more content… From interactions with those professionals, mathematicians have contributed significant and effective tools, called mathematical models of malaria, giving an insight into the interaction between the human and mosquito population, the dynamics of malaria, how to control malaria transmission, and eventually how to eradicate it . Therefore, establishing the transmission dynamics of an epidemic is very important in order to understand and predict the behavior of the disease. Mathematical models are particularly helpful as experimental tools with which to test and compare control and preventive strategies and to investigate the relative effects of various sociological, biological and environmental factors in the spread of the…show more content… He developed a simple SIS-model(Susceptible-Infected-Susceptible) with the assumption that the total population can further be divided into distinct human compartments. He applied a mathematical model to investigate that bringing a mosquito population below a certain threshold was sufficient to eliminate malaria. To estimate the infection and recovery rates, Macdonald  used a model in which he assumed the amount of infective material to which a population exposed remains unchanged. His result reveals hat reducing the number of mosquitoes is not an efficient control strategy that would have little effect on the epidemiology of malaria in areas of strong transmission. The Ross-Macdonald model involves an interaction between infected human and infected mosquito. Some other epidemic models, such as in May and Aron  and Anderson and May , use the assumption that acquired immunity is independent of the duration of exposure.
Bailey  and Aron [5, 6] models considered the acquired immunity to malaria depends on exposure. Tumwiine et al.  used the susceptible-infected-susceptible and susceptible- infected model of the human and mosquito populations, respectively, for the study of