Mode Of Transmission Of Malaria Math

The model is an autonomous system constructed by considering two models.

Mode of transmission of malaria math. The malaria parasites enter that person s bloodstream and travel to the liver. Chitnis 7 analyzed a similar model for malaria transmission. First reported in 1911 transfusion malaria is one of the most common transfusion transmitted infections today 18 19 the risk of acquiring transfusion malaria is very low 1 case per 4 million in nonendemic countries such as the united states whereas in the endemic countries it is much higher 50 cases per million donor units 19 20. Other modes of transmission rarely malaria can spread by the inoculation of blood from an infected person to a healthy person.

Moreover chitnis et al 2008 extended the model of ngwa and shu by. And recovered immune r h. In this paper we extend the chitnis model. We discussed the existence and stability of the disease free dfe and endemic equilibria ee of both models.

The bites bloodmeals of infected mosquitoes are the mode of transmission of the parasite between the human hosts. When the parasites mature they leave the liver and infect red blood cells. People enter the susceptible class either through birth at a constant per capita rate or through. A model of vector population and a model of virus transmission.

Furthermore the lyapunov principle is applied to study the stability of equilibrium points. The common basic reproduction number has been determined using the next generation matrix. Falciparum were sequenced in 2002 10 11. Grassi and ross discovered the mosquito s role in the parasite life cycle and transmission in 1897 1 and the genomes of anopheles mosquito and p.

Therefore this type of malaria has a shorter incubation period and relapses do not occur. The new model figure 1 1 divides the human population into four classes. Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. The threshold dynamics of each model is determined and a relation between them established.

Malaria transmission cycle malaria spreads when a mosquito becomes infected with the disease after biting an infected person and the infected mosquito then bites a noninfected person. Ngwa shu 2000 proposed a model for malaria transmission in which human hosts follow an seirs like pattern and vector hosts follow the sei pattern due to their short life cycle. In this type of malaria asexual forms are directly inoculated into the blood and pre erythrocytic development of the parasite in the liver does not occur. In this paper we present a mathematical model of malaria transmission.

The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. We have studied an seir mathe matical model and applied it to malaria transmission. A major point of malaria modeling.