Dinamika populasi manusia dan vektor pada penularan penyakit malaria oleh plasmodium falciparum dan plasmodium vivax

Abstract

Malaria is a disease that transmitted to human by the bitting of infectious Anopheles mosquitoes. This infectious desease caused by parasite genus Plasmodium. There are two species of the parasites studied here, that cause human malaria namely Plasmodium vivax and Plasmodium falciparum. The mathematical model in discribing the transmission of Plasmodium falciparum and Plasmodium vivax on human population is divided into four classes, the susceptible, the infectious, the dormant, and the recovered classes. Mosquitoes that caused malaria are called the vector. In this case, the vector population is divided into two classes, the susceptible and infectious classes. There are two equilibrium states, a disease free state E0 and an endemic state E1. The stability of E0 and E1 is determined by considering the basic reproductive number (R0). The E0 is stable if R0 is less than one. On the other hand, the point E1 was stable given the value of R0 is greater than one. In this research the dynamic of human population and vector is discribed in to some ilustrative sample with 5% and 50% of the infected vector. It is found that, if R0 < 1, with 5% infected vector could reach the stability faster than the 50% infected vector. For R0 > 1 , it was found that, 5% infected vector could reach the stability slower than the 50% infected vector. This research also showed that the interaction between susceptibles and infectious human has no effect in to the dynamic of the human population.