Analisis Kestabilan Model Seak Pada Penyebaran Penyakit Filariasis

Abstract

Filariasis or elephantiasis is a disease caused by infection of filarial worms. This research studies the spread model of elephantiasis disease that is influenced by the birth rate, the natural mortality rate, the transfer rate of susceptible exposed mosquito to the exposure due to the interaction between susceptible mosquito and infected human population, the transfer rate of exposed mosquito to the infected, the transfer rate of vulnerable human to the exposure human populations as a result of the mosquito and susceptible human intraction, the transfer rate of exposed human population to the infected human population, and the transfer rate of the infected human population to chronically human population. Filariasis disease spread model is built in form of Susceptible - Exposed - Acute - Kronic (Seak). The model is a nonlinear differential equations system of dependent variables that are the vulnerable, exposed, infected human populations, and chronic and vulnerable exposed, and infected mosquito population.  The  model  has  a  critical  point  namely   that represents the free-disease conditions and the critical point  that represents an endemic condition. The critical points is analyzed using the method of linearized stability and Routh Hurwitz criteria.  is the vertical point stable while   is unstable. The result indicates that the free- disease condition is settled, while the endemic will be left in a long time period. It could also be interpreted that the endemic have a chance be overcome.