ANALISIS KESTABILAN MODEL MATEMATIKA PENYEBARAN PENYAKIT SIFILIS PADA MANUSIA

Abstract

Syphilis is a sexually transmitted infection caused by the bacterium Treponema pallidum spiroset subspecies pallidum. Transmitted through sexual contact, the infection can also be transfered from mother to fetus during pregnancy or at birth, that causes congenital syphilis. The mathematical model that represents the spread of the disease was adapted from a mathematical model SEI. The model classifiles human population into vulnerable suscepted  women and men, Exposed , and Infected , sub-populations of women vulnerable , sub-populations women incubation period , sub-populations of women infected  and a sub-population of men vulnerable , sub-populations incubation period male , sub-populations laki- infected men  considered in the model. The derived models gives two critical point that is free disease and endemic critical point. The existence of a critical point  must satisfye  and . The model was  analyzed by the linierized method and Routh-Hurwitz criteria to determine the system stability. The simulation shows that, in case of free-disease  syphilis spread condition, the population of women and men has increased. The growth of women population is higher than the men population. it means that the spread of syphilis occurs faster in the men sub-population. In endemic condition of syphilis disease spread, the women population will growth rapidly than the men population.