Open AccessANALISIS KESTABILAN MODEL MATEMATIKA PENYEBARAN PENYAKIT SIFILIS PADA MANUSIA
Author(s) -
N Muliyani,
Rina Ratianingsih,
N Nacong
Publication year - 2018
Publication title -
jurnal ilmiah matematika dan terapan/jurnal ilmiah matematika dan terapan
Language(s) - English
Resource type - Journals
eISSN - 2540-766X
pISSN - 1829-8133
DOI - 10.22487/2540766x.2018.v15.i1.10189
Subject(s) - syphilis , population , incubation period , treponema , demography , sexually transmitted disease , medicine , biology , incubation , virology , biochemistry , human immunodeficiency virus (hiv) , sociology
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.