Analisis Dinamik Model Sel Kanker Prostat dengan Terapi Vaksin Kuratif

Abstract

                Prostate cancer is a type of cancer that occurs in men and requires an effective therapeutic approach. Treatment of prostate cancer depends on the stage at diagnosis. In advanced stages of prostate cancer can be treated with hormone therapy such as chemotherapy which is then followed by vaccine therapy which aims to help increase the body's immune system response to prostate cancer cells. This model consists of a system of ordinary differential equations with five variables used, including androgen-dependent prostate cancer cells, androgen-independent prostate cancer cells, dendritic cells, effector cells, and curative vaccines. Then two equilibrium point conditions are produced, when there is no vaccine  for disease free conditions  and endemic conditions , then when the vaccine  there are three equilibrium conditions namely disease free , side effects  and local existence between prostate cancer cells with vaccine . The results of the stability analysis for each equilibrium point show that when , the condition  is global asymptotic, while the condition  is stable because the eigenvalue is negative. When  for the condition  it is unstable because the two roots are positive, then for the condition  it is global asymptotic and for the condition  it is asymptotically local because all the eigenvalues are negative. The numerical simulations of equilibrium points obtained using the fourth order runge-kutta method according to different q parameter values show that the larger the dendritic cells and effector cells activated, the greater the vaccine that enters the body, resulting in immune cells that will fight prostate cancer cells.