Penggunaan Metode Perturbasi Homotopi untuk Menyelesaikan Model Penyebaran Penyakit Leptospirosis

Abstract

Leptospirosis disease is a very serious threat for people in the world. One way of analyzing the spread of leptospirosis disease is by constructing a mathematical model. In this work, the leptospirosis transmission model is solved by using homotopy perturbation method. By this method, linear and nonlinear operators are selected based on mathematical model under consideration. The solution of the model is formulated in term of power series with the first term of the solution constitutes as the initial approach. The result from homotopy perturbation method is then compared with numerical method, i.e., Runge-Kutta method. It is demonstrated that both methods provide quite similar results. An illustrative example is presented to describe the transmission dynamic of the disease