Pemodelan dan kontrol optimal dinamika penyebaran Amoebiasis dengan melibatkan efek Lingkungan

Dewi, Hanna Puspita (2025) Pemodelan dan kontrol optimal dinamika penyebaran Amoebiasis dengan melibatkan efek Lingkungan. Sarjana thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

Amoebiasis merupakan penyakit yang disebabkan oleh parasit Entamoeba histolytica. Penyakit ini dapat menimbulkan gejala seperti kram, nyeri perut, dan diare, namun dalam banyak kasus juga bersifat asimtomatik. Amoebiasis telah menyebar luas di seluruh dunia dan menempati peringkat ketiga sebagai penyebab kematian terbanyak akibat infeksi parasit. Dalam penelitian ini, dikembangkan model epidemi SEICRS dengan melibatkan efek lingkungan yang direpresentasikan oleh kompartemen (B), baik dalam bentuk model tanpa kontrol maupun model dengan kontrol. Untuk model tanpa kontrol, dilakukan analisis terhadap titik kesetimbangan bebas penyakit dan endemik, bilangan reproduksi efektif (Re) menggunakan metode Next Generation Matrix (NGM), serta analisis kestabilan global dengan menggunakan Teorema Castillo-Chavez dan fungsi Lyapunov. Strategi pengendalian dalam model dengan kontrol mencakup program edukasi, pengobatan, dan upaya peningkatan sanitasi. Masalah kontrol optimal diselesaikan dengan menerapkan Pontryagin’s Maximum Principle dan simulasi numeriknya dilakukan menggunakan metode forward and backward sweep berdasarkan skema Runge-Kutta orde empat (RK4). Hasil simulasi menunjukkan bahwa penerapan strategi kontrol optimal yang digunakan mampu menurunkan jumlah individu terinfeksi, individu pembawa, dan konsentrasi patogen di lingkungan, serta berkontribusi pada upaya pencapaian kondisi bebas penyakit dalam jangka panjang. Amoebiasis is a disease caused by the parasite Entamoeba histolytica. This disease can lead to symptoms such as cramps, abdominal pain, and diarrhea, but it is often asymptomatic in many cases. Amoebiasis has spread widely across the globe and ranks as the third leading cause of death due to parasitic infections. In this study, an SEICRS epidemiological model is developed by incorporating environmental effects, represented by the compartment (B), in both uncontrolled and controlled forms. For the uncontrolled model, analyses are conducted on the disease-free and endemic equilibrium points, the effective reproduction number (Re) using the Next Generation Matrix (NGM) method, and global stability using the Castillo-Chavez theorem and Lyapunov function. The control strategies in the controlled model include awareness programs, treatment, and sanitation efforts. The optimal control problem is solved by applying Pontryagin’s Maximum Principle, and numerical simulations are carried out using the forward and backward sweep method based on the fourth-order Runge-Kutta (RK4) scheme. The simulation results show that the implementation of the optimal control strategy used is able to reduce the number of infected individuals, carrier individuals, and pathogen concentrations in the environment, and contribute to efforts to achieve disease-free conditions in the long term.

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