Electronic Theses and Dissertation

Pneumonia merupakan salah satu penyebab utama kesakitan dan kematian pada balita, sehingga diperlukan model yang mampu menggambarkan dinamika penyebaran penyakit dan efektivitas pengendaliannya. Penelitian ini mengembangkan model SEITRS-V pneumonia pada balita dengan pendekatan deterministik dan stokastik Continuous Time Markov Chain. Analisis deterministik meliputi penentuan titik kesetimbangan, kestabilan, dan bilangan reproduksi dasar R0, sedangkan analisis stokastik digunakan untuk menentukan probabilitas kepunahan penyakit melalui Probability Generating Function dan multitype branching process. Selain itu, dilakukan analisis sensitivitas serta simulasi numerik menggunakan algoritma Gillespie. Hasil penelitian menunjukkan bahwa diperoleh titik kesetimbangan bebas penyakit dan endemik dengan R0 adalah 1,037, sehingga pneumonia berpotensi menyebar. Titik kesetimbangan bebas penyakit tidak stabil, sedangkan titik kesetimbangan endemik stabil secara lokal. Pada model stokastik diperoleh probabilitas kepunahan penyakit sebesar 0,9704, yang menunjukkan bahwa penyakit masih berpeluang tinggi untuk punah meskipun R0 besar dari 1. Analisis sensitivitas menunjukkan bahwa laju pengobatan merupakan parameter paling berpengaruh dalam meningkatkan probabilitas kepunahan. Simulasi CTMC menunjukkan bahwa peningkatan vaksinasi 50%, pengobatan 50%, dan kombinasi keduanya masing-masing menurunkan rata-rata individu terinfeksi sebesar 53,3%, 68,4%, dan 91,1%. Dengan demikian, kombinasi vaksinasi dan pengobatan merupakan strategi pengendalian paling efektif.

Pneumonia is one of the main causes of morbidity and mortality in toddlers, so a model capable of describing the dynamics of disease spread and the effectiveness of its control is needed. This study developed a SEITRS-V model of pneumonia in toddlers using a deterministic and stochastic Continuous Time Markov Chain approach. Deterministic analysis includes determining the equilibrium point, stability, and basic reproduction number R0, while stochastic analysis is used to determine the probability of disease extinction through the Probability Generating Function and multitype branching process. In addition, sensitivity analysis and numerical simulations were performed using the Gillespie algorithm. The results showed that the disease-free and endemic equilibrium points were obtained with R0 is 1.037, so pneumonia has the potential to spread. The disease-free equilibrium point is unstable, while the endemic equilibrium point is locally stable. In the stochastic model, the probability of disease extinction was obtained at 0.9704, indicating that the disease still has a high chance of extinction even though R0 more than 1. Sensitivity analysis showed that the treatment rate was the most influential parameter in increasing the probability of extinction. CTMC simulations showed that a 50% increase in vaccination, a 50% increase in treatment, and a combination of both reduced the average number of infected individuals by 53.3%, 68.4%, and 91.1%, respectively. Therefore, the combination of vaccination and treatment is the most effective control strategy.