Stability Analysis and Optimal Control of Mathematical Model of Thypoid Fever Spread

AbstractTyphoid fever is an endemic disease caused by infection with Salmonella Typhi. The transmission of typhoid through food and drink contaminated Typhi bacteria, which excreted the feces or urine infected person. problem increasingly complex because increase in carrier cases, making it difficult for treatment prevention efforts. This study develops a mathematical model control fever, consists two equilibrium points, namely non-endemic points. point asymptotically stable if satisfies condition given Routh-Hurwitz criterion. Optimal theory applied to providing health campaigns, screening, minimize number asymptomatic individuals, symptomatic chronic carriers. Pontryagin Minimum principle used determine optimal form. Numerical simulations are performed using Forward-Backward Sweep Runge-Kutta method order 4. simulation results indicate decrease each subpopulation after applying ten months. It found that campaigns has more significant impact than screening decreasing individuals. effectively reduces individuals symptoms becoming In conclusion, most effective strategy controlling spread simultaneously apply controls form treatment.Keywords: campaign; screening; treatment; control; minimum principle; forward-backward sweep. AbstrakDemam tifoid merupakan penyakit endemik yang disebabkan oleh infeksi bakteri Proses penularan demam melalui makanan dan minuman telah terkontaminasi dikeluarkan tinja maupun urin dari orang terinfeksi. Permasalahan tentang semakin kompleks karena meningkatnya kasus - carrier, sehingga menyulitkan upaya pengobatan pencegahan. Model matematika dikembangkan memiliki dua titik kesetimbangan yaitu setimbang nonendemik endemik. Titik akan stabil asimtotik jika memenuhi kondisi diberikan aturan Routh-Hurwitz. Teori kontrol diterapkan pada dengan pemberian berupa kampanye kesehatan, untuk meminimumkan jumlah individu asymptomatic, chronic. Penentuan bentuk menggunakan prinsip Pontryagin. Simulasi numerik dilakukan metode orde Berdasarkan hasil simulasi, terjadi penurunan disetiap subpopulasi terinfeksi setelah penerapan selama 10 bulan. Kontrol kesehatan pengaruh besar dibandingkan dalam menekan symptomatic. Penerapan sangat efektif gejala menjadi chronic.Kata Kunci: kesehatan; pengobatan; optimal; Pontryagin; 2020MSC: 00A71, 92B05