Analisis Model Matematika Penyebaran Penyakit Co-infection Chlamydia dan Pneumonia

Putri, Siti Nur Mareliana Leni Syah (2018) Analisis Model Matematika Penyebaran Penyakit Co-infection Chlamydia dan Pneumonia. Undergraduate thesis, Institut Teknoloi Sepuluh Nopember.

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Abstract

Infeksi chlamydia adalah salah satu masalah utama kesehatan masyarakat. Infeksi chlamydia bersifat asimptomatik serta dapat menyebabkan penyakit lain, salah satunya adalah pneumonia. Co-infection chlamydia dan pneumonia terjadi ketika chlamydia dan pneumonia menginfeksi manusia secara bersamaan. Pada tugas akhir ini dibahas analisis model matematika penyebaran penyakit co-infection chlamydia dan pneumonia. Berdasarkan hasil analisis model diperoleh empat titik setimbang, yaitu titik setimbang non endemik (E_0 ), endemik chlamydia (E_0 )_1, endemik pneumonia (E_0 )_2, dan endemik co-infection chlamydia dan pneumonia (E_0 )_3. Dengan menggunakan metode Next Generation Matrix (NGM) diperoleh dua nilai basic reproduction number, yaitu basic reproduction number penyebaran penyakit chlamydia (R_(0_1 ) ) dan penyakit pneumonia (R_(0_2 ) ). Titik setimbang non endemik (E_0 ) stabil asimtotik lokal jika R_(0_1 )<1 dan R_(0_2 )<1, titik setimbang endemik chlamydia (E_0 )_1 stabil asimtotik lokal jika R_(0_1 )>1 dan R_(0_2 )<1, titik setimbang endemik pneumonia (E_0 )_2 stabil asimtotik lokal jika R_(0_1 )<1 dan R_(0_2 )>1, dan titik setimbang endemik co-infection chlamydia dan pneumonia (E_0 )_3 stabil asimtotik lokal jika R_(0_1 )>1 dan R_(0_2 )>1. Berdasarkan hasil simulasi numerik, laju transmisi pneumonia mempunyai pengaruh besar terhadap jumlah populasi manusia yang menderita co-infection chlamydia dan pneumonia. ===================================================================================================== Chlamydia infection is one of the major public health problems. Chlamydia infection is asymptomatic and can cause other diseases, one of which is pneumonia. Co-infection chlamydia and pneumonia occur when chlamydia and pneumonia infect humans simultaneously.In this final project, we discuss a mathematical model spreading of chlamydia and pneumonia co-infection disease. Based on the analytical result of the model, there are four equilibrium, namely disease-free equilibrium (E_0 ), chlamydia endemic equilibrium (E_0 )_1, pneumonia endemic equilibrium (E_0 )_2 and chlamydia-pneumonia co-infection endemic equilibrium (E_0 )_3. By the Next Generation Matrix (NGM) method, we obtain two basic reproduction numbers, that is basic reproduction number for spreading of chlamydia (R_(0_1 ) ) and basic reproduction number for spreading of pneumonia (R_(0_2 ) ). (E_0 ) equilibrium point is local asymptotically stable if R_(0_1 )<1 and R_(0_2 )<1. (E_0 )_1 equilibrium point is exist and disposed to local asymptotically stable if R_(0_1 )>1 and R_(0_2 )<1. (E_0 )_2 equilibrium point is exist and disposed to local asymptotically stable if R_(0_1 )<1 and R_(0_2 )>1. And (E_0 )_3 equilibrium point is disposed to local asymptotically stable if R_(0_1 )>1 and R_(0_2 )>1. Then, the numerical simulation results show that the value of pneumonia transmission rate has a big influences to the number of chlamydia-pneumonia co-infection people.

Item Type: Thesis (Undergraduate)
Additional Information: RSMa 511.8 Put a-1 3100018077455
Uncontrolled Keywords: Model Matematika, Chlamydia, Pneumonia, Co-infection, Kestabilan.
Subjects: Q Science > QA Mathematics > QA274.7 Markov processes--Mathematical models.
Q Science > QA Mathematics > QA278.3 Structural equation modeling.
Q Science > QA Mathematics > QA402 System analysis.
Divisions: Faculty of Mathematics, Computation, and Data Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User: Siti Nur Mareliana Leni Syah Putri
Date Deposited: 06 Dec 2020 23:38
Last Modified: 18 Dec 2020 07:36
URI: https://repository.its.ac.id/id/eprint/56570

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