MODEL SEIDR DALAM STUDI PENYEBARAN TUBERKULOSIS: ANALISIS INTERVENSI DIAGNOSIS DAN DAMPAKNYA TERHADAP DINAMIKA INFEKSI

Sila Rizqina, Muhammad Afief Balya, Yuni Yulida, Muhammad Ahsar Karim, Hermei Lissa

Abstract


Pulmonary Tuberculosis (TB) is a contagious infectious disease caused by Mycobacterium tuberculosis. A person with tuberculosis serves as a source of transmission to the surrounding population. One way to minimize the transmission is through the implementation of effective diagnostic intervention. One approach to understanding the dynamics of TB spread is through the SEIDR epidemiological mathematical model, which includes susceptible, exposed, infectious, diagnosed, and recovered individuals. This study begins by explaining the construction of the SEIDR model, followed by determining the disease-free equilibrium point, the basic reproduction number, local stability analysis of the disease-free equilibrium, and sensitivity analysis. The final step involves conducting numerical simulations and interpreting the results obtained. There are two equilibrium points derived from the model: the disease-free equilibrium and the endemic equilibrium. The disease-free equilibrium point is asymptotically stable if the basic reproduction number is less than one, while the endemic equilibrium point is determined through simulation. Based on the simulation, it is found that the system experiences an outbreak when the basic reproduction number is greater than one. Sensitivity analysis shows that the birth rate has the highest positive influence on the basic reproduction number, while the natural death rate has the highest negative influence on the basic reproduction number. Numerical simulation results show that when transmission is high, the number of diagnosed individuals increases sharply, while the susceptible and exposed populations decrease drastically; conversely, if transmission is suppressed, active cases decline until they are completely eliminated. Therefore, effective interventions are crucial to reduce transmission and to strengthen diagnostic systems in order to achieve TB elimination at the population level


Keywords


Tuberculosis, Diagnosed, Epidemiological Model, Sensitivity Analysis, Simulation

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References


Annas, S., Isbar Pratama, M., Rifandi, M., Sanusi, W., & Side, S. (2020). Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia. Chaos, Solitons and Fractals, 139. https://doi.org/10.1016/j.chaos.2020.110072

Bellomo, N., Preziosi, L., & Romano, A. (2002). Mechanics and Dynamical Systems with Mathematica.

Braun, M. (1992). Differential Equation and Their Application-Fourth Edition. In Springer.

Chitnis, N., Hyman, J. M., & Cushing, J. M. (2008). Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bulletin of Mathematical Biology, 70(5), 1272–1296. https://doi.org/10.1007/s11538-008-9299-0

Driessche, P. Van Den, & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission (Vol. 180).

Fauzi, I. S., Fakhruddin, M., Nuraini, N., & Wijaya, K. P. (2019). Comparison of Dengue Transmission in Lowland and Highland Area: Case Study in Semarang and Malang, Indonesia. Communication in Biomathematical Sciences, 2(1), 23–37. https://doi.org/10.5614/cbms.2019.2.1.3

Liu, S., Bi, Y., & Liu, Y. (2020). Modeling and dynamic analysis of tuberculosis in mainland China from 1998 to 2017: The effect of DOTS strategy and further control. Theoretical Biology and Medical Modelling, 17(1), 1–10. https://doi.org/10.1186/s12976-020-00124-9

Nuraini, N., Fauzi, I. S., Lestari, B. W., & Rizqina, S. (2022). The Impact of COVID-19 Quarantine on Tuberculosis and Diabetes Mellitus Cases: A Modelling Study. Tropical Medicine and Infectious Disease, 7(12). https://doi.org/10.3390/tropicalmed7120407

Perko, L. (2001). Equations and Dynamical Systems. https://www-users.cse.umn.edu/~scheel/teaching/8501-fall18/perko.pdf

Presiden Republik Indonesia. (2021). Peraturan Presiden Nomor 67 tahun 2021 tentang Penanggulangan Tuberkulosis. Kementerian Kesehatan Re, 67(069394), 107.

Saleng, R. A. S., Nuha, A. R., Yahya, L., & Resmawan, R. (2022). Analisis Dinamik Model Matematika Penyebaran Penyakit Tuberkulosis dengan Pengaruh Vaksin dan Pengobatan di Provinsi Gorontalo. Equator: Journal of Mathematical and Statistical Sciences, 1(1), 18. https://doi.org/10.26418/ejmss.v1i1.59111

Tewa, J. J., Bowong, S., & Mewoli, B. (2012). Mathematical analysis of two-patch model for the dynamical transmission of tuberculosis. Applied Mathematical Modelling, 36(6), 2466–2485. https://doi.org/10.1016/j.apm.2011.09.004

Wikurendra, E. A. (2019). Literatur Review : Faktor Faktor Yang Mempengaruhi Kejadian Tuberkulosis Paru Dan Penanggulangannya. Ilmu Kesehatan Masyarakat, 2(1), 1–12.

Zahwa, N., Nabilla, U., & Nurviana, N. (2022). Model Matematika Sitr pada Penyebaran Penyakit Tuberculosis di Provinsi Aceh. Jurnal Pendidikan Matematika Dan Sains, 10(1), 8–14. https://doi.org/10.21831/jpms.v10i1.50683




DOI: https://doi.org/10.20527/epsilon.v19i1.15641

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