Basic Reproduction Number of Tuberculosis Spread Model in Lamongan With DOTS Strategy

Aris Alfan; Fitroh Resmi; Nihaya Alivia Coraima Dewi

doi:10.31764/jtam.v5i1.3696

Basic Reproduction Number of Tuberculosis Spread Model in Lamongan With DOTS Strategy

Aris Alfan, Fitroh Resmi, Nihaya Alivia Coraima Dewi

Abstract

Tuberculosis (TB) will be a serious threat if not handled quickly and appropriately. The relatively long treatment in time and the high risk of death is a challenge in controlling the spread of this disease. The DOTS (Directly Observed Treatment Short-course) strategy is considered capable of controlling the spread of TB because of the high success rate, reaching 91%. The mathematical model of the spread of TB has been widely studied to determine the potential for the spread of this disease in an area. The purpose of this study is to build a model of tuberculosis spread in Lamongan to determine the rate of its spread and to predict whether it will be endemic or not. Using disease spread mathematical model type SEITR, this research has examined based on 2018 and 2019 data from the Lamongan health office then simulates the result. The research begins with the construction of the model followed by a stability analysis of the model by determining the basic reproduction number ( ), which is simulated after the parameter approach was carried out. From the simulation results, the result shows that means that TB will not endemic in Lamongan. Besides, the results of the effect of parameter ω on I(t) were obtained, which concluded that seeking and treating active TB alone would only reduce infected individuals but not reduce the length of time TB spread. Identification of the effect of parameter φ on I(t) has also been carried out which results in the conclusion that more treatment for susceptible individuals, in addition to reducing the number of infected individuals, will also reduce the length of time TB spreads in that area. This result will be a good suggestion for the government to deal faster with tuberculosis transmission.

Keywords

Tuberculosis Model; DOTS ; Model SEITR; Basic Reproduction Number R_0;

Full Text:

DOWNLOAD [PDF]

References

Abdul Halim, N. (2013). Tuberculosis Model: A Mathematical Analysis. In University of Malaya (Vol. 66, Issue 1997).

ACEH, M. K. B. (2019). Banda Aceh Raih Capaian Tertinggi Penanganan Tuberkulosis Se-Indonesia. http://infopublik.id/kategori/nusantara/389327/banda-aceh-raih-capaian-tertinggi-penanganan-tuberkulosis-se-indonesia?video=

Badan Pusat Statistik. (2013). Proyeksi Penduduk Indonesia 2010-2035. In Badan Pusat Statistika, Jakarta-Indonesia.

BPS Kabupaten Lamongan. (2018). Kabupaten Lamongan dalam Angka 2018. Https://Lamongankab.Bps.Go.Id/.

Castillo-chavez, C. (2013). Dynamical models of tuberculosis and applications. CBMS-NSF Regional Conference Series in Applied Mathematics, 1(84), 191–217.

Dirjen P2&PL Kementerian Kesehatan RI. (2011). Terobosan Menuju Akses Universal, Strategi Nasional Pengendalian TB di Indonesia 2010-2014. Stop TB, 3. http://www.searo.who.int/indonesia/topics/tb/stranas_tb-2010-2014.pdf

Hattaf, K., Rachik, M., Saadi, S., Tabit, Y., & Yousfi, N. (2009). Exogenous Reinfection. 3(5), 231–240.

Imran, R., Pranata, W., & Ismail, S. (2020). Model Matematika SEIT pada Penyebaran Penyakit Tuberculosis Resistensi Primer. 1, 1–11. https://doi.org/10.31219/osf.io/er95a

Kementerian Kesehatan RI. (2018). InfoDatin Tuberculosis. Kementerian Kesehatan RI, 1. https://www.depkes.go.id/article/view/18030500005/waspadai-peningkatan-penyakit-menular.html%0Ahttp://www.depkes.go.id/article/view/17070700004/program-indonesia-sehat-dengan-pendekatan-keluarga.html

Marks, S. M., Dowdy, D. W., Menzies, N. A., Shete, P. B., Salomon, J. A., Parriott, A., Shrestha, S., Flood, J., & Hill, A. N. (2020). Policy Implications of Mathematical Modeling of Latent Tuberculosis Infection Testing and Treatment Strategies to Accelerate Tuberculosis Elimination. Public Health Reports, 135(1_suppl), 38S-43S. https://doi.org/10.1177/0033354920912710

Matteelli, A., Sulis, G., Capone, S., D’Ambrosio, L., Migliori, G. B., & Getahun, H. (2017). Tuberculosis elimination and the challenge of latent tuberculosis. In Presse Medicale (Vol. 46, Issue 2, pp. e13–e21). Elsevier Masson SAS. https://doi.org/10.1016/j.lpm.2017.01.015

Melnichenko, A., & Romanyukha, A. A. (2009). A model of tuberculosis epidemiology: Data analysis and estimation of parameters. Mathematical Models and Computer Simulations, 1(4), 428–444. https://doi.org/10.1134/S2070048209040024

Narula, P., Piratla, V., Bansal, A., Azad, S., & Lio, P. (2016). Parameter estimation of tuberculosis transmission model using Ensemble Kalman filter across Indian states and union territories. Infection, Disease and Health, 21(4), 184–191. https://doi.org/10.1016/j.idh.2016.11.001

Okuonghae, D., & Korobeinikov, A. (2007). Dynamics of tuberculosis: The effect of direct observation therapy strategy (DOTS) in Nigeria. Mathematical Modelling of Natural Phenomena, 2(1), 113–128. https://doi.org/10.1051/mmnp:2008013

Okuonghae, Daniel, & Ikhimwin, B. O. (2016). Dynamics of a mathematical model for tuberculosis with variability in susceptibility and disease progressions due to difference in awareness level. In Frontiers in Microbiology (Vol. 6, Issue JAN). https://doi.org/10.3389/fmicb.2015.01530

Ramadhan, M. R., Waluya, S. B., & Kharis, M. (2012). UNNES Journal of Mathematics. Ujm, 1(2252), 125–130.

Rifki Taufik, M., Lestari, D., & Wijayanti Septiarini, T. (2015). Mathematical Model for Vaccinated Tuberculosis Disease with VEIT Model. International Journal of Modeling and Optimization, 5(3), 192–197. https://doi.org/10.7763/ijmo.2015.v5.460

Sarini, N. K. M. (2012). Universitas Indonesia Universitas Indonesia Jakarta. Fmipa Ui, 1–95.

Tasillo, A., Salomon, J. A., Trikalinos, T. A., Robert Horsburgh Jr, C., Marks, S. M., & Linas, B. P. (2017). Cost-effectiveness of Testing and Treatment for Latent Tuberculosis Infection in Residents Born Outside the United States With and Without Medical Comorbidities in a Simulation Model Supplemental content. JAMA Intern Med, 177(12), 1755–1764. https://doi.org/10.1001/jamainternmed.2017.3941

Zuhri, Z., Hamid, A., Subchan, ., & Rofiki, I. (2020). Optimal Control of Exogenous Reinfection Prevention and Treatment on a Tuberculosis Model. 235–239. https://doi.org/10.5220/0008904702350239

DOI: https://doi.org/10.31764/jtam.v5i1.3696