This article presents a mathematical model of Tuberculosis (TB) transmission considering BCG vaccination in an age- structured population. We used several strategies to simulate the TB dynamic and evaluate the potential impact on active TB. We developed a deterministic compartmental model where the population was distributed into seven compartments, i.e., susceptible individuals that can be vaccinated (S1) and can’t be vaccinated (S2), vaccinated (V), slow (L) and fast (E) exposed, infectious (I), and recovery (R). The mathematical model analysis was done by determining the equilibrium points, the Basic Reproduction Number (ℛ0) of the model, and analysing the stability of the equilibrium point. Some numeric interpretations were given by sensitivity vaccination parameters and percentage vaccine protection to the value of ℛ0 and autonomous model simulations. We find that to reach TB free condition is not enough by maximising one of the vaccination parameters for newborn, adults or percentage vaccine protection. We also find that vaccination into the adult population is more effective to suppress TB spread rather than newborn.
Topics
Mathematical modeling
REFERENCES
1.
Blower
, Sally
M.
, Angela R.
McLean
, Travis C.
Porco
, Peter M.
Small
, Philip C.
Hopewell
, Mellisa A.
Sanchez
& Andrew R.
Moss
. The Intrinsic Transmission Dynamic of Tuberculosis Epidemic
. Nature Medicine.
Volume 1
, Number 8
:815
–821
(1995
).2.
Centers for Disease Control and Prevention (CDC)
. Tuberculosis. Link: https://www.cdc.gov/tb/default.htm (2018
).3.
Dannenberg
, Arthur
M.
Perspectives on Clinical and Preclinical Testing of New Tuberculosis Vaccines
. American Society for Microbiology.
Volume 23
, Number 4
:781
–794
. doi: (2010
).4.
Department of Health and Human Services Victoria
. Management, Control and Prevention of Tuberculosis.
Melbourne Department of Health and Human Services
(2015
).5.
Diekmann
, J. A. P.
Heesterbeek
, & M. G.
Roberts
. The Construction of Next Generation Matrices for Compartmental Epidemic Model
. J. R. Soc. Interface
7
: 873
–885
(2009
).6.
Dipo
Aldila
, Zahra Alya Sari
Ryanto
, & Alhadi
Bustamam
. A mathematical model of TB control with vaccination in an age-structured susceptible population
. IOP Conf. Series: Journal of Physics : Conf. Series
1108
012050
(2018
).7.
Direktorat Jenderal Pengendalian Penyakit dan Penyehatan Lingkungan
. Pedoman Nasional Pengendalian Tuberculosis.
Jakarta
: Kementerian Kesehatan RI
(2014
).8.
Djomo
, Patrick
N.
, Einar
Heldal
, Laura Cunha
Rodrigues
, Ibrahim
Abubakar
, & Punam
Mangtani
. Duration of BCG Protection Against Tuberculosis and Change in Effectiveness with Time since Vaccination in Norway: A Retrospective Population-based Cohort Study. London: Department of Infectious Disease Epi-demiology and Population Health and Tuberculosis Centre
(2015
).9.
Dye
G.
et al. Prospect for Worldwide Tuberculosis Control Under The WHO DOTS Strategy
. Directly ob-served shortcourse therapy.
Lancet 352
:18886
–1891
(1998
).10.
E.
Soewono
and D.
Aldila
. A survey of basic reproductive ratios in vector-borne disease transmission modeling
. AIP Conf. Proceedings
1651
(1-7
), 12
(2015
).11.
E. P.
Hafidh
, N.
Aulida
, B. D.
Handari
, & D.
Aldila
. Optimal control problem from tuberculosis and multidrug resistant tuberculosis transmission model
. AIP Conf. Proceedings
2023
, 020223
(2018
).12.
Febriana Tri
Rahmawati
1, Alhadi
Bustamam
1, & Dipo
Aldila
. A mathematical model for chemotherapy paradoxical reaction in Tuberculosis transmission
. IOP Conf. Series: Journal of Physics: Conf. Series
1108
012057
(2018
).13.
Grange
, J.M.
, L. Rosa
Brunet
, & H.L.
Rieder
. Immune Protection Against Tuberculosis When is Im-munotherapy Preferable to Vaccination
. Elsevier Tuberculosis.
91
: 179
–185
(2011
).14.
Legrand
, Judith
, Alexandra
Sanchez
, Francoise
Le Pont
, Luiz
Camacho
, & Bernard
Larouze
. Modeling the Impact of Tuberculosis Control Strategies in Highly Endemic Overcrowded Prisons
. PloS ONE
3
(5
): e2100
. doi: (2008
).15.
Liu
, S.
, Yong
Li
, Yingjie
Bi
, & Qingdao
Huang
. Mixed Vaccination Strategy for The Control of Tuberculosis: A Case Study in China
. Mathematical Biosciences and Engineering.
Volume 14
, Number 3
: 695
–708
. doi: (2017
).16.
Maulana
Malik
, Monica
Larasati
, & Dipo
Aldila
. Mathematical modeling and numerical simulation of tu-berculosis spread with diabetes effect
. IOP Conf. Series: Journal of Physics: Conf. Series
1108
012061
(2018
).17.
Miyata
, Toshiko
, et. al. An adjunctive therapeutic vaccine against reactivation and post-treatment relapse tuberculosis
. Elsevier Ltd.
doi: (2011
).18.
Steenwinkel
, Jurriaan E.M.
de
, et.al.. Relapse of Tuberculosis Versus Primary Tuberculosis
; Course
, Patho-genesis and Therapy in Mice Elsevier Ltd
. (2012
).19.
Trauer
, James
M.
, Justin T.
Denholm
, & Emma S.
McBryde
. Construction of a mathematical model for tuberculosis transmission in highly endemic regions of the Asia-pacific
. Elsevier Ltd.
(2014
).20.
van der Werf
M.J.
, Langendam
MW
, Huitric
E.
, Manissero
D.
. Multidrug resistance after inappropriate tu-berculosis treatment: a meta-analysis
. Eur Respir J
39
:1511
–1519
(2012
).21.
Verver
S.
, et.al. Rate of re-infection tuberculosis after successful treatment is higher than rate of new tuberculosis
. Am J Respir Crit Care Med.
Vol 171
. pp 14301435
. doi: (2005
).22.
Vynnycky
, E.
and P. E. M.
Fine
. The Natural History of Tuberculosis: The Implications of Age-Dependent Risk of Disease and The Role of Reinfection
. Epidemiol Infect
119
:183
–201
(1997
).23.
World Health Organization. Tuberculosis. Link
: http://www.who.int/mediacentre/factsheets/_fs104/en/ (2017).24.
Yali
Yang
, Sanyi
Tang
, Xiaohong
Ren
, Huiwen
Zhao
, & Chenping
Guo
. Global Stability and Optimal Control for a Tuberculosis Model with Vaccination and Treatment
. Discrete and Continuous Dynamical System Series B.
Volume 21
, Number, 3
. pp. 1009
–1022
. doi: (2016
).
This content is only available via PDF.
© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.
