# Modelling Tuberculosis and Hepatitis B Co-infections

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 6, page 196-242
- ISSN: 0973-5348

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topBowong, S., and Kurths, J.. "Modelling Tuberculosis and Hepatitis B Co-infections." Mathematical Modelling of Natural Phenomena 5.6 (2010): 196-242. <http://eudml.org/doc/197615>.

@article{Bowong2010,

abstract = {Tuberculosis (TB) is the leading cause of death among individuals infected with the
hepatitis B virus (HBV). The study of the joint dynamics of HBV and TB present formidable
mathematical challenges due to the fact that the models of transmission are quite
distinct. We formulate and analyze a deterministic mathematical model which incorporates
of the co-dynamics of hepatitis B and tuberculosis. Two sub-models, namely: HBV-only and
TB-only sub-models are considered first of all. Unlike the HBV-only sub-model, which has a
globally-asymptotically stable disease-free equilibrium whenever the associated
reproduction number is less than unity, the TB-only sub-model undergoes the phenomenon of
backward bifurcation, where a stable disease-free equilibrium co-exists with a stable
endemic equilibrium, for a certain range of the associated reproduction number less than
unity. Thus, for TB, the classical requirement of having the associated reproduction
number to be less than unity, although necessary, is not sufficient for its elimination.
It is also shown, that the full HBV-TB co-infection model undergoes a backward bifurcation
phenomenon. Through simulations, we mainly find that i) the two diseases will co-exist
whenever their partial reproductive numbers exceed unity; (ii) the increased progression
rate due to exogenous reinfection from latent to active TB in co-infected individuals may
play a significant role in the rising prevalence of TB; and (iii) the increased
progression rates from acute stage to chronic stage of HBV infection have increased the
prevalence levels of HBV and TB prevalences.},

author = {Bowong, S., Kurths, J.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {nonlinear dynamical systems; epidemiological models; tuberculosis; hepatitis B; stability},

language = {eng},

month = {9},

number = {6},

pages = {196-242},

publisher = {EDP Sciences},

title = {Modelling Tuberculosis and Hepatitis B Co-infections},

url = {http://eudml.org/doc/197615},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Bowong, S.

AU - Kurths, J.

TI - Modelling Tuberculosis and Hepatitis B Co-infections

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/9//

PB - EDP Sciences

VL - 5

IS - 6

SP - 196

EP - 242

AB - Tuberculosis (TB) is the leading cause of death among individuals infected with the
hepatitis B virus (HBV). The study of the joint dynamics of HBV and TB present formidable
mathematical challenges due to the fact that the models of transmission are quite
distinct. We formulate and analyze a deterministic mathematical model which incorporates
of the co-dynamics of hepatitis B and tuberculosis. Two sub-models, namely: HBV-only and
TB-only sub-models are considered first of all. Unlike the HBV-only sub-model, which has a
globally-asymptotically stable disease-free equilibrium whenever the associated
reproduction number is less than unity, the TB-only sub-model undergoes the phenomenon of
backward bifurcation, where a stable disease-free equilibrium co-exists with a stable
endemic equilibrium, for a certain range of the associated reproduction number less than
unity. Thus, for TB, the classical requirement of having the associated reproduction
number to be less than unity, although necessary, is not sufficient for its elimination.
It is also shown, that the full HBV-TB co-infection model undergoes a backward bifurcation
phenomenon. Through simulations, we mainly find that i) the two diseases will co-exist
whenever their partial reproductive numbers exceed unity; (ii) the increased progression
rate due to exogenous reinfection from latent to active TB in co-infected individuals may
play a significant role in the rising prevalence of TB; and (iii) the increased
progression rates from acute stage to chronic stage of HBV infection have increased the
prevalence levels of HBV and TB prevalences.

LA - eng

KW - nonlinear dynamical systems; epidemiological models; tuberculosis; hepatitis B; stability

UR - http://eudml.org/doc/197615

ER -

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