Tuberculosis Transmission Model with Chemoprophylaxis and Treatment

Bhunu, C. P.; Garira, Winston; Mukandavire, Zindoga; Zimba, M

doi:10.1007/s11538-008-9295-4

Cited by 67 publications

(50 citation statements)

References 24 publications

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“…(Bhunu et al, 2008;LaSalle, 1976;Nelson and Wells, 2004) rc 0.03 (Nelson and Wells, 2004) c1, c2 (1, 100) Estimated F f≤µ Estimated ra (0.5,1) (LaSalle, 1976) The susceptible population of adults initially falls as the infective among adults increase, but later increases to a steady state value over time. The susceptible children increase to a steady state.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Biological considerations entail that we study systematically (2) in the following region: Proof: For the given initial conditions, we prove by contradiction that if x 1 (t), x 2 (t), x 3 (t), x 4 (t), x 5 (t) and x 6 (t) are solutions of a system (2.2), then they are positive (see also Bhunu et al, 2008;Ziv et al, 2004).…”

Section: Methodsmentioning

confidence: 99%

“…Mathematical models for the dynamics of TB have been extensively developed and have been used in designing control programs and as predictive tools (Bhunu et al, 2008;Blower et al, 1995;Blower and Daley, 2002;Castillo-Chavez and Feng, 1997;Castillo-Chavez and Song, 2004;Gomes et al, 2004;Starke, 2003). Models that consider the potential impact of TB vaccines were studied in (Mairais et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

“…Models that consider the potential impact of TB vaccines were studied in (Mairais et al, 2005). Recently, Bhunu et al (2008) considered a model that studied the impact of treatment and chemoprophylaxis in combating TB.…”

Section: Introductionmentioning

confidence: 99%

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Modeling the Dynamics of Tuberculosis Transmission in Children and Adults

Nyabadza¹,

Kgosimore²

2012

Journal of Mathematics and Statistics

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Problem statement:The fight Against Tuberculosis (TB) has mainly focused on the adult population because children were perceived to pose a very low risk in TB transmission. This assumption ignores the potential risk children had as reservoirs of latent infections from which future cases evolve when they become adults. It was therefore important to investigate the dynamics of TB taking into consideration, children. Approach: We formulated a compartmental model for TB with two age classes, children and adults. Qualitative analysis of the model was done to investigate the stability of the model equilibria in terms of the model reproduction number R 0 Numerical simulations were also done to investigate the role played by some key epidemiological parameters in the dynamics of the disease. Results: The model had two equilibria: The disease free equilibrium which was globally stable for R 0 <1 and the endemic equilibrium which was locally asymptotically stable for R 0 >1, for R 0 near 1. The study showed increased latent infections in the adult population as a result of increased latently infected children who mature to adulthood with latent infections. Conclusion/Recommendations: Progression to active TB among adults is epidemiologically significant and interventions should focus on the adult population. Anti-tuberculosis, treatment of adults is crucial in controlling the epidemic and should interventions be proposed, they should target progression to active TB for those latently infected. The fight against TB should also take into consideration tuberculosis among children.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling the Dynamics of Tuberculosis Transmission in Children and Adults

Nyabadza¹,

Kgosimore²

2012

Journal of Mathematics and Statistics

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“…Compared to existing results [15,9,38,3,1,18,32,43,22] and references therein, our work differs from these studies in that our model, in addition to undiagnosed infectious and lost sight population, also considers the aspects of exogenous reinfections, disease relapse as well as primary active TB cases, natural recovery and traditional medicine or self-medication (practiced in Sub-Saharan Africa). Also, it is recognized that undiagnosed population, lost sight population and exogenous reinfections are important components of TB transmission in Sub-Saharan Africa.…”

Section: Accepted Manuscriptmentioning

confidence: 97%

Analysis of a tuberculosis model with undetected and lost-sight cases

Moualeu

Yakam

Bowong

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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A deterministic model of tuberculosis (TB) in sub-Saharan Africa including undetected and lost-sight cases is presented and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, when a stable disease-free equilibrium co-exists with one or more stable endemic equilibrium points when the associated basic reproduction number (R 0 ) is less than unity. Analyzing the model obviously reveals that exogenous reinfection plays a key role on the existence of backward bifurcation. However, an analysis of the ranges of exogenous reinfection suggested that backward bifurcation occurs only for very high and unrealistic ranges of the exogeneous reinfection rate. Random perturbation of reinfection rates was performed to gain insight into the role of this latter on the stability of the disease free equilibrium.

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Mathematics of FIV and BTB dynamics in buffalo and lion populations at Kruger National Park

Garba

Gumel

et al. 2018

Math Methods in App Sciences

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A new deterministic model for the transmission dynamics of feline immunodeficiency virus (FIV) and bovine tuberculosis (BTB) in lion-buffalo population is designed and used to gain insight into the transmission dynamics of the two diseases in the population. The model is shown to undergo a backward bifurcation (a dynamic phenomenon characterized by the coexistence of the stable disease-free equilibrium and a stable endemic equilibrium when the associated reproduction number of the model is less than unity). Two sources for this dynamic phenomenon, namely, the BTB reinfection of exposed buffalos and the BTB-FIV co-infection of lions, have been identified. It is shown that, for the special case of the model when backward bifurcation does not occur, the disease-free equilibrium of the resulting model is globally-asymptotically stable when the associated reproduction number is less than unity. Numerical simulations of the model, using initial and demographic data relevant to the BTB-FIV dynamics in Kruger National Park, show that control strategies, such as the isolation of lions with FIV symptoms or the treatment of lions and buffalos with BTB symptoms, can lead to the effective control or elimination of the disease in the lion-buffalo population if their effectiveness level is high enough. The time to elimination of any of the two diseases is significantly reduced if the strategies are combined.

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Tuberculosis Transmission Model with Chemoprophylaxis and Treatment

Cited by 67 publications

References 24 publications

Modeling the Dynamics of Tuberculosis Transmission in Children and Adults

Modeling the Dynamics of Tuberculosis Transmission in Children and Adults

Analysis of a tuberculosis model with undetected and lost-sight cases

Mathematics of FIV and BTB dynamics in buffalo and lion populations at Kruger National Park

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