The role of screening and treatment in the transmission dynamics of HIV/AIDS and tuberculosis co-infection: a mathematical study

Kaur, Navjot; Ghosh, Mini; Bhatia, S. S.

doi:10.1007/s10867-014-9342-3

“…Agusto et al [91] considered optimal control theory applied to a two-(TB)strain TB/HIV ODE model. Kaur et al [92] studied an ODE TB/HIV model that includes abstractly defined screening and treatment interventions from a dynamical systems perspective. Sharomi et al [93] also applied dynamical systems analysis to a TB/HIV ODE model, but with more explicit representation of intervention strategies including ART.…”

Section: Population-level Impact Of Interventionsmentioning

confidence: 99%

Modelling the HIV-Associated TB Epidemic and the Impact of Interventions Aimed at Epidemic Control

Dodd

¹

,

Pretorius

²

,

Williams

³

2019

HIV and Tuberculosis

1

0

1

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In this chapter, we focus on mathematical models of tuberculosis epidemiology (TB) that include interactions with HIV and an explicit representation of transmission. We review the natural history of TB and illustrate how its features are simplified and incorporated in mathematical models. We then review the ways HIV influences the natural history of TB, the interventions that have been considered in models, and the way these individual-level effects are represented in models. We then go on to consider population-level effects, reviewing the TB/HIV modelling literature. We first review studies whose focus was on purely epidemiological modelling, and then studies whose focus was on modelling the impact of interventions. We conclude with a summary of the uses and achievements of TB/HIV modelling and some suggested future directions.

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“…, it is easy to show that the set Ω 2 is positively invariant and a global attractor of all positive solutions of submodel (9). Hence, it is sufficient to consider the dynamics of model (9) in Ω 2 as epidemiologically and mathematically wellposed.…”

Section: Pneumonia Submodel Analysis From Model (4) We Have Got the Pneumonia Submodel Atmentioning

confidence: 99%

“…AIDS is a common individual immune system disease caused by human immunodeficiency virus (HIV), i.e., RNA retrovirus which has developed into a global pandemic since the first patient was identified in 1981, making it one of the most destructive epidemics in history. HIV attacks human white blood cells and is transmitted through open sex, needle sharing, infected blood, and at childbirth [3,[6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

HIV/AIDS-Pneumonia Codynamics Model Analysis with Vaccination and Treatment

Teklu

¹

,

Koya

²

2022

Computational and Mathematical Methods in Medicine

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In this paper, we proposed and analyzed a realistic compartmental mathematical model on the spread and control of HIV/AIDS-pneumonia coepidemic incorporating pneumonia vaccination and treatment for both infections at each infection stage in a population. The model exhibits six equilibriums: HIV/AIDS only disease-free, pneumonia only disease-free, HIV/AIDS-pneumonia coepidemic disease-free, HIV/AIDS only endemic, pneumonia only endemic, and HIV/AIDS-pneumonia coepidemic endemic equilibriums. The HIV/AIDS only submodel has a globally asymptotically stable disease-free equilibrium if R 1 < 1 . Using center manifold theory, we have verified that both the pneumonia only submodel and the HIV/AIDS-pneumonia coepidemic model undergo backward bifurcations whenever R 2 < 1 and R 3 = max R 1 , R 2 < 1 , respectively. Thus, for pneumonia infection and HIV/AIDS-pneumonia coinfection, the requirement of the basic reproduction numbers to be less than one, even though necessary, may not be sufficient to completely eliminate the disease. Our sensitivity analysis results demonstrate that the pneumonia disease transmission rate β 2 and the HIV/AIDS transmission rate β 1 play an important role to change the qualitative dynamics of HIV/AIDS and pneumonia coinfection. The pneumonia infection transmission rate β 2 gives rises to the possibility of backward bifurcation for HIV/AIDS and pneumonia coinfection if R 3 = max R 1 , R 2 < 1 , and hence, the existence of multiple endemic equilibria some of which are stable and others are unstable. Using standard data from different literatures, our results show that the complete HIV/AIDS and pneumonia coinfection model reproduction number is R 3 = max R 1 , R 2 = max 1.386 , 9.69 = 9.69 at β 1 = 2 and β 2 = 0.2 which shows that the disease spreads throughout the community. Finally, our numerical simulations show that pneumonia vaccination and treatment against disease have the effect of decreasing pneumonia and coepidemic disease expansion and reducing the progression rate of HIV infection to the AIDS stage.

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“…Over two-thirds of people living with HIV live in the Sub-Saharan African region [4]. Human immunodeficiency virus (HIV) is a retrovirus virus which attacks and weakens the human body immunity and the central nervous system and if untreated it continues to multiply into the host until it reaches the peak leading into a very serious disease called AIDS, the stage where the symptoms of the disease occur frequently [5][6][7]. HIV is transmitted through sexual intercourse, needle sharing, and direct contact of blood or other body fluids containing the virus and mother to child during childbirth [1,8].…”

Section: Introductionmentioning

confidence: 99%

“…They have got the treatment of primary and secondary syphilis in both singly and dually infected individuals; especially with high treatment rates for primary syphilis, this will result in a reduction in the incidence of HIV and its coinfection with syphilis in the community. Kaur et al [6] formulated and analyzed a mathematical model for HIV/AIDS-TB coinfection with screening and treatment of both HIV and TB infective. Their numerical results suggested that the rates of transmission of both TB and HIV should be decreased, as an increase causes a rise in the number of infective at the equilibrium level.…”

Section: Introductionmentioning

confidence: 99%

HIV/AIDS-Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation

Teklu

¹

,

Mekonnen

²

2021

Journal of Applied Mathematics

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In the paper, we have considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia coinfection in a human population at different infection stages. Our model revealed that the disease-free equilibrium points of the HIV/AIDS and pneumonia submodels are both locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R H and R P ) are less than unity. Both the submodel endemic equilibrium points are locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R P and R H ) are greater than unity. The full HIV/AIDS-pneumonia coinfection model has both locally and globally asymptotically stable disease-free equilibrium points whenever the basic reproduction number of the coinfection model R H P is less than unity. Using standard values of parameters collected from different kinds of literature, we found that the numerical values of the basic reproduction numbers of the HIV/AIDS-only submodel and pneumonia-only submodel are 17 and 7, respectively, and the basic reproduction number of the HIV/AIDS-pneumonia coinfection model is max 7 , 17 = 17 . Applying sensitive analysis, we identified the most influential parameters to change the behavior of the solution of the considered coinfection dynamical system are the HIV/AIDS and pneumonia transmission rates β 1 and β 2 , respectively. The coinfection model was numerically simulated to investigate the stability of the coinfection endemic equilibrium point, the impacts of transmission rates, and treatment strategies for HIV/AIDS-only, pneumonia-only, and HIV/AIDS-pneumonia coinfected individuals. Finally, we observed that numerical simulations indicate that treatment against infection at every stage lowers the rate of infection or disease prevalence.

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The role of screening and treatment in the transmission dynamics of HIV/AIDS and tuberculosis co-infection: a mathematical study

Cited by 13 publications

References 19 publications

Modelling the HIV-Associated TB Epidemic and the Impact of Interventions Aimed at Epidemic Control

Modelling the HIV-Associated TB Epidemic and the Impact of Interventions Aimed at Epidemic Control

HIV/AIDS-Pneumonia Codynamics Model Analysis with Vaccination and Treatment

HIV/AIDS-Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation

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