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A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection.

Apenteng OO, Ismail NA - PLoS ONE (2015)

Bottom Line: The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic.The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS).Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Statistics, Faculty of Economics & Administration, University of Malaya, Kuala Lumpur, Malaysia.

ABSTRACT
The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 < 1, the disease dies out; and if R0 > 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS.

No MeSH data available.


Related in: MedlinePlus

Pairs plot of the MCMC samples for the ten parameters.The pairs plot shows a strong relationship between parameters γ and ρ (the rate at which an individual will fully move from the A1(t) class to the A2(t) class and the disease-induced mortality rate for A2(t), respectively). This plot visualizes the pairwise relationship in the upper panel, the correlation coefficients in the lower panel, and the marginal distribution for each parameter, represented by a histogram, on the diagonal. This Fig also shows the correlation between mean HIV reported cases and the various parameters, as well as their positive relationships.
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pone.0131950.g005: Pairs plot of the MCMC samples for the ten parameters.The pairs plot shows a strong relationship between parameters γ and ρ (the rate at which an individual will fully move from the A1(t) class to the A2(t) class and the disease-induced mortality rate for A2(t), respectively). This plot visualizes the pairwise relationship in the upper panel, the correlation coefficients in the lower panel, and the marginal distribution for each parameter, represented by a histogram, on the diagonal. This Fig also shows the correlation between mean HIV reported cases and the various parameters, as well as their positive relationships.

Mentions: In Fig 5, the pairs plot shows a strong relationship between parameters γ and ρ (the rate at which an individual will fully move from A1(t) class to A2(t) class and the disease-induced mortality rate for A2(t), respectively). This plot visualizes the pairwise relationship in the upper panel, the correlation coefficients in the lower panel, and the marginal distribution for each parameter, represented by a histogram, on the diagonal. This figure also shows the correlation between the mean HIV reported cases and the various parameters, as well as their positive relationships.


A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection.

Apenteng OO, Ismail NA - PLoS ONE (2015)

Pairs plot of the MCMC samples for the ten parameters.The pairs plot shows a strong relationship between parameters γ and ρ (the rate at which an individual will fully move from the A1(t) class to the A2(t) class and the disease-induced mortality rate for A2(t), respectively). This plot visualizes the pairwise relationship in the upper panel, the correlation coefficients in the lower panel, and the marginal distribution for each parameter, represented by a histogram, on the diagonal. This Fig also shows the correlation between mean HIV reported cases and the various parameters, as well as their positive relationships.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4493079&req=5

pone.0131950.g005: Pairs plot of the MCMC samples for the ten parameters.The pairs plot shows a strong relationship between parameters γ and ρ (the rate at which an individual will fully move from the A1(t) class to the A2(t) class and the disease-induced mortality rate for A2(t), respectively). This plot visualizes the pairwise relationship in the upper panel, the correlation coefficients in the lower panel, and the marginal distribution for each parameter, represented by a histogram, on the diagonal. This Fig also shows the correlation between mean HIV reported cases and the various parameters, as well as their positive relationships.
Mentions: In Fig 5, the pairs plot shows a strong relationship between parameters γ and ρ (the rate at which an individual will fully move from A1(t) class to A2(t) class and the disease-induced mortality rate for A2(t), respectively). This plot visualizes the pairwise relationship in the upper panel, the correlation coefficients in the lower panel, and the marginal distribution for each parameter, represented by a histogram, on the diagonal. This figure also shows the correlation between the mean HIV reported cases and the various parameters, as well as their positive relationships.

Bottom Line: The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic.The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS).Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Statistics, Faculty of Economics & Administration, University of Malaya, Kuala Lumpur, Malaysia.

ABSTRACT
The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 < 1, the disease dies out; and if R0 > 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS.

No MeSH data available.


Related in: MedlinePlus