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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.


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Schematic representation of the SIA1A2 model.The flow chart of the SIA1A2 model.
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pone.0131950.g001: Schematic representation of the SIA1A2 model.The flow chart of the SIA1A2 model.

Mentions: We present the simplest HIV disease models where individuals classified as a sexually active population are divided into four classes: susceptible, S(t); infected, (HIV) I(t); pre-AIDS cases who did not progress to AIDS after HIV infection, A1(t); and AIDS cases who have AIDS after HIV infection at time t, A2(t). HIV can be transmitted to a susceptible person when they come into contact with an infected person via the appropriate transmission routes. In 2003, Rao [14] formulated a model for individuals who did or did not develop AIDS after the HIV epidemic in India. Unlike the model from this report [14], our model assumed that γ is the rate at which an individual will fully move from A1(t) class to A2(t) class, which is a very significant indicator of when an intervention should be introduced. We assumed that the infected individuals are capable of having children that are either infected with HIV or will not have HIV. However, the susceptible class has a recruitment rate equivalent to the birth rate, b, which is independent of vertical transmission. Moreover, this model assumes that infected newborn babies enter the HIV class at the rate of b(I + A1 + A2), for which we assume that I, A1, and A2 are sexually active, and πb(I + A1 + A2) are individuals who are infected and enter the HIV stage. The portion π of these individuals is assumed to be infected with HIV (categorized in the I class), and the complementary portion (1 − π)b(I + A1 + A2) is considered susceptible (and moves to the susceptible class S). The removal rate of infected HIV individuals who enter the AIDS class is represented by α; the portion of HIV-infected individuals is δ. This model also assumes that at rate δα, some of the HIV-infected cases transition to the AIDS group, whereas the remaining HIV-infected cases move to the class of individuals who do not develop AIDS (pre-AIDS) after an HIV infection rate of (1 − δ)α, where 0 ≤ δ ≤ 1. The model also assumes the natural death rate μ of individual deaths from all four compartments. β is the contact rate between susceptible individuals and exposed or HIV-infected individuals. AIDS patients are given an additional disease-induced mortality rate: σ > 0, ε > 0 and ρ > 0 for I(t), A1(t) and A2(t), respectively. This form of a susceptible–infected–pre-AIDS–AIDS (SIA1A2) model can be used to model HIV disease based upon the assumption that once an individual becomes infected, that individual remains infectious for life, as shown in Fig 1.


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

Apenteng OO, Ismail NA - PLoS ONE (2015)

Schematic representation of the SIA1A2 model.The flow chart of the SIA1A2 model.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0131950.g001: Schematic representation of the SIA1A2 model.The flow chart of the SIA1A2 model.
Mentions: We present the simplest HIV disease models where individuals classified as a sexually active population are divided into four classes: susceptible, S(t); infected, (HIV) I(t); pre-AIDS cases who did not progress to AIDS after HIV infection, A1(t); and AIDS cases who have AIDS after HIV infection at time t, A2(t). HIV can be transmitted to a susceptible person when they come into contact with an infected person via the appropriate transmission routes. In 2003, Rao [14] formulated a model for individuals who did or did not develop AIDS after the HIV epidemic in India. Unlike the model from this report [14], our model assumed that γ is the rate at which an individual will fully move from A1(t) class to A2(t) class, which is a very significant indicator of when an intervention should be introduced. We assumed that the infected individuals are capable of having children that are either infected with HIV or will not have HIV. However, the susceptible class has a recruitment rate equivalent to the birth rate, b, which is independent of vertical transmission. Moreover, this model assumes that infected newborn babies enter the HIV class at the rate of b(I + A1 + A2), for which we assume that I, A1, and A2 are sexually active, and πb(I + A1 + A2) are individuals who are infected and enter the HIV stage. The portion π of these individuals is assumed to be infected with HIV (categorized in the I class), and the complementary portion (1 − π)b(I + A1 + A2) is considered susceptible (and moves to the susceptible class S). The removal rate of infected HIV individuals who enter the AIDS class is represented by α; the portion of HIV-infected individuals is δ. This model also assumes that at rate δα, some of the HIV-infected cases transition to the AIDS group, whereas the remaining HIV-infected cases move to the class of individuals who do not develop AIDS (pre-AIDS) after an HIV infection rate of (1 − δ)α, where 0 ≤ δ ≤ 1. The model also assumes the natural death rate μ of individual deaths from all four compartments. β is the contact rate between susceptible individuals and exposed or HIV-infected individuals. AIDS patients are given an additional disease-induced mortality rate: σ > 0, ε > 0 and ρ > 0 for I(t), A1(t) and A2(t), respectively. This form of a susceptible–infected–pre-AIDS–AIDS (SIA1A2) model can be used to model HIV disease based upon the assumption that once an individual becomes infected, that individual remains infectious for life, as shown in Fig 1.

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