Mathematical modelling of the impact of testing, treatment and control of HIV transmission in Kenya

Omondi, Evans Otieno; Mbogo, Rachel Waema; Luboobi, Livingstone S.

doi:10.1080/25742558.2018.1475590

Cited by 26 publications

(15 citation statements)

References 20 publications

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“…Duffin et al [ 4 ] studied the dynamics of the immune deficiency virus of the complete course of infection. Omondi et al [ 5 ] investigated the mathematical modeling of the impact of testing, treatment, and control of HIV transmission in Kenya. Wodarz et al [ 6 ] designed the pathogenesis and treatment compartment in the modeling of HIV.…”

Section: Literature Surveymentioning

confidence: 99%

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

et al. 2020

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In this manuscript, we investigate a nonlinear delayed model to study the dynamics of human-immunodeficiency-virus in the population. For analysis, we find the equilibria of a susceptible–infectious–immune system with a delay term. The well-established tools such as the Routh–Hurwitz criterion, Volterra–Lyapunov function, and Lasalle invariance principle are presented to investigate the stability of the model. The reproduction number and sensitivity of parameters are investigated. If the delay tactics are decreased, then the disease is endemic. On the other hand, if the delay tactics are increased then the disease is controlled in the population. The effect of the delay tactics with subpopulations is investigated. More precisely, all parameters are dependent on delay terms. In the end, to give the strength to a theoretical analysis of the model, a computer simulation is presented.

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Section: Literature Surveymentioning

confidence: 99%

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

et al. 2020

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“…We therefore conclude that the median theorem should be used only when there is no possibility of using the central limit theorem to estimate the population mean, since practically the sample mean gives better estimates than the median. Likewise, the sampling distribution of the median may behave differently for the non-normal distributions [6]. In cases where normality assumptions fail, the bootstrap estimation may be the best option for making inferences.…”

Section: Sampling Distribution Of the Medianmentioning

confidence: 99%

“…We used model (6) to estimate the most likely (median) age at which a woman under reproductive age could be infected using single sample data collected from the field. We let < be the random variable which shows the time to failure (age at which a woman is likely to be infected) and The computer layout for our datasets in a simple counting process (CP) format is shown in table 1.…”

Section: Estimation Of Age At Hiv Infection By Using Non-parametric Mmentioning

confidence: 99%

Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: <i>A Case Study of Tanzania</i>

Mkenda¹,

Nokoe²,

Karoki³

2019

AJTAS

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Estimation of HIV infection time is a crucial step in HIV/AIDS management as it can help to make informed decisions on the best intervention strategies for controlling new infections, and for taking care of the infected individuals. This study demonstrates three approaches for estimating the age at HIV infection in limited resource settings. Using HIV testing history data collected from a sample of 88 HIV positive women in Kilimanjaro region-Tanzania, we developed a model for estimating the most likely age at which HIV infection occurs for women under reproductive age. The sampled data were collected from typical poor resource settings where access to data is very challenging and the gap between last HIV negative test and first HIV positive test is wide. Formulation of the proposed model involved three steps. Through Modified Midpoint approach, we first determined the midpoint of the age at last negative HIV test and the age at first positive HIV test for each subject. Then, the average time at risk prior to infection, taken over all individuals was subtracted from each midpoint value to obtain the distribution of their estimated age at HIV infection (T). In the second step, survival analysis techniques were used to obtain the Kaplan Meier plots and Nelson Aalen cumulative hazards estimates in which the median age for HIV infection and the most risky age were estimated. The plots of Kaplan Meir survival curves for women with different marital status and levels of education helped to assess whether their age at infection were significantly different. In the third step, we used bootstrap estimation procedures to generate 200 samples of random data and obtain the bootstrap median age at HIV infection and its confidence intervals. The estimated median age at HIV infection from survival analysis approach was 28 years while from bootstrap estimation procedures was 27 years. Likewise, the Nelson Aalen cumulative hazards plot indicated that the most risky age for HIV infection is between 18-40 years while the most risky age from bootstrap estimation was 25 to 27 years. The confidence intervals obtained through bootstrap estimation approach was narrower than that obtained from the survival analysis approach, implying that the bootstrap approach gives more precise estimates. Generally, the study findings provide useful information towards the attainment of the 90-90-90 global HIV/AIDS target as it shows where to allocate more resources and establish more focused interventions for HIV/AIDS management and control.

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“…A unique EE existed whenever 0 > 1, it was locally and globally asymptotically stable whereas the DFE was unstable, and thus the model in consideration does not exhibit a backward bifurcation. Omondi et al (2018) presented a HIV-transmission model with five compartments to describe the trend of HIVinfection within different age groups in Kenya. The model analysis showed that the model has two equilibria, the infection free equilibrium and the endemic equilibrium that are both globally asymptotically stable when the threshold 0 < 1 and 0 > 1, respectively.…”

Section: Introduction 11 Background Of the Studymentioning

confidence: 99%

A Deterministic Model Of HIV Transmission Between Two Closed Patches Incorporating The Monod Equation

2019

MTM

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Among other factors, migration has significantly contributed to the spread of HIV. Recent studies have revealed that new infections occur along major transport corridors and truck-drivers have overall higher prevalence rates of HIV and sexually transmitted infections than non-truck drivers' counterparts. Therefore, there exist a link between population mobility and HIV infection, as populations along transport corridors remain substantial contributors of new infections. This research work documents a deterministic model of the dynamics of HIV transmission between two closed patches that incorporates the Monod equation in migration with truck drivers being the agents of HIV transmission. Migration is considered as a social determinant to health and have a significant impact on healthrelated vulnerabilities and access to services. We assumed that susceptible individuals become infected via sexual intercourse with HIV infected truck drivers and all the infected individuals ultimately developed AIDS exponentially. The model also assumed that the patches have different infection and susceptibility rates. The patches basic reproduction number, 0 was determined using the Next Generation Matrix. The results revealed that 0 should be kept below unity to eradicate the transmission of the virus. The Disease-Free Equilibrium Point was obtained based on the signs of the Eigen values of the Jacobian matrix. In the absence, the Disease-Free Equilibrium Point is both Locally Asymptotically and Globally Asymptotically Stable. It was further proved that the model did not display Endemic Equilibrium Point under a special property for epidemic models. The model findings are vital in guiding health practitioners, governmental and non-governmental health agencies in the development of effective mitigation strategies to reduce the spread of HIV.

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Mathematical modelling of the impact of testing, treatment and control of HIV transmission in Kenya

Cited by 26 publications

References 20 publications

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: <i>A Case Study of Tanzania</i>

A Deterministic Model Of HIV Transmission Between Two Closed Patches Incorporating The Monod Equation

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Mathematical modelling of the impact of testing, treatment and control of HIV transmission in Kenya

Cited by 26 publications

References 20 publications

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: &lt;i&gt;A Case Study of Tanzania&lt;/i&gt;

A Deterministic Model Of HIV Transmission Between Two Closed Patches Incorporating The Monod Equation

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Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: <i>A Case Study of Tanzania</i>