Impact of early treatment programs on HIV epidemics: An immunity-based mathematical model

Understanding HIV/AIDS dynamics: insights from CD4+T cells, antiretroviral treatment, and country-specific analysis

In this article, we present a mathematical model for human immunodeficiency virus (HIV)/Acquired immune deficiency syndrome (AIDS), taking into account the number of CD4+T cells and antiretroviral treatment. This model is developed based on the susceptible, infected, treated, AIDS (SITA) framework, wherein the infected and treated compartments are divided based on the number of CD4+T cells. Additionally, we consider the possibility of treatment failure, which can exacerbate the condition of the treated individual. Initially, we analyze a simplified HIV/AIDS model without differentiation between the infected and treated classes. Our findings reveal that the global stability of the HIV/AIDS-free equilibrium point is contingent upon the basic reproduction number being less than one. Furthermore, a bifurcation analysis demonstrates that our simplified model consistently exhibits a transcritical bifurcation at a reproduction number equal to one. In the complete model, we elucidate how the control reproduction number determines the stability of the HIV/AIDS-free equilibrium point. To align our model with the empirical data, we estimate its parameters using prevalence data from the top four countries affected by HIV/AIDS, namely, Eswatini, Lesotho, Botswana, and South Africa. We employ numerical simulations and conduct elasticity and sensitivity analyses to examine how our model parameters influence the control reproduction number and the dynamics of each model compartment. Our findings reveal that each country displays distinct sensitivities to the model parameters, implying the need for tailored strategies depending on the target country. Autonomous simulations highlight the potential of case detection and condom use in reducing HIV/AIDS prevalence. Furthermore, we identify that the quality of condoms plays a crucial role: with higher quality condoms, a smaller proportion of infected individuals need to use them for the potential eradication of HIV/AIDS from the population. In our optimal control simulations, we assess population behavior when control interventions are treated as time-dependent variables. Our analysis demonstrates that a combination of condom use and case detection, as time-dependent variables, can significantly curtail the spread of HIV while maintaining an optimal cost of intervention. Moreover, our cost-effectiveness analysis indicates that the condom use intervention alone emerges as the most cost-effective strategy, followed by a combination of case detection and condom use, and finally, case detection as a standalone strategy.

Modelling Botswana's HIV/AIDS response and treatment policy changes: Insights from a cascade of mathematical models

The management of HIV/AIDS has evolved ever since advent of the disease in the past three decades. Many countries have had to revise their policies as new information on the virus, and its transmission dynamics emerged. In this paper, we track the changes in Botswana's HIV/AIDS response and treatment policies using a piece-wise system of differential equations. The policy changes are easily tracked in three epochs. Models for each era are formulated from a "grand model" that can be linked to all the epochs. The grand model's steady states are determined and analysed in terms of the model reproduction number, $ R_{0}. $ The model exhibits a backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium when $ R_{0} < 1. $ The stability of the models for the other epochs can be derived from that of the grand model by setting some parameters to zero. The models are fitted to HIV/AIDS prevalence data from Botswana for the past three decades. The changes in the populations in each compartment are tracked as the response to the disease and treatment policy changed over time. Finally, projections are made to determine the possible trajectory of HIV/AIDS in Botswana. The implications of the policy changes are easily seen, and a discussion on how these changes impacted the epidemic are articulated. The results presented have crucial impact on how policy changes affected and continue to influence the trajectory of the HIV/AIDS epidemic in Botswana.

Efficient gradient-based parameter estimation for dynamic models using qualitative data

MOTIVATION

Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.

RESULTS

Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.

AVAILABILITY AND IMPLEMENTATION

The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Efficient gradient-based parameter estimation for dynamic models using qualitative data

Motivation

Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.

Results

Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.

Availability and implementation

The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

Supplementary information

Supplementary data are available at Bioinformatics online.

Nationwide Cohort Study of Antiretroviral Therapy Timing: Treatment Dropout and Virological Failure in China, 2011-2015

Background

People living with human immunodeficiency virus (PLWH) are still being diagnosed late, rendering the benefits of "early" antiretroviral therapy (ART) unattainable. Therefore, we aimed to evaluate the benefits of "immediate" ART.

Methods

A nationwide cohort of PLWH in China who initiated ART January 1, 2011, to December 31, 2014 and had baseline CD4 results >200 cells/μL were censored at 12 months, dropout, or death, whichever came first. Treatment dropout and virological failure (viral load ≥400 copies/mL) were measured. Determinants were assessed by Cox and log-binomial regression.

Results

The cohort included 123605 PLWH. The ≤30 days group had a significantly lower treatment dropout rate of 6.72%, compared to 8.91% for the 91-365 days group and to 12.64% for the >365 days group. The ≤30 days group also had a significantly lower virological failure rate of 5.45% (31-90 days: 7.39%; 91-365 days: 9.64%; >365 days: 12.67%). Greater risk of dropout (91-365 days: adjusted hazard ratio [aHR] = 1.33, 95% confidence interval [CI] = 1.25-1.42; >365 days: aHR = 1.55, CI = 1.47-1.54), and virological failure (31-90 days: adjusted risk ratio [aRR] = 1.35, CI = 1.26-1.45; 91-365 days: aRR = 1.66, CI = 1.55-1.78; >365 days: aRR = 1.85, CI = 1.74-1.97) were observed for those who delayed treatment.

Conclusions

ART within 30 days of HIV diagnosis was associated with significantly reduced risk of treatment failure, highlighting the need to implement test-and-immediately-treat policies.

Modelling epidemics with fractional-dose vaccination in response to limited vaccine supply

The control strategies of emergency infectious diseases are constrained by limited medical resources. The fractional dose vaccination strategy as one of feasible strategies was proposed in response to global shortages of vaccine stockpiles. Although a variety of epidemic models have been developed under the circumstances of limited resources in treatment, few models particularly investigated vaccination strategies in resource-limited settings. In this paper, we develop a two-group SIR model with incorporation of proportionate mixing patterns and n-fold fractional dose vaccination related parameters to evaluate the efficiency of fractional dose vaccination on disease control at the population level. The existence and uniqueness of the final size of the two-group SIR epidemic model, the formulation of the basic reproduction number and the relationship between them are established. Moreover, numerical simulations are performed based on this two-group vector-free model to investigate the effectiveness of n-fold fractional dose vaccination by using the emergency outbreaks of yellow fever in Angola in 2016. By employing linear and nonlinear dose-response relationships, we compare the resulting fluctuations of four characteristics of the epidemics, which are the outbreak size, the peak time of the outbreak, the basic reproduction number and the infection attack rate (IAR). For both types of dose-response relationships, dose-fractionation takes positive effects in lowering the outbreak size, delay the peak time of the outbreak, reducing the basic reproduction number and the IAR of yellow fever only when the vaccine efficacy is high enough. Moreover, five-fold fractional dose vaccination strategy may not be the optimal vaccination strategy as proposed by the World Health Organization if the dose-response relationship is nonlinear.

Duration of Human Immunodef iciency Virus Infection at Diagnosis among New Human Immunodef iciency Virus Cases in Dehong, Yunnan, China, 2008-2015

Background:

On diagnosis of human immunodeficiency virus (HIV) infection, a person may have been infected already for many years. This study aimed to estimate the duration of HIV infection at the time of diagnosis.

Methods:

Newly diagnosed HIV cases in Dehong, China, from 2008 to 2015 were studied. Duration of infection at the time of diagnosis was calculated using the first CD4 cell count result after diagnosis and a CD4 depletion model of disease progression. Multiple linear regression analysis was used to investigate the associated risk factors.

Results:

A total of 5867 new HIV cases were enrolled. Overall, mean duration of infection was 6.3 years (95% confidence interval [CI]: 6.2, 6.5). After adjusting for confounding, significantly shorter durations of infection were observed among participants who were female (beta: −0.37, 95% CI: −0.64, −0.09), Dai ethnicity (beta: −0.28, 95% CI: −0.57, 0.01), and infected through injecting drug use (beta: −1.82, 95% CI: −2.25, −1.39). Compared to the hospital setting, durations were shorter for those diagnosed in any other settings, and compared to 2008, durations were shorter for those diagnosed all years after 2010.

Results:

A total of 5867 new HIV cases were enrolled. Overall, mean duration of infection was 6.3 years (95% confidence interval [CI]: 6.2, 6.5). After adjusting for confounding, significantly shorter durations of infection were observed among participants who were female (beta: −0.37, 95% CI: −0.64, −0.09), Dai ethnicity (beta: −0.28, 95% CI: −0.57, 0.01), and infected through injecting drug use (beta: −1.82, 95% CI: −2.25, −1.39). Compared to the hospital setting, durations were shorter for those diagnosed in any other settings, and compared to 2008, durations were shorter for those diagnosed all years after 2010.

Conclusion:

Although the reduction in duration of infection at the time of diagnosis observed in Dehong was significant, it may not have had a meaningful impact.

Use of the AHP methodology in system dynamics: Modelling and simulation for health technology assessments to determine the correct prosthesis choice for hernia diseases

Health technology assessments (HTAs) are often difficult to conduct because of the decisive procedures of the HTA algorithm, which are often complex and not easy to apply. Thus, their use is not always convenient or possible for the assessment of technical requests requiring a multidisciplinary approach. This paper aims to address this issue through a multi-criteria analysis focusing on the analytic hierarchy process (AHP). This methodology allows the decision maker to analyse and evaluate different alternatives and monitor their impact on different actors during the decision-making process. However, the multi-criteria analysis is implemented through a simulation model to overcome the limitations of the AHP methodology. Simulations help decision-makers to make an appropriate decision and avoid unnecessary and costly attempts. Finally, a decision problem regarding the evaluation of two health technologies, namely, the evaluation of two biological prostheses for incisional infected hernias, will be analysed to assess the effectiveness of the model.