The epidemiological impact of antiretroviral use predicted by mathematical models: a review

This review summarises theoretical studies attempting to assess the population impact of antiretroviral therapy (ART) use on mortality and HIV incidence. We describe the key parameters that determine the impact of therapy, and argue that mathematical models of disease transmission are the natural framework within which to explore the interaction between antiviral use and the dynamics of an HIV epidemic. Our review focuses on the potential effects of ART in resource-poor settings. We discuss choice of model type and structure, the potential for risk behaviour change following widespread introduction of ART, the importance of the stage of HIV infection at which treatment is initiated, and the potential for spread of drug resistance. These issues are illustrated with results from models of HIV transmission. We demonstrate that HIV transmission models predicting the impact of ART use should incorporate a realistic progression through stages of HIV infection in order to capture the effect of the timing of treatment initiation on disease spread. The realism of existing models falls short of properly reproducing patterns of diagnosis timing, incorporating heterogeneity in sexual behaviour, and describing the evolution and transmission of drug resistance. The uncertainty surrounding certain effects of ART, such as changes in sexual behaviour and transmission of ART-resistant HIV strains, demands exploration of best and worst case scenarios in modelling, but this must be complemented by surveillance and behavioural surveys to quantify such effects in settings where ART is implemented

Modelling the impact of antiretroviral use in resource-poor settings.

BACKGROUND: The anticipated scale-up of antiretroviral therapy (ART) in high-prevalence, resource-constrained settings requires operational research to guide policy on the design of treatment programmes. Mathematical models can explore the potential impacts of various treatment strategies, including timing of treatment initiation and provision of laboratory monitoring facilities, to complement evidence from pilot programmes. METHODS AND FINDINGS: A deterministic model of HIV transmission incorporating ART and stratifying infection progression into stages was constructed. The impact of ART was evaluated for various scenarios and treatment strategies, with different levels of coverage, patient eligibility, and other parameter values. These strategies included the provision of laboratory facilities that perform CD4 counts and viral load testing, and the timing of the stage of infection at which treatment is initiated. In our analysis, unlimited ART provision initiated at late-stage infection (AIDS) increased prevalence of HIV infection. The effect of additionally treating pre-AIDS patients depended on the behaviour change of treated patients. Different coverage levels for ART do not affect benefits such as life-years gained per person-year of treatment and have minimal effect on infections averted when treating AIDS patients only. Scaling up treatment of pre-AIDS patients resulted in more infections being averted per person-year of treatment, but the absolute number of infections averted remained small. As coverage increased in the models, the emergence and risk of spread of drug resistance increased. Withdrawal of failing treatment (clinical resurgence of symptoms), immunologic (CD4 count decline), or virologic failure (viral rebound) increased the number of infected individuals who could benefit from ART, but effectiveness per person is compromised. Only withdrawal at a very early stage of treatment failure, soon after viral rebound, would have a substantial impact on emergence of drug resistance. CONCLUSIONS: Our analysis found that ART cannot be seen as a direct transmission prevention measure, regardless of the degree of coverage. Counselling of patients to promote safe sexual practices is essential and must aim to effect long-term change. The chief aims of an ART programme, such as maximised number of patients treated or optimised treatment per patient, will determine which treatment strategy is most effective

Cytokinin Accumulation and an Altered Ethylene Response Mediate the Pleiotropic Phenotype of the Pea Nodulation Mutant R50 (\u3cem\u3esym16\u3c/em\u3e)

R50 (sym16), a pleiotropic mutant of Pisum sativum L., is short, has thickened internodes and roots, and has a reduced number of lateral roots and nodules. Its low nodule phenotype can be restored with the application of ethylene inhibitors; furthermore, it can be mimicked by applying cytokinins (CKs) to the roots of the parent line #8216;Sparkle’. Here, we report on the etiolation phenotypes of R50 and ‘Sparkle’, and on the interactive roles of ethylene and CKs in these lines. R50 displayed an altered etiolation phenotype, as it was shorter and thicker, and had more developed leaves than dark-grown ‘Sparkle’. Shoot morphological differences induced by exogenous ethylene or CKs were found to be less severe for R50. Ethylene inhibitor application induced root and shoot elongation and encouraged apical hook opening in both etiolated lines. Liquid chromatography–tandem mass spectrometry analysis indicated that CK concentrations in R50 were higher than in ‘Sparkle’, particularly in mature shoots where the levels were maintained at elevated concentrations. These differences indicate a reduction in the CK catabolism of R50. The accumulation of CKs can be directly related to several traits of R50, with the reduced number of nodules and altered shoot ethylene response being likely indirect effects

Spatial dynamics of the 1918 influenza pandemic in England, Wales and the United States

There is still limited understanding of key determinants of spatial spread of influenza. The 1918 pandemic provides an opportunity to elucidate spatial determinants of spread on a large scale

Antigen-driven T-cell turnover.

A mathematical model is developed to characterize the distribution of cell turnover rates within a population of T lymphocytes. Previous models of T-cell dynamics have assumed a constant uniform turnover rate; here we consider turnover in a cell pool subject to clonal proliferation in response to diverse and repeated antigenic stimulation. A basic framework is defined for T-cell proliferation in response to antigen, which explicitly describes the cell cycle during antigenic stimulation and subsequent cell division. The distribution of T-cell turnover rates is then calculated based on the history of random exposures to antigens. This distribution is found to be bimodal, with peaks in cell frequencies in the slow turnover (quiescent) and rapid turnover (activated) states. This distribution can be used to calculate the overall turnover for the cell pool, as well as individual contributions to turnover from quiescent and activated cells. The impact of heterogeneous turnover on the dynamics of CD4(+) T-cell infection by HIV is explored. We show that our model can resolve the paradox of high levels of viral replication occurring while only a small fraction of cells are infected

Optimal Timing and Duration of Induction Therapy for HIV-1 Infection

The tradeoff between the need to suppress drug-resistant viruses and the problem of treatment toxicity has led to the development of various drug-sparing HIV-1 treatment strategies. Here we use a stochastic simulation model for viral dynamics to investigate how the timing and duration of the induction phase of induction–maintenance therapies might be optimized. Our model suggests that under a variety of biologically plausible conditions, 6–10 mo of induction therapy are needed to achieve durable suppression and maximize the probability of eradicating viruses resistant to the maintenance regimen. For induction regimens of more limited duration, a delayed-induction or -intensification period initiated sometime after the start of maintenance therapy appears to be optimal. The optimal delay length depends on the fitness of resistant viruses and the rate at which target-cell populations recover after therapy is initiated. These observations have implications for both the timing and the kinds of drugs selected for induction–maintenance and therapy-intensification strategies

Eigenvalue sensitivity minimisation for robust pole placement by the receptance method

The problem of robust pole placement in active structural vibration control by the method of receptance is considered in this paper. Expressions are derived for the eigenvalue sensitivities to parametric perturbations, which are subsequently minimised to improve performance robustness of the control of a dynamical system. The described approach has application to a vibrating system where variations are present due to manufacturing and material tolerances, damages and environment variabilities. The closed-loop eigenvalue sensitivities are expressed as a linear function of the velocity and displacement feedback gains, allowing their minimisation with carefully calculated feedback gains. The proposed algorithm involves curve fitting perturbed frequency response functions, FRFs, using the rational fraction polynomial method and implementation of a polynomial fit to the individual estimated rational fraction coefficients. This allows the eigenvalue sensitivity to be obtained entirely from structural FRFs, which is consistent with the receptance method. This avoids the need to evaluate the M,C,K matrices which are typically obtained through finite element modelling, that produces modelling uncertainty. It is also demonstrated that the sensitivity minimisation technique can work in conjunction with the pole placement and partial pole placement technique using the receptance method. To illustrate the working of the proposed algorithm, the controller is first implemented numerically and then experimentally

Hyperinfectivity: A Critical Element in the Ability of V. cholerae to Cause Epidemics?

BACKGROUND: Cholera is an ancient disease that continues to cause epidemic and pandemic disease despite ongoing efforts to limit its spread. Mathematical models provide one means of assessing the utility of various proposed interventions. However, cholera models that have been developed to date have had limitations, suggesting that there are basic elements of cholera transmission that we still do not understand. METHODS AND FINDINGS: Recent laboratory findings suggest that passage of Vibrio cholerae O1 Inaba El Tor through the gastrointestinal tract results in a short-lived, hyperinfectious state of the organism that decays in a matter of hours into a state of lower infectiousness. Incorporation of this hyperinfectious state into our disease model provides a much better fit with the observed epidemic pattern of cholera. These findings help to substantiate the clinical relevance of laboratory observations regarding the hyperinfectious state, and underscore the critical importance of human-to-human versus environment-to-human transmission in the generation of epidemic and pandemic disease. CONCLUSIONS: To have maximal impact on limiting epidemic spread of cholera, interventions should be targeted toward minimizing risk of transmission of the short-lived, hyperinfectious form of toxigenic Vibrio cholerae. The possibility of comparable hyperinfectious states in other major epidemic diseases also needs to be evaluated and, as appropriate, incorporated into models of disease prevention

Inferring pandemic growth rates from sequence data

Using sequence data to infer population dynamics is playing an increasing role in the analysis of outbreaks. The most common methods in use, based on coalescent inference, have been widely used but not extensively tested against simulated epidemics. Here, we use simulated data to test the ability of both parametric and non-parametric methods for inference of effective population size (coded in the popular BEAST package) to reconstruct epidemic dynamics. We consider a range of simulations centred on scenarios considered plausible for pandemic influenza, but our conclusions are generic for any exponentially growing epidemic. We highlight systematic biases in non-parametric effective population size estimation. The most prominent such bias leads to the false inference of slowing of epidemic spread in the recent past even when the real epidemic is growing exponentially. We suggest some sampling strategies that could reduce (but not eliminate) some of the biases. Parametric methods can correct for these biases if the infected population size is large. We also explore how some poor sampling strategies (e.g. that over-represent epidemiologically linked clusters of cases) could dramatically exacerbate bias in an uncontrolled manner. Finally, we present a simple diagnostic indicator, based on coalescent density and which can easily be applied to reconstructed phylogenies, that identifies time-periods for which effective population size estimates are less likely to be biased. We illustrate this with an application to the 2009 H1N1 pandemic

The interaction of transmission intensity, mortality, and the economy: a retrospective analysis of the COVID-19 pandemic

The COVID-19 pandemic has caused over 6.4 million registered deaths to date, and has had a profound impact on economic activity. Here, we study the interaction of transmission, mortality, and the economy during the SARS-CoV-2 pandemic from January 2020 to December 2022 across 25 European countries. We adopt a Bayesian vector autoregressive model with both fixed and random effects. We find that increases in disease transmission intensity decreases Gross domestic product (GDP) and increases daily excess deaths, with a longer lasting impact on excess deaths in comparison to GDP, which recovers more rapidly. Broadly, our results reinforce the intuitive phenomenon that significant economic activity arises from diverse person-to-person interactions. We report on the effectiveness of non-pharmaceutical interventions (NPIs) on transmission intensity, excess deaths and changes in GDP, and resulting implications for policy makers. Our results highlight a complex cost-benefit trade off from individual NPIs. For example, banning international travel increases GDP however reduces excess deaths. We consider country random effects and their associations with excess changes in GDP and excess deaths. For example, more developed countries in Europe typically had more cautious approaches to the COVID-19 pandemic, prioritising healthcare and excess deaths over economic performance. Long term economic impairments are not fully captured by our model, as well as long term disease effects (Long Covid). Our results highlight that the impact of disease on a country is complex and multifaceted, and simple heuristic conclusions to extract the best outcome from the economy and disease burden are challenging