An HIV epidemic model based on viral load dynamics: value in assessing empirical trends in HIV virulence and community viral load

Reactive-diffusion epidemic model on human mobility networks: Analysis and applications to COVID-19 in China

The complex dynamics of human mobility, combined with sporadic cases of local outbreaks, make assessing the impact of large-scale social distancing on COVID-19 propagation in China a challenge. In this paper, with the travel big dataset supported by Baidu migration platform, we develop a reactive-diffusion epidemic model on human mobility networks to characterize the spatio-temporal propagation of COVID-19, and a novel time-dependent function is incorporated into the model to describe the effects of human intervention. By applying the system control theory, we discuss both constant and time-varying threshold behavior of proposed model. In the context of population mobility-mediated epidemics in China, we explore the transmission patterns of COVID-19 in city clusters. The results suggest that human intervention significantly inhibits the high correlation between population mobility and infection cases. Furthermore, by simulating different population flow scenarios, we reveal spatial diffusion phenomenon of cases from cities with high infection density to cities with low infection density. Finally, our model exhibits acceptable prediction performance using actual case data. The localized analytical results verify the ability of the PDE model to correctly describe the epidemic propagation and provide new insights for controlling the spread of COVID-19.

Virologic Outcomes Among People Living With Human Immunodeficiency Virus With High Pretherapy Viral Load Burden Initiating on Common Core Agents

Background

People living with human immunodeficiency virus (PLWH) initiating antiretroviral therapy (ART) with viral loads (VLs) ≥100 000 copies/mL are less likely to achieve virologic success, but few studies have characterized real-world treatment outcomes.

Methods

ART-naive PLWH with VLs ≥100 000 copies/mL initiating dolutegravir (DTG), elvitegravir (EVG), raltegravir (RAL), or darunavir (DRV) between 12 August 2013 and 31 July 2017 were identified from the OPERA database. Virologic failure was defined as (i) 2 consecutive VLs ≥200 copies/mL after 36 weeks of ART; (ii) 1 VL ≥200 copies/mL with core agent discontinuation after 36 weeks; (iii) 2 consecutive VLs ≥200 copies/mL after suppression (≤50 copies/mL) before 36 weeks; or (iv) 1 VL ≥200 copies/mL with discontinuation after suppression before 36 weeks. Cox modeling estimated the association between regimen and virologic failure.

Results

There were 2038 ART-naive patients with high VL who initiated DTG (36%), EVG (46%), DRV (16%), or RAL (2%). Median follow-up was 18.1 (interquartile range, 12.4–28.9) months. EVG and DTG initiators were similar at baseline, but RAL initiators were older and more likely to be female with low CD4 cell counts while DRV initiators differed notably on factors associated with treatment failure. Virologic failure was experienced by 9.2% DTG, 13.2% EVG, 18.4% RAL, and 18.8% DRV initiators. Compared to DTG, the adjusted hazard ratio (95% confidence interval) was 1.46 (1.05–2.03) for EVG, 2.24 (1.50–3.34) for DRV, and 4.13 (1.85–9.24) for RAL.

Conclusions

ART-naive PLWH with high VLs initiating on DTG were significantly less likely to experience virologic failure compared to EVG, RAL, and DRV initiators.

Antiretroviral therapy-naïve people living with HIV (PLWH) initiating therapy with viral loads ≥100,000 copies/mL varied markedly at baseline. In adjusted models, PLWH initiating dolutegravir-based regimens were less likely to experience virologic failure as compared to elvitegravir, raltegravir and darunavir initiators.

Influence of sexual risk behaviour and STI co-infection dynamics on the evolution of HIV set point viral load in MSM

HIV viral load (VL) is an important predictor of HIV progression and transmission. Anti-retroviral therapy (ART) has been reported to reduce HIV transmission by lowering VL. However, apart from this beneficial effect, increased levels of population mean set-point viral load (SPVL), an estimator for HIV virulence, have been observed in men who have sex with men (MSM) in the decade following the introduction of ART in The Netherlands. Several studies have been devoted to explain these counter-intuitive trends in SPVL. However, to our knowledge, none of these studies has investigated an explanation in which it arises as the result of a sexually transmitted infection (STI) co-factor in detail. In this study, we adapted an event-based, individual-based model to investigate how STI co-infection and sexual risk behaviour affect the evolution of HIV SPVL in MSM before and after the introduction of ART. The results suggest that sexual risk behaviour has an effect on SPVL and indicate that more data are needed to test the effect of STI co-factors on SPVL. Furthermore, the observed trends in SPVL cannot be explained by sexual risk behaviour and STI co-factors only. We recommend to develop mathematical models including also factors related to viral evolution as reported earlier in the literature. However, this requires more complex models, and the collection of more data for parameter estimation than what is currently available.

Effects of a peer educator program for HIV status disclosure and health system strengthening: Findings from a clinic-based disclosure support program in Mozambique

BACKGROUND

In Mozambique, HIV counseling and testing (HCT) rates are low and the cascade (or continuum) of care is poor. Perhaps more importantly, low disclosure rates and low uptake of joint testing are also related to both (1) limitations on access to services and (2) the availability of trained staff. We describe the implementation and impact of a disclosure support implemented by peer educators (PE).

METHODS

Ten PEs, previously trained in basic HIV and post-test counseling, completed additional training on providing disclosure support for newly-diagnosed persons living with HIV (PLH).

RESULTS

Of the 6,092 persons who received HCT, 677 (11.1%) tested positive. Any newly-diagnosed PLH who was tested when PEs were present (606 / 677) was approached about participating in the disclosure program; of these, 94.2% of PLH (n = 574) agreed to participate. Of these, at follow-up (between 1 day and 3 months later, depending on client inclination and availability) 91.9% (n = 528) said that they had disclosed their HIV infection, of whom 66.9% (n = 384) were female and 24.1% (n = 144) male. In turn, 92.7% of partners (n = 508) who had received HIV-related exposure information were tested; of these, 78.7% (n = 400) were found to be HIV-positive. Of the latter, 96.3% (n = 385) were then seen by health care providers and referred for further diagnosis and treatment.

CONCLUSIONS

Supporting newly-diagnosed PLH is important both for their own health and that of others. For the newly-diagnosed, there are extensive challenges related to understanding the implications of their illness; social support from clinical care teams can be vital in planning and coping. Our study has shown that such support of PLH is also crucial to disclosure, in part via improving awareness of positive health implications for (and from) family, friends and other support networks.

Modelling immune deterioration, immune recovery and state-specific duration of HIV-infected women with viral load adjustment: using parametric multistate model

BACKGROUND

CD4 cell and viral load count are highly correlated surrogate markers of human immunodeficiency virus (HIV) disease progression. In modelling the progression of HIV, previous studies mostly dealt with either CD4 cell counts or viral load alone. In this work, both biomarkers are in included one model, in order to study possible factors that affect the intensities of immune deterioration, immune recovery and state-specific duration of HIV-infected women.

METHODS

The data is from an ongoing prospective cohort study conducted among antiretroviral treatment (ART) naïve HIV-infected women in the province of KwaZulu-Natal, South Africa. Participants were enrolled in the acute HIV infection phase, then followed-up during chronic infection up to ART initiation. Full-parametric and semi-parametric Markov models were applied. Furthermore, the effect of the inclusion and exclusion viral load in the model was assessed.

RESULTS

Inclusion of a viral load component improves the efficiency of the model. The analysis results showed that patients who reported a stable sexual partner, having a higher educational level, higher physical health score and having a high mononuclear component score are more likely to spend more time in a good HIV state (particularly normal disease state). Patients with TB co-infection, with anemia, having a high liver abnormality score and patients who reported many sexual partners, had a significant increase in the intensities of immunological deterioration transitions. On the other hand, having high weight, higher education level, higher quality of life score, having high RBC parameters, high granulocyte component scores and high mononuclear component scores, significantly increased the intensities of immunological recovery transitions.

CONCLUSION

Inclusion of both CD4 cell count based disease progression states and viral load, in the time-homogeneous Markov model, assisted in modeling the complete disease progression of HIV/AIDS. Higher quality of life (QoL) domain scores, good clinical characteristics, stable sexual partner and higher educational level were found to be predictive factors for transition and length of stay in sequential adversity of HIV/AIDS.

Evolution of the Envelope Glycoprotein of HIV-1 Clade B toward Higher Infectious Properties over the Course of the Epidemic

We showed previously that during the HIV/AIDS epidemic, the envelope glycoprotein (Env) of HIV-1, and in particular, the gp120 subunit, evolved toward an increased resistance to neutralizing antibodies at a population level. Here, we considered whether the antigenic evolution of the HIV-1 Env is associated with modifications of its functional properties, focusing on cell entry efficacy and interactions with the receptor and coreceptors. We tested the infectivity of a panel of Env-pseudotyped viruses derived from patients infected by subtype B viruses at three periods of the epidemic (1987 to 1991, 1996 to 2000, and 2006 to 2010). Pseudotyped viruses harboring Env from patients infected during the most recent period were approximately 10-fold more infectious in cell culture than those from patients infected at the beginning of the epidemic. This was associated with faster viral entry kinetics: contemporary viruses entered target cells approximately twice as fast as historical viruses. Contemporary viruses were also twice as resistant as historical viruses to the fusion inhibitor enfuvirtide. Resistance to enfuvirtide correlated with a resistance to CCR5 antagonists, suggesting that contemporary viruses expanded their CCR5 usage efficiency. Viruses were equally captured by DC-SIGN, but after binding to DC-SIGN, contemporary viruses infected target cells more efficiently than historical viruses. Thus, we report evidence that the infectious properties of the envelope glycoprotein of HIV-1 increased during the course of the epidemic. It is plausible that these changes affected viral fitness during the transmission process and might have contributed to an increasing virulence of HIV-1.IMPORTANCE Following primary infection by HIV-1, neutralizing antibodies (NAbs) exert selective pressure on the HIV-1 envelope glycoprotein (Env), driving the evolution of the viral population. Previous studies suggested that, as a consequence, Env has evolved at the HIV species level since the start of the epidemic so as to display greater resistance to NAbs. Here, we investigated whether the antigenic evolution of the HIV-1 Env is associated with modifications of its functional properties, focusing on cell entry efficacy and interactions with the receptor and coreceptors. Our data provide evidence that the infectious properties of the HIV-1 Env increased during the course of the epidemic. These changes may have contributed to increasing virulence of HIV-1 and an optimization of transmission between individuals.

Modelling the dynamics of population viral load measures under HIV treatment as prevention

In 2011 the Centers for Disease Control and Prevention (CDC) published guidelines for the use of population viral load (PVL), community viral load (CVL) and monitored viral load (MVL), defined as the average viral load (VL) of all HIV infected individuals in a population, of all diagnosed individuals, and of all individuals on antiretroviral treatment (ART), respectively. Since then, CVL has been used to assess the effectiveness of ART on HIV transmission and as a proxy for HIV incidence. The first objective of this study was to investigate how aggregate VL measures change with the HIV epidemic phase and the drivers behind these changes using a mathematical transmission model. Secondly, we aimed to give some insight into how well CVL correlates with HIV incidence during the course of the epidemic and roll out of ART. We developed a compartmental model for disease progression and HIV transmission with disease stages that differ in viral loads for epidemiological scenarios relevant to a concentrated epidemic in a population of men who have sex with men (MSM) in Western Europe (WE) and to a generalized epidemic in a heterosexual population in Sub-Saharan Africa (SSA). The model predicts that PVL and CVL change with the epidemic phase, while MVL stays constant. These dynamics are linked to the dynamics of infected subgroups (undiagnosed, diagnosed untreated and treated) in different disease stages (primary, chronic and AIDS). In particular, CVL decreases through all epidemic stages: before ART, since chronic population builds up faster than AIDS population and after ART, due to the build-up of treated population with low VL. The trends in CVL and incidence can be both opposing and coinciding depending on the epidemic phase. Before ART is scaled up to sufficiently high levels, incidence increases while CVL decreases. After this point, CVL is a useful indicator of changes in HIV incidence. The model predicts that during the ART scale-up HIV transmission is driven by undiagnosed and diagnosed untreated individuals, and that new infections decline due to the increase in the number of treated. Although CVL is not able to capture the contribution of undiagnosed population to HIV transmission, it declines due to the increase of people on ART too. In the scenarios described by our model, the present epidemic phase corresponds to declining trends in CVL and incidence.

Relational concurrency, stages of infection, and the evolution of HIV set point viral load

HIV viral load (VL) predicts both transmission potential and rate of disease progression. For reasons that are still not fully understood, the set point viral load (SPVL) established after acute infection varies across individuals and populations. Previous studies have suggested that population mean SPVL (MSPVL) has evolved near an optimum that reflects a trade-off between transmissibility and host survival. Sexual network structures affect rates of potential exposure during different within-host phases of infection marked by different transmission probabilities, and thus affect the number and timing of transmission events. These structures include relational concurrency, which has been argued to explain key differences in HIV burden across populations. We hypothesize that concurrency will alter the fitness landscape for SPVL in ways that differ from other network features whose impacts accrue at other times during infection. To quantitatively test this hypothesis, we developed a dynamic, stochastic, data-driven network model of HIV transmission, and evolution to assess the impact of key sexual network phenomena on MSPVL evolution. Experiments were repeated in sensitivity runs that made different assumptions about transmissibility during acute infection, SPVL heritability, and the functional form of the relationship between VL and transmissibility. For our main transmission model, scenarios yielded MSPVLs ranging from 4.4 to 4.75 log10 copies/ml, covering much of the observed empirical range. MSPVL evolved to be higher in populations with high concurrency and shorter relational durations, with values varying over a clinically significant range. In linear regression analyses on these and other predictors, main effects were significant (P < 0.05), as were interaction terms, indicating that effects are interdependent. We also noted a strong correlation between two key emergent properties measured at the end of the simulations-MSPVL and HIV prevalence-most clearly for phenomena that affect transmission networks early in infection. Controlling for prevalence, high concurrency yielded higher MSPVL than other network phenomena. Interestingly, we observed lower prevalence in runs in which SPVL heritability was zero, indicating the potential for viral evolution to exacerbate disease burden over time. Future efforts to understand empirical variation in MSPVL should consider local HIV burden and basic sexual behavioral and network structure.

Reduction in HIV community viral loads following the implementation of a "Treatment as Prevention" strategy over 2 years at a population-level among men who have sex with men in Hangzhou, China

Background

Previous studies have shown that the increased coverage of antiretroviral therapy (ART) could reduce the community viral load (CVL) and reduce the occurrence of new HIV infections. However, the impact on the reduction of HIV transmission among men who have sex with men (MSM) is much less certain. The frequency of HIV infections in MSM have been rapidly increasing in recent years in Hangzhou, China. The “Treatment as Prevention” strategy was implemented at a population-level for HIV-infected MSM from January 2014 to June 2016 in Hangzhou; it aimed to increase the ART coverage, reduce the CVL, and reduce HIV transmission.

Methods

We investigated a subset of MSM diagnosed with HIV pre- and post-implementation of the strategy, using random sampling methods. Viral load (VL) testing was performed for all enrolled individuals; the lower limits of detection were 20 and 50 copies/mL. The data on infections were collected from the national epidemiology database of Hangzhou. Logistic regression analyses were conducted to identify factors associated with the differences in social demographic characteristics and available VL data.

Results

The ART coverage increased from 60.7% (839/1383) during the pre-implementation period to 92.3% (2183/2365) during the post-implementation period in Hangzhou. A total of 940 HIV-infected MSM were selected for inclusion in this study: 490 (52.1%) and 450 (47.9%) MSM in the pre- and post-implementation periods, respectively. In total, 89.5% (841/940) of patients had data available on VL rates. The mean CVL was 579 copies/mL pre-implementation and this decreased to 33 copies/mL post-implementation (Kruskal-Wallis < 0.001). The mean CVL decreased for all variables investigated post-implementation of the treatment strategy (P < 0.05). The undetectable VL (≤400 copies/mL) rate pre-implementation period was 50.0% which increased to 84.7% post-implementation (P < 0.001). The mean CVL at the county level significantly decreased in each county post-implementation (Kruskal-Wallis < 0.05).

Conclusion

Our study confirmed a population-level association between increased ART coverage and decreased mean CVL; overall 84.7% of HIV infected MSM had an undetectable VL and were no longer infectious.

Modeling HIV disease progression and transmission at population-level: The potential impact of modifying disease progression in HIV treatment programs

INTRODUCTION

Mathematical models that incorporate HIV disease progression dynamics can estimate the potential impact of strategies that delay HIV disease progression and reduce infectiousness for persons not on antiretroviral therapy (ART). Suppressive treatment of HIV-positive persons co-infected with herpes simplex virus-2 (HSV-2) with valacyclovir, an HSV-2 antiviral, can lower HIV viral load, but the impact of partially-suppressive valacyclovir relative to fully-suppressive ART on population HIV transmission has not been estimated.

METHODS

We modeled HIV disease progression as a function of changes in viral load and CD4 count over time among ART naïve persons. The disease progression Markov model was nested within a dynamic model of HIV transmission at population level. We assumed that valacyclovir reduced HIV viral load by 1.23 log copies/μL, and that persons treated with valacyclovir initiated ART more rapidly when their CD4 fell below 500 due to retention in HIV care. We estimated the potential impact of valacyclovir on onward transmission of HIV in three scenarios of different ART and valacyclovir population coverage.

RESULTS

The average duration of HIV infection was 9.5 years. The duration of disease before reaching CD4 200cells/μL was 2.53 years longer for females than males. Relative to a baseline of ART initiation at CD4≤500cells/μL, the valacyclovir scenario resulted in 167,000 fewer HIV infections over ten years, with an incremental cost-effectiveness ratio (ICER) of $5276 per HIV infection averted. A Test and Treat scenario with 70% ART coverage and no valacyclovir resulted in 350,000 fewer HIV infections at an ICER of $2822 and $812 per HIV infection averted and QALY gained, respectively.

CONCLUSION

Even when compared with valacyclovir suppression, a drug that reduces HIV viral load, universal treatment for HIV is the optimal strategy for averting new infections and increasing public health benefit. Universal HIV treatment would most effectively and efficiently reduce the HIV burden.

Estimating the impact of antiretroviral treatment on adult mortality trends in South Africa: A mathematical modelling study

BACKGROUND

Substantial reductions in adult mortality have been observed in South Africa since the mid-2000s, but there has been no formal evaluation of how much of this decline is attributable to the scale-up of antiretroviral treatment (ART), as previous models have not been calibrated to vital registration data. We developed a deterministic mathematical model to simulate the mortality trends that would have been expected in the absence of ART, and with earlier introduction of ART.

METHODS AND FINDINGS

Model estimates of mortality rates in ART patients were obtained from the International Epidemiology Databases to Evaluate AIDS-Southern Africa (IeDEA-SA) collaboration. The model was calibrated to HIV prevalence data (1997-2013) and mortality data from the South African vital registration system (1997-2014), using a Bayesian approach. In the 1985-2014 period, 2.70 million adult HIV-related deaths occurred in South Africa. Adult HIV deaths peaked at 231,000 per annum in 2006 and declined to 95,000 in 2014, a reduction of 74.7% (95% CI: 73.3%-76.1%) compared to the scenario without ART. However, HIV mortality in 2014 was estimated to be 69% (95% CI: 46%-97%) higher in 2014 (161,000) if the model was calibrated only to HIV prevalence data. In the 2000-2014 period, the South African ART programme is estimated to have reduced the cumulative number of HIV deaths in adults by 1.72 million (95% CI: 1.58 million-1.84 million) and to have saved 6.15 million life years in adults (95% CI: 5.52 million-6.69 million). This compares with a potential saving of 8.80 million (95% CI: 7.90 million-9.59 million) life years that might have been achieved if South Africa had moved swiftly to implement WHO guidelines (2004-2013) and had achieved high levels of ART uptake in HIV-diagnosed individuals from 2004 onwards. The model is limited by its reliance on all-cause mortality data, given the lack of reliable cause-of-death reporting, and also does not allow for changes over time in tuberculosis control programmes and ART effectiveness.

CONCLUSIONS

ART has had a dramatic impact on adult mortality in South Africa, but delays in the rollout of ART, especially in the early stages of the ART programme, have contributed to substantial loss of life. This is the first study to our knowledge to calibrate a model of ART impact to population-level recorded death data in Africa; models that are not calibrated to population-level death data may overestimate HIV-related mortality.

Comparing viral load metrics and evaluating their use for HIV surveillance

OBJECTIVES

To investigate the value of in-care viral load (ICVL) and other viral load (VL) metrics for HIV surveillance by comparing time trends and associations with numbers of new HIV diagnoses.

METHODS

Data from 20,740 HIV patients registered in the Dutch ATHENA-cohort between 2002 and 2013 were used. We compared: six ICVL metrics (i.e. mean of the mean/first/last/highest log VL, median of the median log VL, first log VL for newly diagnosed combined with mean log VL for all others), log VL at diagnosis, proportion of patients with transmission risk (>400 copies/ml) or suppressed VL (≤200 copies/ml). Subgroup differences were assessed using Kruskal-Wallis and chi-square tests. Negative binomial regression was used for studying associations between VL metrics and numbers of new diagnoses 1-4 years later.

RESULTS

Most ICVL metrics showed similar decreasing trends over time. Differences in covariables were found for all VL metrics. Mean ICVL showed the strongest association with new diagnoses: a decrease of one log unit in mean ICVL was associated with a 21% decrease in new diagnoses two years later.

CONCLUSIONS

VL metrics may be of value for enhancing HIV surveillance by identifying subgroup differences in impact of treatment on viral suppression, and by predicting numbers of new diagnoses in subsequent years.

Racial/Ethnic Disparities at the End of an HIV Epidemic: Persons Who Inject Drugs in New York City, 2011-2015

OBJECTIVES

To examine whether racial/ethnic disparities persist at the "end of the HIV epidemic" (prevalence of untreated HIV infection < 5%; HIV incidence < 0.5 per 100 person-years) among persons who inject drugs (PWID) in New York City.

METHODS

We recruited 2404 PWID entering New York City substance use treatment in 2001 to 2005 and 2011 to 2015. We conducted a structured interview, and testing for HIV and herpes simplex virus 2 (HSV-2; a biomarker for high sexual risk). We estimated incidence by using newly diagnosed cases of HIV. Disparity analyses compared HIV, untreated HIV, HIV-HSV-2 coinfection, HIV monoinfection, and estimated HIV incidence among Whites, African Americans, and Latinos.

RESULTS

By 2011 to 2015, Whites, African Americans, and Latino/as met both criteria of our operational "end-of-the-epidemic" definition. All comparisons that included HIV-HSV-2-coinfected persons had statistically significant higher rates of HIV among racial/ethnic minorities. No comparisons limited to HIV monoinfected persons were significant.

CONCLUSIONS

"End-of-the-epidemic" criteria were met among White, African American, and Latino/a PWID in New York City, but elimination of disparities may require a greater focus on PWID with high sexual risk.

Effects of contact structure on the transient evolution of HIV virulence

Early in an epidemic, high densities of susceptible hosts select for relatively high parasite virulence; later in the epidemic, lower susceptible densities select for lower virulence. Thus over the course of a typical epidemic the average virulence of parasite strains increases initially, peaks partway through the epidemic, then declines again. However, precise quantitative outcomes, such as the peak virulence reached and its timing, may depend sensitively on epidemiological details. Fraser et al. proposed a model for the eco-evolutionary dynamics of HIV that incorporates the tradeoffs between transmission and virulence (mediated by set-point viral load, SPVL) and their heritability between hosts. Their model used implicit equations to capture the effects of partnership dynamics that are at the core of epidemics of sexually transmitted diseases. Our models combine HIV virulence tradeoffs with a range of contact models, explicitly modeling partnership formation and dissolution and allowing for individuals to transmit disease outside of partnerships. We assess summary statistics such as the peak virulence (corresponding to the maximum value of population mean log₁₀ SPVL achieved throughout the epidemic) across models for a range of parameters applicable to the HIV epidemic in sub-Saharan Africa. Although virulence trajectories are broadly similar across models, the timing and magnitude of the virulence peak vary considerably. Previously developed implicit models predicted lower virulence and slower progression at the peak (a maximum of 3.5 log₁₀ SPVL) compared both to more realistic models and to simple random-mixing models with no partnership structure at all (both with a maximum of ≈ 4.7 log₁₀ SPVL). In this range of models, the simplest random-mixing structure best approximates the most realistic model; this surprising outcome occurs because the dominance of extra-pair contact in the realistic model swamps the effects of partnership structure.

Pathogens such as HIV can evolve rapidly when the environment changes. One important aspect of a pathogen’s environment is the probability that an infectious contact (a sneeze for a respiratory disease, or an unprotected sex act for a sexually transmitted disease) encounters an uninfected person and thus has a chance to transmit the pathogen. As an epidemic grows the number of uninfected people shrinks, changing evolutionary pressures on the pathogen. While researchers have used models to explore pathogen evolution during epidemics, their models usually neglect important processes such as people entering and leaving sexual partnerships. We compared several evolutionary models for HIV that include partnership dynamics as well as sexual contact outside of stable partnerships. Models of intermediate complexity predicted lower virulence midway through the epidemic (a minimum of 15 years to progress to AIDS) than either more realistic models or simple models with no partnership structure (both with a minimum of 7.25 years to progress to AIDS), because random sexual contacts tended to wash out the effects of stable partnerships. Researchers trying to predict the evolution of pathogens must try to understand the implications of their modeling choices; models of intermediate complexity may not produce intermediate conclusions.

Modelling the evolution of HIV-1 virulence in response to imperfect therapy and prophylaxis

Average HIV-1 virulence appears to have evolved in different directions in different host populations since antiretroviral therapy first became available, and models predict that HIV drugs can select for either higher or lower virulence, depending on how treatment is administered. However, HIV virulence evolution in response to "leaky" therapy (treatment that imperfectly suppresses viral replication) and the use of preventive drugs (pre-exposure prophylaxis) has not been explored. Using adaptive dynamics, we show that higher virulence can evolve when antiretroviral therapy is imperfectly effective and that this evolution erodes some of the long-term clinical and epidemiological benefits of HIV treatment. The introduction of pre-exposure prophylaxis greatly reduces infection prevalence, but can further amplify virulence evolution when it, too, is leaky. Increasing the uptake rate of these imperfect interventions increases selection for higher virulence and can lead to counterintuitive increases in infection prevalence in some scenarios. Although populations almost always fare better with access to interventions than without, untreated individuals could experience particularly poor clinical outcomes when virulence evolves. These findings predict that antiretroviral drugs may have underappreciated evolutionary consequences, but that maximizing drug efficacy can prevent this evolutionary response. We suggest that HIV virulence evolution should be closely monitored as access to interventions continues to improve.

A transmission-virulence evolutionary trade-off explains attenuation of HIV-1 in Uganda

Evolutionary theory hypothesizes that intermediate virulence maximizes pathogen fitness as a result of a trade-off between virulence and transmission, but empirical evidence remains scarce. We bridge this gap using data from a large and long-standing HIV-1 prospective cohort, in Uganda. We use an epidemiological-evolutionary model parameterised with this data to derive evolutionary predictions based on analysis and detailed individual-based simulations. We robustly predict stabilising selection towards a low level of virulence, and rapid attenuation of the virus. Accordingly, set-point viral load, the most common measure of virulence, has declined in the last 20 years. Our model also predicts that subtype A is slowly outcompeting subtype D, with both subtypes becoming less virulent, as observed in the data. Reduction of set-point viral loads should have resulted in a 20% reduction in incidence, and a three years extension of untreated asymptomatic infection, increasing opportunities for timely treatment of infected individuals.

The impact of antiretroviral therapy on population-level virulence evolution of HIV-1

In HIV-infected patients, an individual's set point viral load (SPVL) strongly predicts disease progression. Some think that SPVL is evolving, indicating that the virulence of the virus may be changing, but the data are not consistent. In addition, the widespread use of antiretroviral therapy (ART) has the potential to drive virulence evolution. We develop a simple deterministic model designed to answer the following questions: what are the expected patterns of virulence change in the initial decades of an epidemic? Could administration of ART drive changes in virulence evolution and, what is the potential size and direction of this effect? We find that even without ART we would not expect monotonic changes in average virulence. Transient decreases in virulence following the peak of an epidemic are not necessarily indicative of eventual evolution to avirulence. In the short term, we would expect widespread ART to cause limited downward pressure on virulence. In the long term, the direction of the effect is determined by a threshold condition, which we define. We conclude that, given the surpassing benefits of ART to the individual and in reducing onward transmission, virulence evolution considerations need have little bearing on how we treat.

Evolution of HIV virulence in response to widespread scale up of antiretroviral therapy: a modeling study

There are global increases in the use of HIV antiretroviral therapy (ART), guided by clinical benefits of early ART initiation and the efficacy of treatment as prevention of transmission. Separately, it has been shown theoretically and empirically that HIV virulence can evolve over time; observed virulence levels may reflect an adaptive balance between infected lifespan and per-contact transmission rate. However, the potential effects of widespread ART usage on HIV virulence are unknown. To predict these effects, we used an agent-based stochastic model to simulate evolutionary trends in HIV virulence, using set point viral load as a proxy for virulence. We calibrated our model to prevalence and incidence trends of South Africa. We explored two distinct ART scenarios: (1) ART initiation based on HIV-infected individuals reaching a CD4 count threshold; and (2) ART initiation based on individual time elapsed since HIV infection (a scenario that mimics "universal testing and treatment" (UTT) aspirations). In each case, we considered a range in population uptake of ART. We found that HIV virulence is generally unchanged in scenarios of CD4-based initiation. However, with ART initiation based on time since infection, virulence can increase moderately within several years of ART rollout, under high coverage levels and early treatment initiation (albeit within the context of epidemics that are rapidly decreasing in size). Sensitivity analyses suggested the impact of ART on virulence is relatively insensitive to model calibration. Our modeling study suggests that increasing HIV virulence driven by UTT is likely not a major public health concern, but should be monitored in sentinel surveillance, in a manner similar to transmitted resistance to antiretroviral drugs.

Potential Pitfalls in Estimating Viral Load Heritability

In HIV patients, the set-point viral load (SPVL) is the most widely used predictor of disease severity. Yet SPVL varies over several orders of magnitude between patients. The heritability of SPVL quantifies how much of the variation in SPVL is due to transmissible viral genetics. There is currently no clear consensus on the value of SPVL heritability, as multiple studies have reported apparently discrepant estimates. Here we illustrate that the discrepancies in estimates are most likely due to differences in the estimation methods, rather than the study populations. Importantly, phylogenetic estimates run the risk of being strongly confounded by unrealistic model assumptions. Care must be taken when interpreting and comparing the different estimates to each other.

Modeling Immune Response to BK Virus Infection and Donor Kidney in Renal Transplant Recipients

In this paper we develop and validate with bootstrapping techniques a mechanistic mathematical model of immune response to both BK virus infection and a donor kidney based on known and hypothesized mechanisms in the literature. The model presented does not capture all the details of the immune response but possesses key features that describe a very complex immunological process. We then estimate model parameters using a least squares approach with a typical set of available clinical data. Sensitivity analysis combined with asymptotic theory is used to determine the number of parameters that can be reliably estimated given the limited number of observations.

Evolutionary Stability of Minimal Mutation Rates in an Evo-epidemiological Model

We consider the evolution of mutation rate in a seasonally forced, deterministic, compartmental epidemiological model with a transmission-virulence trade-off. We model virulence as a quantitative genetic trait in a haploid population and mutation as continuous diffusion in the trait space. There is a mutation rate threshold above which the pathogen cannot invade a wholly susceptible population. The evolutionarily stable (ESS) mutation rate is the one which drives the lowest average density, over the course of one forcing period, of susceptible individuals at steady state. In contrast with earlier eco-evolutionary models in which higher mutation rates allow for better evolutionary tracking of a dynamic environment, numerical calculations suggest that in our model the minimum average susceptible population, and hence the ESS, is achieved by a pathogen strain with zero mutation. We discuss how this result arises within our model and how the model might be modified to obtain a nonzero optimum.