Hill Lab @JohnsHopkins

Major bed bug outbreaks pose a unique challenge to public health and economic infrastructure in cities. While bed bugs have resurged dramatically since the early 2000s, little has been done to characterize the epidemic or evaluate how policy may have influenced spatial-temporal trends in reported bed bug metrics as a proxy for infestations. In this study we used publicly-available administrative data to assess the dynamics of reported bed bug infestations in New York City over a decade. Our results indicate that reported bed bug infestations are significantly decreasing, which may indicate the success of interventions employed by New York City by residents and policy makers

Massive unemployment during the COVID-19 pandemic could result in an eviction crisis in US cities. In this study we modeled the effect of evictions on SARS-CoV-2 epidemics, simulating viral transmission within and among households in a theoretical metropolitan area. We recreated a range of urban epidemic trajectories and project the course of the epidemic under two counterfactual scenarios, one in which a strict moratorium on evictions is in place and enforced, and another in which evictions are allowed to resume at baseline or increased rates. We found, across scenarios, that evictions lead to significant increases in infections. Applying our model to Philadelphia using locally-specific parameters showed that the increase is especially profound in models that consider realistically heterogenous cities in which both evictions and contacts occur more frequently in poorer neighborhoods. Our results provide a basis to assess eviction moratoria and show that policies to stem evictions are a warranted and important component of COVID-19 control.

Based on some of our preliminary findings, co-author Mike Levy filed an affidavit on Aug 7 with the US District Court in Philadelphia, in regards to a case that an association of property owners, managers, and investers had filed against the City of Philadelphia to prevent them from continuing to enforce anti-eviction polices under their Emergency Housing Protection Act. On Aug 28, the court ruled in favor of the city, and this mathematical modeling work was cited as evidence that policies enacted by the city and state to prevent evictions were indeed related to reducing the spread of COVID-19. The judge's opinion statement, which cites the evidence from models, is here. On Sept 4 2020, the CDC imposed a national moratorium on evictions until December 31st, 2020. Shortly after, it was challenged in federal court (Brown vs Azar). Some of our preliminary results were included as part of an amici curiae brief submitted by a consortium of public health and legal groups in relation to the case, which is available here. On Oct 29, 2020 the court ruled in favor of the CDC. As of writing, the CDC moratorium has been extended until June 30, 2021, and the order references our work

Around the world, “social distancing” measures have been used to try to slow the spread of COVID-19. In some regions, they have been very successful, leading to rapid near-elimination of disease, but in other regions, cases and deaths have continued to increase long after implementation, and in yet other regions, the curve appears to be flat but not declining. What factors determine the efficacy and the timescale of social distancing policies? In this study we examine the clinical and epidemiological factors that can explain the variable and delayed outcomes of social distancing measures. Using a stochastic, network-structured epidemic model of COVID-19, we track clinical progression from infection through hospitalization and death, and incorporate transmission via realistic human contact patterns. We find that the strength of within-household transmission is a critical and overlooked determinant of intervention success, governing the timing and size of the epidemic peak, the rate of decline, individual risks of infection, and the success of partial relaxation measures. Uncertainty about household spread for COVID-19 and its apparent variability across regions makes precise estimation of intervention effects impossible. We examine the role of residual connections between households, driven by continued work outside the home and essential errands, and find that the structure of these contacts can lead to long persistence times of outbreaks despite strong interventions. Household composition - including household size and the presence of individuals continuing to work - is predicted to be a strong determinant of individual infection risk. Finally, we predict the impact of partial-relaxation of social distancing, by the formation of multi-family household “bubbles”. We suggest conditions under which such policies could be safe, versus when they are expected to lead to resurgence. These findings can improve future predictions of the timescale and efficacy of interventions needed to control similar outbreaks - or subsequent waves of COVID-19 - and highlight the need for better quantification and control of household transmission.

The COVID-19 pandemic is unfolding in cities around the world, with very different dynamics in different places. It is not clear how key geographic variables influence these dynamics. This study, led by Ben Rader, Sam Scarpino, Moritz Kraemer, and Oliver Pybus, examined the trajectories of COVID-19 cases across hundreds of cities in China and looked at the role of climate, urbanization, and variation in interventions in the shape of the epidemic curve. They found that the the degree to which cases of COVID-19 are compressed into a short period of time (peakedness of the epidemic) is strongly shaped by population aggregation and heterogeneity, such that epidemics in crowded cities are more spread over time, and crowded cities have larger total epidemic sizes than less populated cities. In addition, epidemics were more peaked in cities with lower mean specific humidity and with smaller reductions in mobility due to the pandemic. These results also held across Italian provinces. Our role was to compare these findings to various mathematical models that described different impacts of population structure on disease spread. We found that the observed differences in the peakedness of epidemics were consistent with a metapopulation model of COVID-19 that explicitly accounts for spatial hierarchies.

The populations of small towns and riverine communities in Amazonia are extremely vulnerable to COVID-19 due to the absence of basic health care infrastructure in the region. This study was conducted by a team of researchers at the Federal University of Manaus and Mamiraua Institute for Sustainable Development in Brazil, led by Emiliano Ramalho, to understand the risk to their local communities. The objective was to (1) evaluate the effect of social distancing measures in the spread of COVID-19 in small towns, and (2) to estimate the impact of reducing contact between rural and urban populations on the contamination of riverine communities of Central Amazon. I helped them out with the epidemiological modeling of COVID-19. Their results indicate that social distancing can significantly reduce the speed of dissemination of COVID-19 in the population of small towns. However, they also observed that even in towns with intense actions to combat COVID-19, social distancing is well below the ideal 70% isolation. They recommend that, given the low effectiveness of social distancing measures and the rapid contamination of urban populations, each municipality should evaluate implementing more restrictive measures such as a full or partial lockdown. Their results also suggest that three measures can be effective in delaying the arrival of COVID-19 in riverine communities of Amazonia: (1) reduction of the number of visits that each riverine community resident makes to a town, (2) reduction in duration of each visit, and (3) avoiding visits during the five weeks with the largest number of infected people in towns. It is imperative that implementation of any of the restrictive measures to riverine communities suggested in this publication be accompanied by a vast communication campaign as well as social assistance actions (e.g. distribution of food and other basic items) for the rural population and poor families of small towns to guarantee their basic needs for survival.

HIV/AIDS can be treated with antiretroviral drugs, but if therapy is stopped, the infection rapidly rebounds. A new class of “immunotherapy” drugs are being developed to permanently cure infection. This paper presents a mathematical/statistical modeling approach to characterize the impact of immunotherapy on infection dynamics, using a collection of recent animal studies. We quantified the amount by which each therapy (TLR7-agonist, PGT121 antibody, Ad26/MVA therapeutic vaccine) reduced latent virus reactivation or boosted antiviral immunity, alone and in combination. In addition, we calibrated our model to human data to predict how these interventions may perform in clinical trials. These results provide new insight into the mechanism of action of HIV immunotherapy and can help optimize future trial design. This project was conducted in close collaboration with biostaticians at the University of Bordeaux, led by Melanie Prague.

Currently, individuals receiving antiretroviral therapy for HIV must continue treatment for life, because if at any time therapy is stopped, the virus rapidly rebounds. New therapies are under investigation to prevent, delay, or suppress this viral rebound, but they are difficult to test, because subjects must undergo a supervised therapy interruption with frequent monitoring in order to know if they will experience remission or rebound. A major goal of the field is to identify biomarkers that could predict viral rebound, to better design and ideally avoid treatment interruption studies. In this study, led by Rui Wang, a large cohort of patients who underwent HIV therapy interruption in previous clinical studies were collected and a panel of biomarkers were assessed for their relationship to viral rebound. Two methods of characterizing rebound were compared: i) a closed form mathematical expression that was created to describe typical rebound trajectories with a minimal number of parameters but no mechanistic basis, and ii) a mathematical model expressed as a system of ordinary differential equations that describes the biological interactions between cells, virus, and the immune response (see Prague/Gerold et al 2019). We found that both methods could describe the data well, and similar predictors were identified by either method. 

The burden of drug-resistant bacterial infections is rising, and experts warn that we could be nearing a “post-antibiotic” era. Scientists and public health officials often rely on mathematical models to predict changes in resistance levels over time and the effects of hypothetical interventions. However, most models struggle to reproduce common trends seen in real-world data, limiting their practical use. In this paper we propose a simple model to account for variations in the likelihood of taking antibiotics if infected, which arise within and between regions due to factors like drug-prescribing practices, healthcare access or care-seeking behavior, or the co-occurrence of other diseases. We found that this model extension robustly reproduces trends seen in data, such as sustained coexistence of both drug-resistant and drug-sensitive strains of bacteria in a population, and differences in resistance levels between similar or adjacent regions. We hope that this work will motivate future studies into the underlying causes of the spatio-temporal patterns of antibiotic resistance, and improve the design of mathematical models to predict resistance spread.

This study led by Ravi Gupta at University of Cambridge describes the second person ever who we believe is completely cured of HIV. Termed “the London Patient” in the popular press, this individual living with treated HIV infection developed a blood cancer and had to undergo a bone marrow transplant. Similar to the well-known case of the “Berlin Patient” (the first case of HIV cure), doctors were able to find a matched bone marrow donor who carried a naturally-occuring genetic variant that renders white blood cells resistant to HIV. The transplant was successful, and this study describes the in-depth search conducted on blood and tissues samples from this patient to find any remaining virus. No virus could be detected, and the individual eventually stopped all anti-HIV drugs (under clinical supervision). Despite 2.5 years without therapy, the virus did not rebound. I used a mathematical model we had previously developed for latent HIV reactivation and rebound to estimate how likely it was that this individual was really cured, and how long it would take to be more certain. The calculations were based on different assumptions about the relative importance of two potential mechanisms contributing to cure: clearance of latently infected cells, and genetic resistance of remaining target cells to infection. The combination of ultrasensitive viral load assays and mathematical models presented in this study suggest it is highly likely that this individual is truly cured of HIV. 

Bed bugs are household pests that bite humans and cause medical, psychological, social, and economic problems. Infestation levels have resurged across the United States in recent decades, and cities and states are debating strategies to deal with them. In this study we introduce a mathematical model to study the spread of bed bugs and predict the costs and benefits of policies aimed at controlling them. In particular, we evaluate disclosure, a policy that requires landlords to notify potential tenants of recent infestations in a unit. While disclosure aims to protect individual tenants, our results suggest that these policies also reduce infestation prevalence market-wide. Disclosure results in some initial cost to landlords but leads to significant savings in the long term. This paper came out of a recurring workshop on bed bugs that took place at the National Socio-Ecological Synthesis Center (SESYNC), and brought together experts in housing policy, entomology, infectious disease dynamics, and economics. 

The major barrier to curing HIV infection is the persistence of a long-lived “reservoir” of cells that are latently infected with virus, and are not impacted by antiretroviral therapy. Reactivation of these latent cells can restart infection if therapy is ever stopped, and so clearing this reservoir or preventing its formation are goals of HIV cure research. Previous work by our collaborators, James Whitney and Dan Barouch of Harvard’s Center for Virology and Vaccine Research, showed that in a primate model of HIV infection (SIV), even starting therapy as early as 3 days was not enough to reduce this reservoir to a small enough size to prevent viral rebound. In this continuation of that work, study subjects were started on antiretroviral therapy even earlier: either 6 hrs, 1 day, 2 days, or 3 days after infection. Some animals treated < 3 days post-infection did not rebound, with lower rebound probability the earlier treatment was started. We analyzed the study data to show that the relationship between measures of the pre-therapy viral burden, the latent reservoir size, and the probability of viral rebound agreed with predictions of mathematical models, and identified the reservoir measure that best predicted rebound. This study suggest the latent reservoir is seeded extremely early in infection, and that dramatic reductions from its typical size are needed for cure. 

This review is part of a special issue on "Modeling Viral Infection and Immunity", organized by Alan Perelson and Ruy Ribiero. The odds of living a long and healthy life with HIV infection have dramatically improved with the advent of combination antiretroviral therapy. Along with the early development and clinical trials of these drugs, and new field of research emerged called viral dynamics, which uses mathematical models to interpret and predict the time-course of viral levels during infection and how they are altered by treatment. In this review, we summarize the contributions that virus dynamics models have made to understanding the pathophysiology of infection and to designing effective therapies. This includes studies of the multiphasic decay of viral load when antiretroviral therapy is given, the evolution of drug resistance, the long-term persistence latently infected cells, and the rebound of viremia when drugs are stopped. We additionally discuss new work applying viral dynamics models to new classes of investigational treatment for HIV, including latency-reversing agents and immunotherapy.

This review is part of a special collection entitled "Progress in Achieving Long-Term HIV Remission". It summarizes work during the period of 2016-2018 related to using mathematical models to better understand the mechanisms of persistence of HIV despite antiretroviral therapy, and to design new therapies to cure infection.

Anti-HIV drugs must be taken for life, because latent (dormant) virus persists indefinitely and will restart the infection if treatment is stopped. Scientists are searching for new therapies that will permanently cure the infection, either by perturbing latent virus or boosting the immune system's ability to control reactivating virus. This study, which was led by James Whitney at Harvard's Center for Virology & Vaccine Research, tested out a new immunotherapy in the primate model of HIV (SIV). The therapy involved a small-molecule drug developed by Gilead Sciences that stimulates the TLR7 receptor of the innate immune system, and was given to animals who while they were on antiretroviral drugs. This study found that the drugs completely prevented viral rebound in some animals, and altered it in others. We used mathematical models to help understand what the mechanism of action of these drugs were, based on the patterns of viral rebound.

A major barrier to curing HIV is the long-term persistence of latent virus in memory T cells. It is not completely understood how this "reservoir" of latently infected cells last for up to decades during antiretroviral therapy. This study, lead by Bob Siliciano's lab, examined the genotype and phenotype of the latent reservoir over time in a cohort of treated patients. They found that there are many genetically identical infectious viruses archived in cells and that the population shifts over time. Because of the very high mutation rate of HIV during active infection and the lack of active infection during treatment, finding genetically identical latent viruses suggests that latently infected cells can proliferate without "waking up", and that this contributes to their persistence. This was confirmed with cell culture experiments that stimulated cells to proliferate. We designed and implemented statistical tests to compare the changes in viral populations over time to what would be expected just by chance due to random sampling. Overall, this study contributes to the idea that latency may be a more dynamic phenomenon than originally thought.

Virus such as HIV, Hepatitis B and C, and influenza are a major source of illness and death worldwide. As the availability of targeted drug therapies to these infections has increased, so has the prevalence of drug-resistant strains. Usually, we think that drug resistance is caused by altering drug binding, but here we propose an alternative mechanism available to viruses. Using large-scale simulations of evolving viral populations, we show that regular patterns of drug intake select for viruses whose life cycle length is synchronized with the drug period. These strains can grow to high levels and cause therapy failure. We demonstrate this new type of resistance is robust to missed or mistimed pills, and realistic drug kinetics, but the degree of resistance depends most critically on the ability of the virus to control its life cycle across generations. More generally, we show that the common mathematical method of calculating the critical therapy efficacy needed to control infections fails under periodic antiviral dosing, and develop an alternative method. This finding suggests that existing tests for drug-resistant virus may miss a major pathway: genotypic tests often only look for mutations in viral proteins bound by the drug, not those controlling lifecycle, and phenotypic tests are always conducted in the presence of constant drug levels, not physiologically-relevant periodic levels. We hope this work will inspire new experimental studies to test for life cycle synchronization in vivo and design more comprehensive screens for drug-resistant strains.

This chapter will appear in the forthcoming textbook "HIV Latency", edited by Guido Silvestri and Mathias Lichterfeld, and published by Springer. Viral latency is a major barrier to curing HIV infection with antiretroviral therapy, and consequently, for eliminating the disease globally. The establishment, maintenance, and potential clearance of latent infection are complex dynamic processes and can be best understood and described with the help of mathematical models. Here we review the use of viral dynamics models for HIV, with a focus on applications to the latent reservoir. Such models have been used to explain the multiphasic decay of viral load during antiretroviral therapy, the early seeding of the latent reservoir during acute infection and the limited inflow during treatment, the dynamics of viral blips, and the phenomenon of posttreatment control. In addition, mathematical models have been used to predict the efficacy of potential HIV cure strategies, such as latency-reversing agents, early treatment initiation, or gene therapies, and to provide guidance for designing trials of these novel interventions.

Antiretroviral therapy is very effective at suppressing HIV infection, but since it's not curative, pills must be taken every day for life. This makes it expensive and logistically challenging to get drugs to the millions of infected individuals around the world, and makes it hard for patients to consistently adhere to treatment. In this paper, a grouped of engineers led by Bob Langer and Gio Traverso at MIT developed a proof-of-concept device to allow for once-weekly oral delivery of antiretroviral drugs. We used mathematical models of HIV dynamics to understand how the altered drug-level trajectories with this drug-delivery strategy could impact treatment outcomes, including the likelihood of drug resistance. Our modeling framework can also be used to evaluate other "long-acting" antiretroviral strategies under development.

Current antiretroviral drugs dramatically suppress HIV levels in the body but cannot cure the infection. Low level virus persists despite years of treatment, and whenever drugs are stopped, the infection rapidly rebounds. There is debate in the field about the source of this persistent virus. Some believe that the drugs are not fully effective, and that virus continually replicates in some sanctuaries in the body. Others believe that the drugs fully suppress viral replication, but that long-lived latent virus can survive years of treatment. A 2016 Nature paper claimed to find evidence of ongoing replication and evolution in virus that persisted during treatment, supporting the claim of ineffective drugs. In this response paper, we show that problems with the experimental design and phylogenetic analysis used in that paper mean that false signals of evolution would be detected even in the absence of viral replication. More generally, we show that classic phylogenetic methods should be used with extreme caution when applied to populations with demographic processes not captured by the models underlying the inference procedures.

It is not known if starting antiretroviral therapy extremely early after HIV infection could limit the creation of latently infected cells enough such that an individual could eventually be cured and stop all therapy. This study led by Tim Henrich examined two individuals who started therapy an estimated 10 and 12 days after HIV infection, with very low peak viral load measurement. Extensive testing of blood and tissue for HIV persistence was performed while they were on therapy.  No HIV could be definitively detected for up to 2 years in the participant who initiated ART approximately 10 days after HIV infection. Intermittent, very low levels of HIV were detected in blood but not tissue in the participant who initiated ART an estimated 12 days following infection. The participant with no detectable HIV during therapy stopped ART in order to test if and when HIV would rebound. Rebound occurred suddenly 225 days later. We used previously developed mathematical models to estimate the number of latently infected cells remaining in these individuals and the probability of cure over time. These findings show that HIV can relapse despite starting therapy at one of the earliest stages of acute HIV infection possible, and that near complete loss of detectable HIV in blood and tissues did not lead to indefinite therapy-free remission.

Anti-HIV drugs must be taken for life, because latent (dormant) virus persists indefinitely and will restart the infection if treatment is stopped. Scientists are searching for new therapies that will permanently cure the infection, either by perturbing latent virus or boosting the immune system's ability to control reactivating virus. This study, which was a collaboration between Dan Barouch at Harvard's Center for Virology & Vaccine Research, the US Military HIV Research Program, and industry partners Gilead and Janssen, tested out a new immunotherapy in the primate model of HIV (SIV). The therapy involved a small-molecular drug that stimulates the TLR7 receptor of the innate immune system, and a vaccine, which were both given to animals who while they were on antiretroviral drugs. This study found that the drugs altered the kinetics of viral rebound in some animals, even leading a subset of them to fully control the infection after a brief rebound. We used mathematical models to help understand what the mechanism of action of these drugs were, based on the patterns of viral rebound.

HIV cannot be cured by current antiviral drugs, as it persists indefinitely in a latent form. When drugs are stopped, this latent virus can reactivate and restart infection. An important parameters that HIV researchers, in particular modelers, have been trying to estimate is how often a latently infected cells wakes up, because it determines how much the pool of latent virus would need to be reduced to delay or prevent the infection from rebounding. In this paper we debate the statistical methods that modelers have used to try to back out this pattern, and argue that reactivation of latency is likely to be more common than others have claimed, which makes the prospect of curing HIV by reducing latency bleak.

New therapies are being developed to permanently cure HIV infection. Many aim to reduce the pool of latent virus that persists despite years of treatment with antiretroviral drugs. Because latent virus is so difficult to sample and measure, often the only way to know if these new therapies have worked is to interrupt all treatment, and wait indefinitely to see if the infection rebounds. In this study we use a set of mathematical and statistical models to suggest optimal ways to design and interpret these treatment interruption trials. For various scenarios, we predict how long patients should be followed to be confident that they are cured, how frequent viral load sampling should occur, and how large clinical trials will need to be to estimate and compare drug efficacy. We demonstrate how to infer a range for number of remaining latent cells based on the timing of rebound after a long remission. As a case study, we apply these results to data from two HIV-positive patients who underwent bone marrow transplants and remained off treatment for months before suddenly rebounding. These findings can help inform the testing of new potentially-curative HIV therapies.

The evolution of drug resistance is a major health threat. In chronic infections with rapidly mutating pathogens—including HIV, tuberculosis, and hepatitis B and C viruses—multidrug re- sistance can cause even aggressive combination drug treatment to fail. Oftentimes, individual drugs within a combination do not penetrate equally to all infected regions of the body. In this paper we used evolutionary dynamics models to suggest that this imperfect penetration can dramatically increase the chance of treatment failure by creating regions where only one drug from a combination reaches a therapeutic concentration. The resulting single-drug compartments allow the pathogen to evolve resistance to each drug sequentially, rapidly causing multidrug resistance. More broadly, our model provides a quantitative framework for reasoning about trade-offs between aggressive and moderate drug therapies.

Limiting dilution assays are widely used in infectious disease research. These assays are crucial for current HIV-1 cure research in particular, where they are used to quantify latent virus that persists despite antiretroviral treatment. In this paper we offer new tools to help investigators design and analyze dilution assays based on their specific research needs. The IUPMStats tool to analyze output from these assays is available online.

Anti-HIV drugs can stop the virus from actively replicating but don't target latent virus, which can persist for a lifetime. New investigational drugs are being tested for their ability to rapidly "wake-up" latent virus and purge the infection from the body. This study evaluated a panel of such drugs in latently infected cells isolated from patients and tested their efficacy individually and in combination. We developed a mathematical model of latent HIV infection to make predictions about how results observed in the lab would translate to measurable outcomes in patients.

One of the most important advancements in modeling infectious disease spread has been the development of methods that account for realistic host population structure. The central finding is that heterogeneity in contact networks, such as the presence of ‘superspreaders’, accelerates infectious disease spread in real epidemics. Disease control is also complicated by the continuous evolution of pathogens in response to changing environments and medical interventions. It remains unclear, however, how population structure influences these adaptive processes. Here we examine the evolution of infectious disease in empirical and theoretical networks. We show that the heterogeneity in contact structure, which facilitates the spread of a single disease, surprisingly renders a resident strain more resilient to invasion by new variants. Our results suggest that many host contact structures suppress invasion of new strains and may slow disease adaptation. These findings are important to the natural history of disease evolution and the spread of drug-resistant strains

HIV infection cannot be cured by current antiretroviral drugs, due to the presence of long-lived latently infected cells. New anti-latency drugs are being tested in clinical trials, but major unknowns remain. It is unclear how much latent virus must be eliminated for a cure, which remains difficult to answer empirically due to few case studies and limited sensitivity of assays for latent virus. In this paper, we introduce a mathematical model of HIV dynamics to calculate the likelihood and timing of viral rebound following anti-latency treatment. We derive predictions for the required efficacy of anti-latency drugs, and demonstrate that rebound times may be highly variable and occur after years of remission. These results will aid in designing and interpreting HIV cure studies.

A small fraction of cells that HIV infects revert to a state of latency, where the virus can persist for years, despite antiretroviral treatment. This study investigated whether initiating antiretroviral treatment very early after infection could restrict the amount of latent virus formed, so that after some period of treatment,  it could be stopped without the risk of infection rebounding. In a primate model of HIV (SIV), treatment as early as 3 days after infection did not prevent viral resurgence after treatment interruption. We used viral dynamics models to understand the relationship between time of treatment, reservoir size, and rebound kinetics when treatment was stopped. This study suggests that even with extremely early detection and intervention for individuals infected with HIV, antiretroviral therapy will not be curative.

To date we only know of one individual who was completely cured of HIV. Commonly known in the literature as the "Berlin patient", this HIV-positive individual also developed leukemia, and was treated with chemotherapy and a bone marrow transplant, which was received from a donor who had a naturally-occuring mutation rendering cells resistant to HIV infection. Despite remaining off antiretroviral therapy, no virus has been detected for almost a decade. While the high risk of this procedure and the rarity of HIV-resistant donors means this is not a practical solution to cure most people living with HIV, scientists want to understand how it worked to help design new treatments. It was unclear if the "Berlin patient" was cured due to the transplant procedure, which could have reduced latent virus, or the HIV-resistant cells. To help understand this cure, two other HIV-positive individuals requiring bone marrow transplants were studied. They could not be matched with HIV-resistant donors, but they were able to stay on their antiretroviral drugs during the transplant. After the procedure they had no detectable virus, and eventually stopped therapy. Virus did not rebound, and for many months they appeared to be cured. However, they both eventually experienced sudden and rapid resurgence of the infection. This work showed that even dramatic reductions in latent virus could not revent eventual rebound, raising the bar for anti-latency therapy and confirming predictions of our earlier models.

One of the most important quantities in infectious disease epidemiology is the basic reproductive ratio (R₀) - defined as the average number of new infections caused by a single infected individual during its lifetime in an otherwise susceptible population. The magnitude of R₀ determines how difficult it is to eradicate a disease, and in addition, models of competition for hosts between multiple disease strains conclude that evolution favors the strain with the highest R₀. In this paper we show that this picture fails if we assume a finite population. Using a simple stochastic SIS model, we show that in general there is no analogous optimization principle. We find that successive invasions may in some cases lead to strains that infect a smaller fraction of the host population, and that mutually invasible pathogen strains exist. In the limit of weak selection we demonstrate that an optimization principle does exist, although it differs from R₀ maximization. We show that this effect alters the outcomes of evolution in the presence of a trade-off between the virulence and the transmission rate of a pathogen.

We built a model for the evolutionary dynamics of HIV during antiviral drug treatment, which incorporated dose-response curves for a large panel of drugs and resistance mutants measured by a novel ex vivo assay developed in Bob Siliciano's lab at Johns Hopkins. This work showed that temporal variation in selection pressures during HIV treatment, due to drug pharmacology and imperfect patient adherence, is needed to explain drug resistance trends, and must be taken into account when designing dosing strategies. We were able to explain why patients can fail some drugs without developing resisance, and provide suggestions on how to optimize combination therapy.

This review paper was part of a special issue on evolutionary medicine. We discuss the critical role that evolution plays in the dynamics of HIV within and between hosts, including its original emergence from primate-specific ancestors, immune evasion and pathogenesis, the evolution of virulence, and de novo and transmitted drug resistance. We cover the role of mathematical models and of population genetics in understanding the infection.

In 2010 I spent a summer working at St. John's Research Insitute, an academic public health research center in Bangalore, India. In collaboration with nutritional researchers, I designed a model of iron regulation to help predict the effects of a particular iron intake on hemoglobin levels. Experimental results from the institute showed that iron absorption is a dynamic variable that depends on the current iron status of an individual, and their studies measured the specific values for typical South Indian meals. This and other experimental results and known physiological mechanisms for iron regulation were combined to construct a compartmental differential equation model for the feedback between iron status and absorption, and distribution between storage and hemoglobin compartments in the body. Importantly, this model suggests that recommended dietary allowance values for iron should not be solely based on achieving iron balance, since balance can be achieved for many intake values by regulating absorption and doesn’t guarantee a healthy hemoglobin level. The model can be used to predict hemoglobin recovery following blood loss, hemoglobin changes with increase or decreases in intake, and the effect of de- worming on hemoglobin levels.

Information, trends, behaviors and even health states may spread between contacts in a social network, similar to disease transmission. However, a major difference is that as well as being spread infectiously, it is possible to acquire this state spontaneously. For example, you can gain knowledge of a particular piece of information either by being told about it, or by discovering it yourself. In this paper we introduce a mathematical modeling framework that allows us to compare the dynamics of these social contagions to traditional infectious diseases. We can also extract and compare the rates of spontaneous versus contagious acquisition of a behavior from longitudinal data and can use this to predict the implications for future prevalence and control strategies. As an example, we study the spread of obesity, and find that the current rate of becoming obese is about 2% per year and increases by 0.5 percentage points for each obese social contact, while the rate of recovering from obesity is 4% per year. The rates of spontaneous infection and transmission have steadily increased over time since 1970, driving the increase in obesity prevalence. Our model thus provides a quantitative way to analyze the strength and implications of social contagions.

Human populations are arranged in social networks that determine interactions and influence the spread of diseases, behaviours and ideas. In this paper we evaluate the spread of long-term emotional states across a social network. We introduce a novel form of the classical susceptible–infected–susceptible disease model which includes the possibility for ‘spontaneous’ (or ‘automatic’) infection, in addition to disease trans- mission (the SISa model). Using this framework and data from the Framingham Heart Study, we provide formal evidence that positive and negative emotional states behave like infectious diseases spreading across social networks over long periods of time. The probability of becoming content is increased by 0.02 per year for each content contact, and the probability of becoming discontent is increased by 0.04 per year per discontent contact. Our mathematical formalism allows us to derive various quantities from the data, such as the average lifetime of a contentment ‘infection’ (10 years) or discontentment ‘infection’ (5 years). Our results give insight into the transmissive nature of positive and negative emotional states. Determining to what extent particular emotions or behaviours are infectious is a promising direction for further research with important implications for social science, epidemiology and health policy. Our model provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviours, health states, ideas or diseases with reservoirs.

Magnetic Resonance Imaging (MRI) is one of the most powerful and safe medical imaging modalities, but the contrast achieved in images is limited to certain types of anatomical differences in tissues. A future vision for medical imaging is that targeted molecular probes could be designed to hone to any type of biomarker and allow it to be detectable at low concentrations by non-invasive imaging. Magnetically active nanoparticles have been developed for this purpose, but their signal is difficult to quantify, has low signal-to-noise, and is hard to distinguish from other causes of image contrast. This project was a collaboration between the laboratories of Ron Walsworth (Harvard Physics), Charlie Marcus (Harvard Pyhsics), and Bruce Rosen (MGH Martinos Center) to develop silicon-based molecular imaging probes for MRI. This technique is based on the resonance signal from the naturally-occuring 29-Si isotope, which can be enhanced before administration by a technique known as hyperpolarization. As a rotation student, I contributed to manufacturing and characterizing the magenetic resonance properties of the silicon nanoparticles.

The evolution of multicellular organisms depends on genetically identical cells performing specialized functions. A 3.5 billion-year-old example of this is filamentous cyanobacteria, or “blue-green algae”. When starved of fixed nitrogen, a regular pattern of cells differentiate to become specialized nitrogen-fixing “heterocysts”. Experiments have identified a number of pattern forming proteins, but even without these proteins the pattern is not entirely random. As a summer student with Andrew Rutenberg at Dalhousie University, I helped developed a model heterocyst formation; showing that stochastic cell growth and slow nitrogen diffusion are important factors in establishing the observed patterns.