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Within the human respiratory tract (HRT), virus diffuses through the periciliary fluid (PCF) bathing the epithelium. But virus also undergoes advection: as the mucus layer sitting atop the PCF is pushed along by the ciliated cell’s beating cilia, the PCF and its virus content are also pushed along, upwards towards the nose and mouth. While many mathematical models (MMs) have described the course of influenza A virus (IAV) infections in vivo, none have considered the impact of both diffusion and advection on the kinetics and localization of the infection. The MM herein represents the HRT as a one-dimensional track extending from the nose down towards the lower HRT, wherein stationary cells interact with IAV which moves within (diffusion) and along with (advection) the PCF. Diffusion was found to be negligible in the presence of advection which effectively sweeps away IAV, preventing infection from disseminating below the depth at which virus first deposits. Higher virus production rates (10-fold) are required at higher advection speeds (40 μm/s) to maintain equivalent infection severity and timing. Because virus is entrained upwards, upper parts of the HRT see more virus than lower parts. As such, infection peaks and resolves faster in the upper than in the lower HRT, making it appear as though infection progresses from the upper towards the lower HRT, as reported in mice. When the spatial MM is expanded to include cellular regeneration and an immune response, it reproduces tissue damage levels reported in patients. It also captures the kinetics of seasonal and avian IAV infections, via parameter changes consistent with reported differences between these strains, enabling comparison of their treatment with antivirals. This new MM offers a convenient and unique platform from which to study the localization and spread of respiratory viral infections within the HRT., Author summary This work proposes a new way to think about and model the dissemination of an influenza A virus (IAV) infection within the human respiratory tract (HRT). The computational model takes into account the physiological environment in which the infection takes place by representing the HRT spatially in one dimension (depth), and by incorporating the effect of virion diffusion within the periciliary fluid that bathes infectable cells, and the remarkable physiological barrier that is the mucus escalator, sweeping virus upwards. Cell regeneration, the immune response, and infection with human vs avian IAV strains are explored in this spatial context. The numerical efficiency of this model, compared to agent-based models, makes it an attractive alternative to model respiratory virus infections in vivo.

Epstein-Barr virus (EBV) is transmitted by saliva and is a major cause of cancer, particularly in people living with HIV/AIDS. Here, we describe the frequency and quantity of EBV detection in the saliva of Ugandan adults with and without HIV-1 infection and use these data to develop a novel mathematical model of EBV infection in the tonsils. Eligible cohort participants were not taking antiviral medications, and those with HIV-1 infection had a CD4 count >200 cells/mm3. Over a 4-week period, participants provided daily oral swabs that we analysed for the presence and quantity of EBV. Compared with HIV-1 uninfected participants, HIV-1 coinfected participants had an increased risk of EBV detection in their saliva (IRR = 1.27, 95% CI = 1.10–1.47) and higher viral loads in positive samples. We used these data to develop a stochastic, mechanistic mathematical model that describes the dynamics of EBV, infected cells, and immune response within the tonsillar epithelium to analyse potential factors that may cause EBV infection to be more severe in HIV-1 coinfected participants. The model, fit using Approximate Bayesian Computation, showed high fidelity to daily oral shedding data and matched key summary statistics. When evaluating how model parameters differed among participants with and without HIV-1 coinfection, results suggest HIV-1 coinfected individuals have higher rates of B cell reactivation, which can seed new infection in the tonsils and lower rates of an EBV-specific immune response. Subsequently, both these traits may explain higher and more frequent EBV detection in the saliva of HIV-1 coinfected individuals., Author summary Epstein-Barr virus (EBV) is a ubiquitous infection worldwide associated with the development of several kinds of cancer, including B cell lymphoma and nasopharyngeal carcinoma. Rates of EBV replication and disease are higher in individuals who are coinfected with HIV-1. HIV-1 infection is associated with increased B cell activation as well as immunodeficiency resulting from loss of T cells; however, whether these factors contribute to higher rates of EBV replication during coinfection, and by how much, has remained unknown. We analysed oral EBV shedding data from a cohort of Ugandan adults taken at multiple time points and found that participants coinfected with HIV-1 maintained higher quantities of EBV in their saliva. To better understand this finding, we developed a mathematical model to describe the dynamics of EBV infection within the tonsils. By rigorously matching our model to our participant data, we determined that both high rates of infected B cell activation and worse cellular immune control of EBV may cause higher EBV loads in saliva during HIV-1 coinfection. These results help explain the impact of HIV-1 on EBV and suggest potential therapeutic targets to prevent EBV-related malignancy in people who are coinfected with HIV-1.

During sporogony, malaria-causing parasites infect a mosquito, reproduce and migrate to the mosquito salivary glands where they can be transmitted the next time blood feeding occurs. The time required for sporogony, known as the extrinsic incubation period (EIP), is an important determinant of malaria transmission intensity. The EIP is typically estimated as the time for a given percentile, x, of infected mosquitoes to develop salivary gland sporozoites (the infectious parasite life stage), which is denoted by EIPx. Many mechanisms, however, affect the observed sporozoite prevalence including the human-to-mosquito transmission probability and possibly differences in mosquito mortality according to infection status. To account for these various mechanisms, we present a mechanistic mathematical model, which explicitly models key processes at the parasite, mosquito and observational scales. Fitting this model to experimental data, we find greater variation in the EIP than previously thought: we estimated the range between EIP10 and EIP90 (at 27°C) as 4.5 days compared to 0.9 days using existing statistical methods. This pattern holds over the range of study temperatures included in the dataset. Increasing temperature from 21°C to 34°C decreased the EIP50 from 16.1 to 8.8 days. Our work highlights the importance of mechanistic modelling of sporogony to (1) improve estimates of malaria transmission under different environmental conditions or disease control programs and (2) evaluate novel interventions that target the mosquito life stages of the parasite., Author summary Anopheles mosquitoes become infected with malaria-causing parasites when blood feeding on an infectious host. The parasites then reproduce via a number of life stages, which begin in the mosquito gut and end in the salivary glands, where the newly formed infectious parasites can be transmitted to another host the next time a mosquito blood feeds. This delay in the mosquito becoming infectious, known as the extrinsic incubation period (EIP), is long relative to mosquito life expectancy. Consequently, the EIP is important in determining whether a mosquito is able to transmit malaria. The EIP is typically estimated by fitting a statistical model to parasite data from the dissection of numerous mosquitoes. The large variability in development times and parasite numbers that exists between parasites, mosquitoes and environments means that estimating the EIP is difficult. Here, we introduce a mathematical model of the population dynamics of the mosquito life stages of the parasite, which mimics key characteristics of the biology. We show that the model’s parameters can be fit so that its predictions correspond with experimental observations. Our work is a step towards a realistic model of within-mosquito parasite dynamics, which can be applied to help understand heterogeneity in malaria transmission.

Persistent bacteremia caused by Staphylococcus aureus (SA), especially methicillin-resistant SA (MRSA), is a significant cause of morbidity and mortality. Despite susceptibility phenotypes in vitro, persistent MRSA strains fail to clear with appropriate anti-MRSA therapy during bacteremia in vivo. Thus, identifying the factors that cause such MRSA persistence is of direct and urgent clinical relevance. To address the dynamics of MRSA persistence in the face of host immunity and typical antibiotic regimens, we developed a mathematical model based on the overarching assumption that phenotypic heterogeneity is a hallmark of MRSA persistence. First, we applied an ensemble modeling approach and obtained parameter sets that satisfied the condition of a minimum inoculum dose to establish infection. Second, by simulating with the selected parameter sets under vancomycin therapy which follows clinical practices, we distinguished the models resulting in resolving or persistent bacteremia, based on the total SA exceeding a detection limit after five days of treatment. Third, to find key determinants that discriminate resolving and persistent bacteremia, we applied a machine learning approach and found that the immune clearance rate of persister cells is a key feature. But, fourth, when relapsing bacteremia was considered, the growth rate of persister cells was also found to be a key feature. Finally, we explored pharmacological strategies for persistent and relapsing bacteremia and found that a persister killer, but not a persister formation inhibitor, could provide for an effective cure the persistent bacteremia. Thus, to develop better clinical solutions for MRSA persistence and relapse, our modeling results indicate that we need to better understand the pathogen-host interactions of persister MRSAs in vivo., Author summary Staphylococcus aureus causes potentially lethal infections of the bloodstream and target organs when able to enter the body, often via skin trauma or catheterization. Methicillin-resistant Staphylococcus aureus (MRSA) resist common antibiotics, but are often successfully treated with vancomycin. However, in some MRSA patients, vancomycin is less effective. This results in persistent bacteremia, even though the isolates can be effectively killed in vitro. MRSA bacteria are thought to switch between two forms, normal and persister cells, that are genetically identical. Persisters, the minor subpopulation, are slow-growing and show lower susceptibility to vancomycin than normal MRSA. To understand the dynamic interplay between the two bacterial populations when challenged by host immunity and vancomycin treatment, we developed a mathematical model and analyzed it in simulations of clinically relevant scenarios. Our work suggests that the immune clearance rate of persister MRSA rather than the MRSA switch rate is a key determinant to establish persistent bacteremia. The model also suggests that increasing killing rate of persisters is a promising therapeutic strategy. Our findings emphasize the need to better understand the interactions of persister MRSAs with host cells and immune responses in vivo.

Identifying biomarkers for tuberculosis (TB) is an ongoing challenge in developing immunological correlates of infection outcome and protection. Biomarker discovery is also necessary for aiding design and testing of new treatments and vaccines. To effectively predict biomarkers for infection progression in any disease, including TB, large amounts of experimental data are required to reach statistical power and make accurate predictions. We took a two-pronged approach using both experimental and computational modeling to address this problem. We first collected 200 blood samples over a 2- year period from 28 non-human primates (NHP) infected with a low dose of Mycobacterium tuberculosis. We identified T cells and the cytokines that they were producing (single and multiple) from each sample along with monkey status and infection progression data. Machine learning techniques were used to interrogate the experimental NHP datasets without identifying any potential TB biomarker. In parallel, we used our extensive novel NHP datasets to build and calibrate a multi-organ computational model that combines what is occurring at the site of infection (e.g., lung) at a single granuloma scale with blood level readouts that can be tracked in monkeys and humans. We then generated a large in silico repository of in silico granulomas coupled to lymph node and blood dynamics and developed an in silico tool to scale granuloma level results to a full host scale to identify what best predicts Mycobacterium tuberculosis (Mtb) infection outcomes. The analysis of in silico blood measures identifies Mtb-specific frequencies of effector T cell phenotypes at various time points post infection as promising indicators of infection outcome. We emphasize that pairing wetlab and computational approaches holds great promise to accelerate TB biomarker discovery., Author Summary Tuberculosis (TB) is a disease that is caused by infection after inhaling the bacterium Mycobacterium tuberculosis. Not everyone infected with TB bacteria becomes sick. As a result, two TB-related conditions have been categorized: latent TB infection (not sick but still harboring the bacteria) and active TB disease. If not treated properly, active TB disease can be fatal. Almost 1.3 million die of TB worldwide each year, with ~8,6 million new infections in 2013. No effective vaccine is available to protect against TB and treatment of infection with multiple antibiotics is lengthy (6–9 months), with non-compliance being a major factor for the emergence of drug-resistant strains. A key step in developing effective vaccines and possibly shorter treatment regimens is the ability to identify biomarkers that correlate prognosis and progression to infection (similar to how cholesterol levels are a measure of heart health). In this study we show how pairing computer modeling, statistics and mathematics with datasets derived from non-human primate studies can accelerate biomarker discovery, and offer a new approach to identifying correlates of protection that will be useful in clinical practice, particularly in developing countries where TB is most prevalent.

Diseases of humans and wildlife are typically tracked and studied through incidence, the number of new infections per time unit. Estimating incidence is not without difficulties, as asymptomatic infections, low sampling intervals and low sample sizes can introduce large estimation errors. After infection, biomarkers such as antibodies or pathogens often change predictably over time, and this temporal pattern can contain information about the time since infection that could improve incidence estimation. Antibody level and avidity have been used to estimate time since infection and to recreate incidence, but the errors on these estimates using currently existing methods are generally large. Using a semi-parametric model in a Bayesian framework, we introduce a method that allows the use of multiple sources of information (such as antibody level, pathogen presence in different organs, individual age, season) for estimating individual time since infection. When sufficient background data are available, this method can greatly improve incidence estimation, which we show using arenavirus infection in multimammate mice as a test case. The method performs well, especially compared to the situation in which seroconversion events between sampling sessions are the main data source. The possibility to implement several sources of information allows the use of data that are in many cases already available, which means that existing incidence data can be improved without the need for additional sampling efforts or laboratory assays., Author Summary Human and wildlife diseases can be tracked by looking at incidence, which is the number of new infections per time unit (typically day, week or month). While theoretically this would only be a matter of counting the number of newly infected individuals, in reality these data are difficult to acquire due to limited sampling possibilities and undetectable cases. This means that a method must be used to estimate the real incidence using a limited amount of data. For many infections, the concentration and quality of antibodies changes predictably over time, which means that one could use the antibody level at any point in time to back-calculate how much time passed since the infection entered the body. Other information, such as the age of the individual, or the presence of the pathogen, can also help to estimate when an individual became infected. Improving on existing methods, we developed a method that allows the use of a wide range of information sources for estimating individual time since infection. Using arenavirus infection in mice, we show that this method works well when sufficient background data are available, and that it can greatly improve the estimation of incidence patterns.