Inference of Type-Specific HPV Transmissibility,Progression and Clearance Rates: A Mathematical Modelling Approach

Quantifying rates governing the clearance of Human Papillomavirus (HPV) and its progression to clinical disease, together with viral transmissibility and the duration of naturally-acquired immunity, is essential in estimating the impact of vaccination programmes and screening or testing regimes. However, the complex natural history of HPV makes this difficult. We infer the viral transmissibility, rate of waning natural immunity and rates of progression and clearance of infection of 13 high-risk and 2 non-oncogenic HPV types, making use of a number of rich datasets from Sweden. Estimates of viral transmissibility, clearance of initial infection and waning immunity were derived in a Bayesian framework by fitting a susceptible-infectious-recovered-susceptible (SIRS) transmission model to age- and type-specific HPV prevalence data from both a cross-sectional study and a randomised controlled trial (RCT) of primary HPV screening. The models fitted well, but over-estimated the prevalence of four high-risk types with respect to the data. Three of these types (HPV-33, -35 and -58) are among the most closely related phylogenetically to the most prevalent HPV-16. The fourth (HPV-45) is the most closely related to HPV-18; the second most prevalent type. We suggest that this may be an indicator of cross-immunity. Rates of progression and clearance of clinical lesions were additionally estimated from longitudinal data gathered as part of the same RCT. Our estimates of progression and clearance rates are consistent with the findings of survival analysis studies and we extend the literature by estimating progression and clearance rates for non-16 and non-18 high-risk types. We anticipate that such type-specific estimates will be useful in the parameterisation of further models and in developing our understanding of HPV natural history.     

Mathematical Modelling of an Ischemic Stroke: An Integrative Approach

Understanding the mechanisms and the time and spatial evolution of penumbra following an ischemic stroke is crucially important for developing therapeutics aimed at preventing this area from evolving towards infarction. To help in integrating the available data, we decided to build a formal model. We first collected and categorised the major available evidence from animal models and human observations and summarized this knowledge in a flow-chart with the potential key components of an evolving stroke. Components were grouped in ten sub-models that could be modelled and tested independently: the sub-models of tissue reactions, ionic movements, oedema development, glutamate excitotoxicity, spreading depression, NO synthesis, inflammation, necrosis, apoptosis, and reperfusion. Then, we figured out markers, identified mediators and chose the level of complexity to model these sub-models. We first applied this integrative approach to build a model based on cytotoxic oedema development following a stroke. Although this model includes only three sub-models and would need to integrate more mechanisms in each of these sub-models, the characteristics and the time and spatial evolution of penumbra obtained by simulation are qualitatively and, to some extent, quantitatively consistent with those observed using medical imaging after a permanent occlusion or after an occlusion followed by a reperfusion.     

A Multiscale Approach to the Migration of Cancer Stem Cells: Mathematical Modelling and Simulations

We propose a multiscale model for the invasion of the extracellular matrix by two types of cancer cells, the differentiated cancer cells and the cancer stem cells. We investigate the epithelial mesenchymal-like transition between them being driven primarily by the epidermal growth factors. We moreover take into account the transdifferentiation program of the cancer stem cells towards the cancer-associated fibroblast cells as well as the fibroblast-driven remodelling of the extracellular matrix. The proposed haptotaxis model combines the macroscopic phenomenon of the invasion of the extracellular matrix by both types of cancer cells with the microscopic dynamics of the epidermal growth factors. We analyse our model in a component-wise manner and compare our findings with the literature. We investigate pathological situations regarding the epidermal growth factors and accordingly propose “mathematical-treatment” scenarios to control the aggressiveness of the tumour.     

Impact of High-Risk Sex and Focused Interventions in Heterosexual HIV Epidemics: A Systematic Review of Mathematical Models

Background

The core-group theory of sexually transmitted infections suggests that targeting prevention to high-risk groups (HRG) could be very effective. We aimed to quantify the contribution of heterosexual HRGs and the potential impact of focused interventions to HIV transmission in the wider community.

Methods

We systematically identified studies published between 1980 and 2011. Studies were included if they used dynamical models of heterosexual HIV transmission, incorporated behavioural heterogeneity in risk, and provided at least one of the following primary estimates in the wider community (a) the population attributable fraction (PAF) of HIV infections due to HRGs, or (b) the number per capita or fraction of HIV infections averted, or change in HIV prevalence/incidence due to focused interventions.

Findings

Of 267 selected articles, 22 were included. Four studies measured the PAF, and 20 studies measured intervention impact across 265 scenarios. In low-prevalence epidemics (≤5% HIV prevalence), the estimated impact of sex-worker interventions in the absence of risk compensation included: 6–100% infections averted; 0.9–6.2 HIV infections averted per 100,000 adults; 11–94% and 4–47% relative reduction in prevalence and incidence respectively. In high-prevalence epidemics (>5% HIV prevalence), sex-worker interventions were estimated to avert 6.8–40% of HIV infections and up to 564 HIV infections per 100,000 adults, and reduce HIV prevalence and incidence by 13–27% and 2–14% respectively. In both types of epidemics, greater heterogeneity in HIV risk was associated with a larger impact on the fraction of HIV infections averted and relative reduction in HIV incidence.

Conclusion

Focused interventions, as estimated by mathematical models, have the potential to reduce HIV transmission in the wider community across low- and high-prevalence regions. However, considerable variability exists in estimated impact, suggesting that a targeted approach to HIV prevention should be tailored to local epidemiological context.     

Predicting the Impact of Vaccination on the Transmission Dynamics of Typhoid in South Asia: A Mathematical Modeling Study

Background

Modeling of the transmission dynamics of typhoid allows for an evaluation of the potential direct and indirect effects of vaccination; however, relevant typhoid models rooted in data have rarely been deployed.

Methodology/Principal Findings

We developed a parsimonious age-structured model describing the natural history and immunity to typhoid infection. The model was fit to data on culture-confirmed cases of typhoid fever presenting to Christian Medical College hospital in Vellore, India from 2000–2012. The model was then used to evaluate the potential impact of school-based vaccination strategies using live oral, Vi-polysaccharide, and Vi-conjugate vaccines. The model was able to reproduce the incidence and age distribution of typhoid cases in Vellore. The basic reproductive number (R ₀) of typhoid was estimated to be 2.8 in this setting. Vaccination was predicted to confer substantial indirect protection leading to a decrease in the incidence of typhoid in the short term, but (intuitively) typhoid incidence was predicted to rebound 5–15 years following a one-time campaign.

Conclusions/Significance

We found that model predictions for the overall and indirect effects of vaccination depend strongly on the role of chronic carriers in transmission. Carrier transmissibility was tentatively estimated to be low, consistent with recent studies, but was identified as a pivotal area for future research. It is unlikely that typhoid can be eliminated from endemic settings through vaccination alone.     

Effectiveness of Community-Wide and Individual High-Risk Strategies to Prevent Diabetes: A Modelling Study

Background

Diabetes has been described as one of the most important threats to the health of developed countries. Effective population strategies to prevent diabetes have not been determined but two broad strategies have been proposed: “high-risk” and “community-wide” strategies.

Methods

We modelled the potential effectiveness of two strategies to prevent 10% of new cases of diabetes in Ontario, Canada over a 5-year period. The 5-year risk of developing physician-diagnosed diabetes was estimated for respondents to the Canadian Community Health Survey 2003 (CCHS 2.1, N = 26 232) using a validated and calibrated diabetes risk tool (Diabetes Population Risk Tool [DPoRT]). We estimated how many cases of diabetes could be prevented using two different strategies: a) a community-wide strategy that would uniformly reduce body mass index (BMI) in the entire population; and b) a high baseline risk strategy using either pharmacotherapy or lifestyle counselling to treat people who have an increased risk of developing diabetes.

Results

In 2003, the 5-year risk of developing diabetes was 4.7% (383 600 new diagnosed cases of diabetes in 8 189 000 Ontarians aged 20+) and risk was moderately diffused (0.5%, 3.1% and 17.9% risk in the 1^st, 5^th (median) and 10^th deciles of risk). A 10% reduction in new cases of diabetes would have been achieved under any of the following scenarios: if BMI was 3.5% lower in the entire population; if lifestyle counselling covered 32.2% of high-risk people (371 900 of 1 155 000 people with 5 year diabetes risk greater than 10%); or, if pharmacotherapy covered 65.2% of high-risk people.

Conclusions

Prevention using pharmacotherapy alone requires unrealistically high coverage levels to achieve modest population reduction in new diabetes cases. On the other hand, in recent years few jurisdictions have been able to achieve a reduction in BMI at the population level, let alone a reduction of BMI of 3.5%.     

Household Epidemics: Modelling Effects of Early Stage Vaccination

A Markovian susceptible → infectious → removed (SIR) epidemic model is considered in a community partitioned into households. A vaccination strategy, which is implemented during the early stages of the disease following the detection of infected individuals is proposed. In this strategy, the detection occurs while an individual is infectious and other susceptible household members are vaccinated without further delay. Expressions are derived for the influence on the reproduction numbers of this vaccination strategy for equal and unequal household sizes. We fit previously estimated parameters from influenza and use household distributions for Sweden and Tanzania census data. The results show that the reproduction number is much higher in Tanzania (6 compared with 2) due to larger households, and that infected individuals have to be detected (and household members vaccinated) after on average 5 days in Sweden and after 3.3 days in Tanzania, a much smaller difference.     

Mapping Risk of Malaria Transmission in Mainland Portugal Using a Mathematical Modelling Approach

Malaria is currently one of the world´s major health problems. About a half-million deaths are recorded every year. In Portugal, malaria cases were significantly high until the end of the 1950s but the disease was considered eliminated in 1973. In the past few years, endemic malaria cases have been recorded in some European countries. With the increasing human mobility from countries with endemic malaria to Portugal, there is concern about the resurgence of this disease in the country. Here, we model and map the risk of malaria transmission for mainland Portugal, considering 3 different scenarios of existing imported infections. This risk assessment resulted from entomological studies on An. atroparvus, the only known mosquito capable of transmitting malaria in the study area. We used the malariogenic potential (determined by receptivity, infectivity and vulnerability) applied over geospatial data sets to estimate spatial variation in malaria risk. The results suggest that the risk exists, and the hotspots are concentrated in the northeast region of the country and in the upper and lower Alentejo regions.     

Transmission and Control of Plasmodium knowlesi: A Mathematical Modelling Study

Introduction

Plasmodium knowlesi is now recognised as a leading cause of malaria in Malaysia. As humans come into increasing contact with the reservoir host (long-tailed macaques) as a consequence of deforestation, assessing the potential for a shift from zoonotic to sustained P. knowlesi transmission between humans is critical.

Methods

A multi-host, multi-site transmission model was developed, taking into account the three areas (forest, farm, and village) where transmission is thought to occur. Latin hypercube sampling of model parameters was used to identify parameter sets consistent with possible prevalence in macaques and humans inferred from observed data. We then explore the consequences of increasing human-macaque contact in the farm, the likely impact of rapid treatment, and the use of long-lasting insecticide-treated nets (LLINs) in preventing wider spread of this emerging infection.

Results

Identified model parameters were consistent with transmission being sustained by the macaques with spill over infections into the human population and with high overall basic reproduction numbers (up to 2267). The extent to which macaques forage in the farms had a non-linear relationship with human infection prevalence, the highest prevalence occurring when macaques forage in the farms but return frequently to the forest where they experience higher contact with vectors and hence sustain transmission. Only one of 1,046 parameter sets was consistent with sustained human-to-human transmission in the absence of macaques, although with a low human reproduction number (R_0H = 1.04). Simulations showed LLINs and rapid treatment provide personal protection to humans with maximal estimated reductions in human prevalence of 42% and 95%, respectively.

Conclusion

This model simulates conditions where P. knowlesi transmission may occur and the potential impact of control measures. Predictions suggest that conventional control measures are sufficient at reducing the risk of infection in humans, but they must be actively implemented if P. knowlesi is to be controlled.     

In Silico Synergism and Antagonism of an Anti-tumour System Intervened by Coupling Immunotherapy and Chemotherapy: A Mathematical Modelling Approach

Based on the logistic growth law for a tumour derived from enzymatic dynamics, we address from a physical point of view the phenomena of synergism, additivity and antagonism in an avascular anti-tumour system regulated externally by dual coupling periodic interventions, and propose a theoretical model to simulate the combinational administration of chemotherapy and immunotherapy. The in silico results of our modelling approach reveal that the tumour population density of an anti-tumour system, which is subject to the combinational attack of chemotherapeutical as well as immune intervention, depends on four parameters as below: the therapy intensities D, the coupling intensity I, the coupling coherence R and the phase-shifts Φ between two combinational interventions. In relation to the intensity and nature (synergism, additivity and antagonism) of coupling as well as the phase-shift between two therapeutic interventions, the administration sequence of two periodic interventions makes a difference to the curative efficacy of an anti-tumour system. The isobologram established from our model maintains a considerable consistency with that of the well-established Loewe Additivity model (Tallarida, Pharmacology 319(1):1–7, 2006). Our study discloses the general dynamic feature of an anti-tumour system regulated by two periodic coupling interventions, and the results may serve as a supplement to previous models of drug administration in combination and provide a type of heuristic approach for preclinical pharmacokinetic investigation.     

Species Invasiveness in Biological Invasions: A Modelling Approach

The study of invasiveness, the traits that enable a species to invade a habitat, and invasibility, the habitat characteristics that determine its susceptibility to the establishment and spread of an invasive species, provide a useful conceptual framework to formulate the biological invasion problem in a modelling context. Another important aspect is the complex interaction emerging among the invader species, the noninvader species already present in the habitat, and the habitat itself. Following a modelling approach to the biological invasion problem, we present a spatially explicit cellular automaton model (Interacting Multiple Cellular Automata (IMCA)). We use field parameters from the invader Gleditsia triacanthos and the native Lithraea ternifolia in montane forests of central Argentina as a case study to compare outputs and performance of different models. We use field parameters from another invader, Ligustrum lucidum, and the native Fagara coco from the same system to run the cellular automaton model. We compare model predictions with invasion values from aerial photographs. We discuss in detail the importance of factors affecting species invasiveness, and give some insights into habitat invasibility and the role of interactions between them. Finally, we discuss the relevance of mathematical modelling for studying and predicting biological invasions. The IMCA model provided a suitable context for integrating invasiveness, invasibility, and the interactions. In the invasion system studied, the presence of an invader's juvenile bank not only accelerated the rate of invasion but was essential to ensure invasion. Using the IMCA model, we were able to determine that not only adult survival but particularly longevity of the native species influenced the spread velocity of the invader, at least when a juvenile bank is present. Other factors determining velocity of invasion detected by the IMCA model were seed dispersal distance and age of reproductive maturity. We derived relationships between species' adult survival, fecundity and longevity of both theoretical and applied relevance for biological invasions. Invasion velocities calculated from the aerial photographs agreed well with predictions of the IMCA model.     

Polarization and Movement of Keratocytes: A Multiscale Modelling Approach

Eukariotic cell motility is a complex phenomenon, in which the cytoskeleton and its major constituent, actin, play an essential role. Actin forms polymers of long, stiff filaments that are cross-linked into an anisotropic network inside a thin sheet-like cellular protrusion, the lamellipod. At the leading edge of this structure, polymerization of actin filaments creates the force that pushes out the membrane and leads to translocation of a motile cell. Dynamics of the actin network account for changes in cell shape, crawling motion and turning of the cell in response to external cues. Regulating the dynamics of the cytoskeleton, and playing a central role in signal transduction in the cell, are Cdc42, Rac and Rho (GTPases of the rho family, collectively known as the small G-proteins) and the actin nucleating complex, Arp2/3.In this paper, we use a multiscale modelling approach in a 2D model of a motile cell. We describe the mutual interactions of the small G-proteins, and their effects on capping and side-branching of actin filaments. We incorporate the pushing exerted by oriented actin filament ends on the cell edge, and a Rho-dependent contraction force. Combining these biochemical and mechanical aspects, we investigate the dynamics of a model epidermal fish keratocyte through in silico experiments. Our model gives insight into how, in response to some cue, a cell can polarize, form a leading edge, and move; concomitantly it explains how a keratocyte cell can maintain its shape and polarity, even after removal of the initial stimulus, and how it can change direction quickly in response to changes in its environment. We show that establishment of polarity stems from interactions of Cdc42, Rac and Rho, while maintenance and robustness of polarity is due to the rapid cytosolic diffusion of the inactive (GDI-bound) forms of the small G-proteins. Our model produces a cell shape that closely resembles the keratocytes and correct speeds for biologically reasonable parameter values. Movies of the simulations can be obtained from http://theory.bio.uu.nl/stan/keratocyte.     

Diagnosis of Bacterial Bloodstream Infections: A 16S Metagenomics Approach

Background

Bacterial bloodstream infection (bBSI) is one of the leading causes of death in critically ill patients and accurate diagnosis is therefore crucial. We here report a 16S metagenomics approach for diagnosing and understanding bBSI.

Methodology/Principal Findings

The proof-of-concept was delivered in 75 children (median age 15 months) with severe febrile illness in Burkina Faso. Standard blood culture and malaria testing were conducted at the time of hospital admission. 16S metagenomics testing was done retrospectively and in duplicate on the blood of all patients. Total DNA was extracted from the blood and the V3–V4 regions of the bacterial 16S rRNA genes were amplified by PCR and deep sequenced on an Illumina MiSeq sequencer. Paired reads were curated, taxonomically labeled, and filtered. Blood culture diagnosed bBSI in 12 patients, but this number increased to 22 patients when combining blood culture and 16S metagenomics results. In addition to superior sensitivity compared to standard blood culture, 16S metagenomics revealed important novel insights into the nature of bBSI. Patients with acute malaria or recovering from malaria had a 7-fold higher risk of presenting polymicrobial bloodstream infections compared to patients with no recent malaria diagnosis (p-value = 0.046). Malaria is known to affect epithelial gut function and may thus facilitate bacterial translocation from the intestinal lumen to the blood. Importantly, patients with such polymicrobial blood infections showed a 9-fold higher risk factor for not surviving their febrile illness (p-value = 0.030).

Conclusions/Significance

Our data demonstrate that 16S metagenomics is a powerful approach for the diagnosis and understanding of bBSI. This proof-of-concept study also showed that appropriate control samples are crucial to detect background signals due to environmental contamination.     

Oxygen-Driven Tumour Growth Model: A Pathology-Relevant Mathematical Approach

Xenografts -as simplified animal models of cancer- differ substantially in vasculature and stromal architecture when compared to clinical tumours. This makes mathematical model-based predictions of clinical outcome challenging. Our objective is to further understand differences in tumour progression and physiology between animal models and the clinic.To achieve that, we propose a mathematical model based upon tumour pathophysiology, where oxygen -as a surrogate for endocrine delivery- is our main focus. The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia and necrosis. The ODM describes two key physiological parameters. Apparent oxygen uptake rate (kR′) represents the amount of oxygen cells seem to need to proliferate. The more oxygen they appear to need, the more the oxygen transport. kR′ gathers variability from the vasculature, stroma and tumour morphology. Proliferating rate (k _p) deals with cell line specific factors to promote growth. The K _H,K _N describe the switch of hypoxia and necrosis. Retrospectively, using archived data, we looked at longitudinal tumour volume datasets for 38 xenografted cell lines and 5 patient-derived xenograft-like models.Exploration of the parameter space allows us to distinguish 2 groups of parameters. Group 1 of cell lines shows a spread in values of kR′ and lower k _p, indicating that tumours are poorly perfused and slow growing. Group 2 share the value of the oxygen uptake rate (kR′) and vary greatly in k _p, which we interpret as having similar oxygen transport, but more tumour intrinsic variability in growth.However, the ODM has some limitations when tested in explant-like animal models, whose complex tumour-stromal morphology may not be captured in the current version of the model. Incorporation of stroma in the ODM will help explain these discrepancies. We have provided an example. The ODM is a very simple -and versatile- model suitable for the design of preclinical experiments, which can be modified and enhanced whilst maintaining confidence in its predictions.     

Hemodynamic Changes following Aortic Valve Bypass: A Mathematical Approach

Aortic valve bypass (AVB) has been shown to be a viable solution for patients with severe aortic stenosis (AS). Under this circumstance, the left ventricle (LV) has a double outlet. The objective was to develop a mathematical model capable of evaluating the hemodynamic performance following the AVB surgery. A mathematical model that captures the interaction between LV, AS, arterial system, and AVB was developed. This model uses a limited number of parameters that all can be non-invasively measured using patient data. The model was validated using in vivo data from the literature. The model was used to determine the effect of different AVB and AS configurations on flow proportion and pressure of the aortic valve and the AVB. Results showed that the AVB leads to a significant reduction in transvalvular pressure gradient. The percentage of flow through the AVB can range from 55.47% to 69.43% following AVB with a severe AS. LV stroke work was also significantly reduced following the AVB surgery and reached a value of around 1.2 J for several AS severities. Findings of this study suggest: 1) the AVB leads to a significant reduction in transvalvular pressure gradients; 2) flow distribution between the AS and the AVB is significantly affected by the conduit valve size; 3) the AVB leads to a significant reduction in LV stroke work; and 4) hemodynamic performance variations can be estimated using the model.     

A Model of Disease and Vaccination for Infections with Acute and Chronic Phases

A general model is presented of a disease in which both recovered and vaccinated individuals are protected from acute disease, but are still susceptible to chronic infection. The special threshold conditions for the establishment and persistence of such a disease are derived and explained in full. The efficacies of alternative vaccination strategies are detailed and a specific example of such a disease is given by examining feline calicivirus (FCV), a cause of upper respiratory tract disease in cats.     

Estimating PMTCT's Impact on Heterosexual HIV Transmission: A Mathematical Modeling Analysis

Introduction

Prevention of mother-to-child HIV transmission (PMTCT) strategies include combined short-course antiretrovirals during pregnancy (Option A), triple-drug antiretroviral treament (ART) during pregnancy and breastfeeding (Option B), or lifelong ART (Option B+). The WHO also recommends ART for HIV treatment and prevention of sexual transmission of HIV. The impact of PMTCT strategies on prevention of sexual HIV transmission of HIV is not known. We estimated the population-level impact of PMTCT interventions on heterosexual HIV transmission in southwestern Uganda and KwaZulu-Natal, South Africa, two regions with different HIV prevalence and fertility rates.

Materials and Methods

We constructed and validated dynamic, stochastic, network-based HIV transmission models for each region. PMTCT Options A, B, and B+ were simulated over ten years under three scenarios: 1) current ART and PMTCT coverage, 2) current ART and high PMTCT coverage, and 3) high ART and PMTCT coverage. We compared adult HIV incidence after ten years of each intervention to Option A (and current ART) at current coverage.

Results

At current coverage, Options B and B+ reduced heterosexual HIV incidence by about 5% and 15%, respectively, in both countries. With current ART and high PMTCT coverage, Option B+ reduced HIV incidence by 35% in Uganda and 19% in South Africa, while Option B had smaller, but meaningful, reductions. The greatest reductions in HIV incidence were achieved with high ART and PMTCT coverage. In this scenario, all PMTCT strategies yielded similar results.

Discussion

Implementation of Options B/B+ reduces adult HIV incidence, with greater effect (relative to Option A at current levels) in Uganda than South Africa. These results are likely driven by Uganda’s higher fertility rates.