ORCID Profile
0000-0003-4371-5340
Current Organisations
University of Ottawa
,
University Hospital Southampton NHS Foundation Trust
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Publisher: Elsevier BV
Date: 21-03-2008
DOI: 10.1016/J.JTBI.2007.11.032
Abstract: Mathematical models of HIV therapy have traditionally amalgamated the action of antiretroviral drugs, trading the complexity of the situation in favour of simpler-and hence mathematically tractable-models. However, the effects of ignoring such dynamics remain underexamined. In this paper, the traditional method of dosing (where the dose is modelled implicitly as a proportional inhibition of viral infection and production) is compared to a model that accounts for drug dynamics via explicit compartments. Four limiting cases are examined: frequent dosing of both major classes of drugs, absence of either drug, frequent dosing of one drug alone, or frequent dosing of the other drug alone. When drugs are absent, both models predict that the virus will dominate and the uninfected T cell counts will be low. When reverse transcriptase inhibitors are given frequently, both models predict that the virus will be theoretically eliminated and the uninfected T cell counts will be high this is true regardless of whether the reverse transcriptase inhibitors act alone or in conjunction with protease inhibitors. However, if protease inhibitors alone are given frequently, then the implicit model predicts that the virus will be eliminated and the uninfected T cell counts will be high, whereas the (more realistic) explicit model predicts that the reverse situation may occur. In the latter case, critically, protease-only regimens may ultimately result in the death of the patient. It follows that the impact of drug regimens consisting only of protease inhibitors must be urgently re-examined, if such outcomes have been based on overly simplistic modelling.
Publisher: Elsevier BV
Date: 2011
DOI: 10.1016/J.JTBI.2010.09.039
Abstract: Recently, the first drug in a new class of antiretroviral HIV drugs was approved, the fusion inhibitor enfuvirtide. We develop a mathematical model that describes the binding of the virus to T cells. We model the effect of enfuvirtide upon this process using impulsive differential equations. We find equilibria and determine stability in the case of no therapy and then when therapy is taken with perfect adherence. We determine analytical thresholds for the dosage and dosing intervals to ensure the disease-free equilibrium remains stable. We also explore the effects of partial adherence. Our theoretical results suggest that partial adherence may, at times, be worse than no therapy at all, but at other times may in fact as good as perfect adherence. It follows that patients should be counselled on the importance of adherence to this new antiretroviral drug.
Publisher: Hindawi Limited
Date: 20-04-2022
DOI: 10.1155/2022/3954598
Abstract: With the multiple waves of COVID-19 in China and other countries, there is an urgent need to design effective containment, especially nonpharmaceutical interventions, to combat the transmission. Media reports on COVID-19—which can induce precautionary behaviour such as social distancing, by providing disease-related information to the public—are thought to be effective in containing the spread. We include the media-reporting data collected from authoritative and popular websites, along with the corresponding IP-visiting data, to study the effects of media reports in curbing the outbreak of COVID-19 in Beijing. To quantify how social distancing affects the spread of COVID-19, we differentiate the fully susceptible from those susceptibles who are media aware and practice social distancing or are quarantined. We propose a discrete compartment model with the fully susceptible, the media-aware susceptible, and the quarantined susceptible as three separate classes. We adopt functions dependent on the media reports and the contacts of media-aware susceptibles to describe the progression rate of susceptibles to media-aware susceptibles. By fitting the targeted model to data on the two Beijing outbreaks, we estimated the reproduction numbers for the two outbreaks as R 0 = 1.6818 and R 0 = 1.3251 , respectively. Cross-correlation analysis on our collected data suggests a strong correlation between the media reporting and epidemic case data. Sensitivity and uncertainty analysis show that even with the intensified interventions in force, reducing either the social distancing uptake rate or the average duration of social distancing for media-aware susceptibles could aggravate the severity of the two outbreaks in Beijing by magnifying the final confirmed cases and lengthening the end time of the pandemic. Our findings demonstrate that enhancing social distancing and media reporting alone, if done in sufficient measures, are enough to alleviate the COVID-19 epidemic.
Publisher: Mary Ann Liebert Inc
Date: 03-2007
Publisher: Oxford University Press (OUP)
Date: 25-09-2020
DOI: 10.1002/BJS.12050
Publisher: Elsevier BV
Date: 2013
DOI: 10.1016/J.JTBI.2012.09.037
Abstract: HIV has spread widely in mainland China, but there is significant geographic variation in the severity of the epidemic. We aimed to assess the HIV/AIDS epidemic in mainland China accurately, and address the effect of population mobility on it. Markov-Chain Monte-Carlo simulations and Latin Hypercube S ling were used to estimate the basic reproductive ratio and its sensitivity to parameter variations. We estimated a mean reproduction number of 1.708 (95% CI 1.440-1.977). Our analysis using national surveillance data indicates that HIV-positive in iduals most likely move from economically developed regions to regions with more numerous HIV cases, while mobility of AIDS patients likely flows in the opposite direction, due to the current policy that AIDS patients must return to their registered residence to receive free antiretroviral therapy. Our results based on a spatially stratified population dynamical model show increasing mobility rates of HIV/AIDS cases can have a significant effect on the number of HIV/AIDS cases per province and has the potential to decrease the overall number of HIV/AIDS cases in the country. We recommend that the community-based HIV/AIDS support and care program should be implemented by some local governments (especially in epidemically severe areas) to mitigate HIV infections in China.
Publisher: Springer Science and Business Media LLC
Date: 23-01-2009
DOI: 10.1007/S00285-008-0245-4
Abstract: The majority of cells infected with the human immunodeficiency virus are activated CD4(+) T cells, which can be treated with antiretoviral drugs. However, an obstacle to eradication is the presence of viral reservoirs, such as latently infected CD4(+) T cells. Such cells may be less susceptible to antiretroviral drugs and may persist at low levels during treatment. We introduce a model of impulsive differential equations that describe T cell and drug interactions. We make the extreme assumption that latently infected cells are unaffected by drugs, in order to answer the research question: Can the viral reservoir of latently infected cells be eradicated using current antiretroviral therapy? We analyse the model in both the presence and absence of drugs, showing that, if the frequency of drug taking is sufficiently high, then the number of uninfected CD4(+) T cells approaches the number of T cells in the uninfected immune system. In particular, this implies that the latent reservoir will be eliminated. It follows that, with sufficient application of drugs, latently infected cells cannot sustain a viral reservoir on their own. We illustrate the results with numerical simulations.
Publisher: Elsevier BV
Date: 11-2016
DOI: 10.1016/J.JTBI.2016.08.031
Abstract: Eradication of malaria from the world in the latter part of the twentieth century proved an elusive, albeit desirable, objective. Unfortunately, resurgence of malarial incidence is currently underway. Key to understanding effective control schemes such as indoor residual spraying (spraying insecticide inside houses to kill the malarial vector mosquitoes) is the impact of spatial distributions for communities exposed to the malarial vector mosquito populations. Densities of human dwellings in small communities vary considerably in regions exposed to larval breeding sites. We extend prior modelling work to explore the spatial impact and diffusive transport of mosquito population densities on various distributions of human populations on relatively small landscape representations. Bistable dynamics of our reaction-diffusion model, which excludes advective transport, suggest two temporal phases for infection. An initial rapid phase occurs during transitions from initial homogeneous or spatially confined infections to peak levels over the course of days, and a relaxation phase develops to a steady state over weeks or months, suggesting successful intervention methods likely require recognising the phase of infection. We further observe a strong dependence of human infection and recovery on distributions of susceptible human populations with some degree of independence from mosquito distributions given an adequate supply of mosquito vectors to sustain infections. A subtle and complex interplay between human dwelling densities, mosquito diffusion and infection rates also emerges. With a sufficiently fast diffusive transport of mosquitoes, our model indicates that relative timescales for infection rates are slower, leading to lower rates of infection. This suggests that, although we here only include diffusive transport, if mosquitoes are subject to rapid enough movement (e.g., wind), communities situated in windy areas are exposed to less infectious risk than those in non-windy areas. This should help to guide intervention strategies with geographical considerations in mind. Our implementation of a reaction-diffusion model here further reveals some issues regarding continuum methods for population and infectious disease models that suggest consideration of discrete spatial methods (e.g., agent-based) for future work.
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 08-2016
DOI: 10.3934/MBE.2017024
Abstract: This paper presents a mathematical model for malaria--schistosomiasis co-infection in order to investigate their synergistic relationship in the presence of treatment. We first analyse the single infection steady states, then investigate the existence and stability of equilibria and then calculate the basic reproduction numbers. Both the single-infection models and the co-infection model exhibit backward bifurcations. We carrying out a sensitivity analysis of the co-infection model and show that schistosomiasis infection may not be associated with an increased risk of malaria. Conversely, malaria infection may be associated with an increased risk of schistosomiasis. Furthermore, we found that effective treatment and prevention of schistosomiasis infection would also assist in the effective control and eradication of malaria. Finally, we apply Pontryagin's Maximum Principle to the model in order to determine optimal strategies for control of both diseases.
Publisher: Hindawi Limited
Date: 2015
DOI: 10.1155/2015/781270
Abstract: Recent mathematical modelling has advocated for rapid “test-and-treat” programs for HIV in the developing world, where HIV-positive in iduals are identified and immediately begin a course of antiretroviral treatment, regardless of the length of time they have been infected. However, the foundations of this modelling ignored the effects of drug resistance on the epidemic. It also disregarded the heterogeneity of behaviour changes that may occur, as a result of education that some in iduals may receive upon testing and treatment. We formulate an HIV/AIDS model to theoretically investigate how testing, educating HIV-positive cases, treatment, and drug resistance affect the HIV epidemic. We consider a variety of circumstances: both when education is included and not included, when testing and treatment are linked or are separate, when education is only partly effective, and when treatment leads to drug resistance. We show that education, if it is properly harnessed, can be a force strong enough to overcome the effects of antiretroviral drug resistance however, in the absence of education, “test and treat” is likely to make the epidemic worse.
Publisher: Elsevier BV
Date: 12-2011
Publisher: Hindawi Limited
Date: 2011
DOI: 10.1155/2011/527610
Abstract: The basic reproductive ratio, R 0 , is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R 0 1 , the disease dies out, whereas if R 0 1 , the disease persists. R 0 has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, R 0 is flawed. Diseases can persist with R 0 1 , while diseases with R 0 1 can die out. We show that the same model of malaria gives many different values of R 0 , depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of R 0 for a variety of diseases, and examine some of the alternatives that have been proposed. If R 0 is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.
Publisher: Elsevier BV
Date: 03-2023
Publisher: American Medical Association (AMA)
Date: 22-07-2009
Publisher: Public Library of Science (PLoS)
Date: 14-06-2017
Publisher: Springer Science and Business Media LLC
Date: 10-04-2008
Publisher: Springer Science and Business Media LLC
Date: 29-11-2012
DOI: 10.1007/S11538-012-9790-5
Abstract: Substance abuse remains a global problem, with immense health and social consequences. Crystal meth, known as 'tik' in South Africa, is a growing problem, and its supply chains have equally grown due to increased numbers of 'tik' users, especially in the Western Cape province of South Africa. We consider a model for 'tik' use that tracks drug-supply chains, and accounts for rehabilitation and amelioration for the addicted. We analyse the model and show that it has a unique drug-free equilibrium. We prove that the drug-free equilibrium is globally stable when the reproduction number is less than one. We also consider both slow and fast dynamics, and show that there is a unique drug-persistent equilibrium when the reproduction number exceeds one. The model is fitted to data on 'tik' users in rehabilitation in the Western Cape province. A sensitivity analysis reveals that the parameters with the most control over the epidemic are the quitting rate of light-drug users and the person-to-person contact rate between susceptible in iduals and 'tik' users. This suggests that programs aimed at light-drug users that encourage them to quit will be significantly more effective than targeting hard-drug users, either in quitting or in rehabilitation. Similarly, the person-to-person contact rate may be reduced by social programs that raise awareness of the dangers of 'tik' use and discourage light users from recruiting others.
Publisher: MDPI AG
Date: 14-12-2020
Abstract: In order to limit the disease burden and economic costs associated with the COVID-19 pandemic, it is important to understand how effective and widely distributed a vaccine must be in order to have a beneficial impact on public health. To evaluate the potential effect of a vaccine, we developed risk equations for the daily risk of COVID-19 infection both currently and after a vaccine becomes available. Our risk equations account for the basic transmission probability of COVID-19 (β) and the lowered risk due to various protection options: physical distancing face coverings such as masks, goggles, face shields or other medical equipment handwashing and vaccination. We found that the outcome depends significantly on the degree of vaccine uptake: if uptake is higher than 80%, then the daily risk can be cut by 50% or more. However, if less than 40% of people get vaccinated and other protection options are abandoned—as may well happen in the wake of a COVID-19 vaccine—then introducing even an excellent vaccine will produce a worse outcome than our current situation. It is thus critical that effective education strategies are employed in tandem with vaccine rollout.
Publisher: Birkhäuser Boston
Date: 2008
Publisher: Springer Science and Business Media LLC
Date: 11-2009
Publisher: Springer Science and Business Media LLC
Date: 11-2009
Publisher: Elsevier BV
Date: 08-2015
Publisher: Oxford University Press (OUP)
Date: 03-05-2010
DOI: 10.1093/IJE/DYQ063
Publisher: MDPI AG
Date: 27-05-2014
Publisher: Springer Science and Business Media LLC
Date: 10-07-2020
DOI: 10.1038/S41598-020-67090-7
Abstract: Pine wilt disease is a lethal tree disease caused by nematodes carried by pine sawyer beetles. Once affected, the trees are destroyed within a few months, resulting in significant environmental and economic losses. The role of asymptomatic carrier trees in the disease dynamics remains unclear. We developed a mathematical model to investigate the effect of asymptomatic carriers on the long-term outcome of the disease. We performed a stability and sensitivity analysis to identify key parameters and used optimal control to examine several intervention options. Our model shows that, with the application of suitable controls, the disease can be eliminated in the vector population and all tree populations except for asymptomatic carriers. Of the possible controls (tree injection, elimination of infected trees, insecticide spraying), we determined that elimination of infected trees is crucial. However, if the costs of insecticide spraying increase, it can be supplemented (although not replaced entirely) by tree injection, so long as some spraying is still undertaken.
Publisher: Elsevier BV
Date: 2018
Publisher: Project MUSE
Date: 02-2010
DOI: 10.1353/HPU.0.0270
Abstract: We survey the current state of a group of parasitic and microbial diseases called the Neglected Tropical Diseases (NTDs). These diseases currently infect a billion people, primarily in socioeconomically depressed areas of the world, are a leading cause of worldwide disability, and are responsible for approximately 534,000 deaths per year. We focus on several subcategories: protozoans, helminthes and bacterial diseases. We identify the populations most at risk from these diseases, and outline symptoms and other disease burdens. We examine the progress being made in controlling NTDs, including the current state of drug development. We also examine mathematical modeling of NTDs. While mathematical modeling is not bound by many of the strictures of access, data collection and infrastructure funding, we nevertheless demonstrate that few NTDs have received much attention from mathematical models, and that some have received no attention at all. Simple mathematical models could contribute significantly to our understanding of these diseases and the efforts required to control them, at very little cost. Further investment in prevention, treatment and awareness of NTDs is urgently warranted.
Publisher: World Scientific Pub Co Pte Ltd
Date: 12-2013
DOI: 10.1142/S021833901340007X
Abstract: Cholera, characterized by severe diarrhea and rapid dehydration, is a water-borne infectious disease caused by the bacterium Vibrio cholerae. Haiti offers the most recent ex le of the tragedy that can befall a country and its people when cholera strikes. While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate and analyze a mathematical model that includes two essential and affordable control measures: water chlorination and education. We calculate the basic reproduction number and determine the global stability of the disease-free equilibrium for the model without chlorination. We use Latin Hypercube S ling to demonstrate that the model is most sensitive to education. We also derive the minimal effective chlorination period required to control the disease for both fixed and variable chlorination. Numerical simulations suggest that education is more effective than chlorination in decreasing bacteria and the number of cholera cases.
Publisher: Springer Science and Business Media LLC
Date: 31-01-2019
DOI: 10.1007/S00285-018-1313-Z
Abstract: Releasing infectious pests could successfully control and eventually maintain the number of pests below a threshold level. To address this from a mathematical point of view, two non-smooth microbial pest-management models with threshold policy are proposed and investigated in the present paper. First, we establish an impulsive model with state-dependent control to describe the cultural control strategies, including releasing infectious pests and spraying chemical pesticide. We examine the existence and stability of an order-1 periodic solution, the existence of order-k periodic solutions and chaotic phenomena of this model by analyzing the properties of the Poincaré map. Secondly, we establish and analyze a Filippov model. By examining the sliding dynamics, we investigate the global stability of both the pseudo-equilibria and regular equilibria. The findings suggest that we can choose appropriate threshold levels and control intensity to maintain the number of pests at or below the economic threshold. The modelling and control outcomes presented here extend the results for the system with impulsive interventions at fixed moments.
Publisher: Elsevier BV
Date: 08-2003
DOI: 10.1016/S8756-3282(03)00157-1
Abstract: Bone remodeling occurs asynchronously at multiple sites in the adult skeleton and involves resorption by osteoclasts, followed by formation of new bone by osteoblasts. Disruptions in bone remodeling contribute to the pathogenesis of disorders such as osteoporosis, osteoarthritis, and Paget's disease. Interactions among cells of osteoblast and osteoclast lineages are critical in the regulation of bone remodeling. We constructed a mathematical model of autocrine and paracrine interactions among osteoblasts and osteoclasts that allowed us to calculate cell population dynamics and changes in bone mass at a discrete site of bone remodeling. The model predicted different modes of dynamic behavior: a single remodeling cycle in response to an external stimulus, a series of internally regulated cycles of bone remodeling, or unstable behavior similar to pathological bone remodeling in Paget's disease. Parametric analysis demonstrated that the mode of dynamic behavior in the system depends strongly on the regulation of osteoclasts by autocrine factors, such as transforming growth factor beta. Moreover, simulations demonstrated that nonlinear dynamics of the system may explain the differing effects of immunosuppressants on bone remodeling in vitro and in vivo. In conclusion, the mathematical model revealed that interactions among osteoblasts and osteoclasts result in complex, nonlinear system behavior, which cannot be deduced from studies of each cell type alone. The model will be useful in future studies assessing the impact of cytokines, growth factors, and potential therapies on the overall process of remodeling in normal bone and in pathological conditions such as osteoporosis and Paget's disease.
Publisher: Springer Science and Business Media LLC
Date: 12-01-2010
Publisher: Hindawi Limited
Date: 21-09-2008
DOI: 10.1155/2008/745463
Abstract: Indoor residual spraying—spraying insecticide inside houses to kill mosquitoes—is an important method for controlling malaria vectors in sub-Saharan Africa. We propose a mathematical model for both regular and non-fixed spraying, using impulsive differential equations. First, we determine the stability properties of the nonimpulsive system. Next, we derive minimal effective spraying intervals and the degree of spraying effectiveness required to control mosquitoes when spraying occurs at regular intervals. If spraying is not fixed, then we determine the “next best” spraying times. We also consider the effects of climate change on the prevalence of mosquitoes. We show that both regular and nonfixed spraying will result in a significant reduction in the overall number of mosquitoes, as well as the number of malaria cases in humans. We thus recommend that the use of indoor spraying be re-examined for widespread application in malaria-endemic areas.
Publisher: Elsevier BV
Date: 2020
Publisher: Informa UK Limited
Date: 2018
Publisher: The Royal Society
Date: 16-11-2005
Abstract: The question of determining how many doses may be skipped before HIV treatment response is adversely affected by the emergence of drug-resistance is addressed. Impulsive differential equations are used to develop a prescription to minimize the emergence of drug-resistance for protease-sparing regimens. A threshold for the maximal number of missable doses is determined. If the number of missed doses is below this threshold, then resistance levels are negligible and dissipate quickly, assuming perfect adherence subsequently. If the number of missed doses exceeds this threshold, even for 24 h, resistance levels are extremely high and will not dissipate for weeks, even assuming perfect adherence subsequently. After this interruption, the minimum number of successive doses that should be taken is determined. Estimates are provided for all protease-sparing drugs approved by the US Food and Drug Administration. Estimates for the basic reproductive ratios for the wild-type and mutant strains of the virus are also calculated, for a long-term average fractional degree of adherence. There are regions within this fraction of adherence where the outcome is not predictable and may depend on a patient's entire history of drug-taking.
Publisher: Elsevier BV
Date: 08-2017
Publisher: Elsevier BV
Date: 09-2012
Publisher: Elsevier BV
Date: 2013
Publisher: Public Library of Science (PLoS)
Date: 25-08-2022
DOI: 10.1371/JOURNAL.PONE.0272600
Abstract: Much effort has been devoted by the World Health Organization (WHO) to eliminate soil-transmitted helminth (STH) infections by 2030 using mass drug administration targeted at particular risk groups alongside the availability to access water, sanitation and hygiene services. The targets set by the WHO for the control of helminth infections are typically defined in terms of the prevalence of infection, whereas the standard formulation of STH transmission models typically describe dynamic changes in the mean-worm burden. We develop a prevalence-based deterministic model to investigate the transmission dynamics of soil-transmitted helminthiasis in humans, subject to continuous exposure to infection over time. We analytically determine local stability criteria for all equilibria and find bifurcation points. Our model predicts that STH infection will either be eliminated (if the initial prevalence value, y (0), is sufficiently small) or remain endemic (if y (0) is sufficiently large), with the two stable points of endemic infection and parasite eradication separated by a transmission breakpoint. Two special cases of the model are analysed: (1) the distribution of the STH parasites in the host population is highly aggregated following a negative binomial distribution, and (2) no density-dependent effects act on the parasite population. We find that disease extinction is always possible for Case (1), but it is not so for Case (2) if y (0) is sufficiently large. However, by introducing stochastic perturbation into the deterministic model, we discover that chance effects can lead to outcomes not predicted by the deterministic model alone, with outcomes highly dependent on the degree of worm clumping, k . Specifically, we show that if the reproduction number and clumping are sufficiently bounded, then stochasticity will cause the parasite to die out. It follows that control of soil-transmitted helminths will be more difficult if the worm distribution tends towards clumping.
Publisher: MDPI AG
Date: 06-03-2023
DOI: 10.3390/V15030691
Abstract: Equine Infectious Anemia Virus (EIAV) is an important infection in equids, and its similarity to HIV creates hope for a potential vaccine. We analyze a within-host model of EIAV infection with antibody and cytotoxic T lymphocyte (CTL) responses. In this model, the stability of the biologically relevant endemic equilibrium, characterized by the coexistence of long-term antibody and CTL levels, relies upon a balance between CTL and antibody growth rates, which is needed to ensure persistent CTL levels. We determine the model parameter ranges at which CTL and antibody proliferation rates are simultaneously most influential in leading the system towards coexistence and can be used to derive a mathematical relationship between CTL and antibody production rates to explore the bifurcation curve that leads to coexistence. We employ Latin hypercube s ling and least squares to find the parameter ranges that equally ide the endemic and boundary equilibria. We then examine this relationship numerically via a local sensitivity analysis of the parameters. Our analysis is consistent with previous results showing that an intervention (such as a vaccine) intended to control a persistent viral infection with both immune responses should moderate the antibody response to allow for stimulation of the CTL response. Finally, we show that the CTL production rate can entirely determine the long-term outcome, regardless of the effect of other parameters, and we provide the conditions for this result in terms of the identified ranges for all model parameters.
Publisher: Springer Science and Business Media LLC
Date: 30-07-2014
DOI: 10.1007/S00285-014-0810-Y
Abstract: Mass-vaccination c aigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation c aigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, Re, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase Re and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination. Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of Re when pulse vaccination is present.
Publisher: Springer Science and Business Media LLC
Date: 04-06-2013
DOI: 10.1007/S12064-013-0183-6
Abstract: The widespread impact of avian influenza viruses not only poses risks to birds, but also to humans. The viruses spread from birds to humans and from human to human In addition, mutation in the primary strain will increase the infectiousness of avian influenza. We developed a mathematical model of avian influenza for both bird and human populations. The effect of half-saturated incidence on transmission dynamics of the disease is investigated. The half-saturation constants determine the levels at which birds and humans contract avian influenza. To prevent the spread of avian influenza, the associated half-saturation constants must be increased, especially the half-saturation constant H m for humans with mutant strain. The quantity H m plays an essential role in determining the basic reproduction number of this model. Furthermore, by decreasing the rate β m at which human-to-human mutant influenza is contracted, an outbreak can be controlled more effectively. To combat the outbreak, we propose both pharmaceutical (vaccination) and non-pharmaceutical (personal protection and isolation) control methods to reduce the transmission of avian influenza. Vaccination and personal protection will decrease β m, while isolation will increase H m. Numerical simulations demonstrate that all proposed control strategies will lead to disease eradication however, if we only employ vaccination, it will require slightly longer to eradicate the disease than only applying non-pharmaceutical or a combination of pharmaceutical and non-pharmaceutical control methods. In conclusion, it is important to adopt a combination of control methods to fight an avian influenza outbreak.
Publisher: Public Library of Science (PLoS)
Date: 02-08-2021
DOI: 10.1371/JOURNAL.PNTD.0009625
Abstract: The World Health Organization has recommended the application of mass drug administration (MDA) in treating high prevalence neglected tropical diseases such as soil-transmitted helminths (STHs), schistosomiasis, lymphatic filariasis, onchocerciasis and trachoma. MDA—which is safe, effective and inexpensive—has been widely applied to eliminate or interrupt the transmission of STHs in particular and has been offered to people in endemic regions without requiring in idual diagnosis. We propose two mathematical models to investigate the impact of MDA on the mean number of worms in both treated and untreated human subpopulations. By varying the efficay of drugs, initial conditions of the models, coverage and frequency of MDA (both annual and biannual), we examine the dynamic behaviour of both models and the possibility of interruption of transmission. Both models predict that the interruption of transmission is possible if the drug efficacy is sufficiently high, but STH infection remains endemic if the drug efficacy is sufficiently low. In between these two critical values, the two models produce different predictions. By applying an additional round of biannual and annual MDA, we find that interruption of transmission is likely to happen in both cases with lower drug efficacy. In order to interrupt the transmission of STH or eliminate the infection efficiently and effectively, it is crucial to identify the appropriate efficacy of drug, coverage, frequency, timing and number of rounds of MDA.
Publisher: Walter de Gruyter GmbH
Date: 29-01-2016
Abstract: Enfuvirtide (formerly T20) is an injectable fusion inhibitor that has established effective antiretroviral activity and excellent tolerability in extensively pretreated patients. This fusion inhibitor does not affect the metabolism of other co-administrated drugs for metabolic drug interactions involving enfuvirtide. Few mathematical models have considered co-administration of antiretroviral drugs. We develop a mathematical model to study the effect of enfuvirtide upon this process in combination with protease inhibitors (PIs) using impulsive differential equations. We ide the T cells into several classes to describe the drug activity. Analytical results show that a combination of enfuvirtide and PIs gives a better outcome than single drug activity furthermore, use of enfuvirtide clearly outranks PIs if only one class of drugs were to be used. We determine the threshold value for the dosage and dosing intervals to ensure the stability of the disease-free state and illustrate our results with numerical simulations. We recommend that use of enfuvirtide, in combination with PIs, be expanded beyond salvage therapy.
Publisher: Elsevier BV
Date: 02-2018
Publisher: Springer Science and Business Media LLC
Date: 07-2005
DOI: 10.1016/J.BULM.2004.10.004
Abstract: We consider an SIR-type model of immunological behaviour for HIV dynamics, including the effects of reverse transcriptase inhibitors and other drugs which prevent cellular infection. We use impulsive differential equations to model drug behaviour. We classify different regimes according to whether the drug efficacy is negligible, intermediate or high. We consider two strains of the virus: a wild-type strain that can be controlled by both intermediate and high drug concentrations, and a mutant strain that can only be controlled by high drug concentrations. Drug regimes may take trajectories through one, two or all three regimes, depending on the dosage and the dosing schedule. We demonstrate that drug resistance arises at both intermediate and high drug levels. At low drug levels resistance does not emerge, but the total T cell count is proven to be significantly lower than in the disease-free state. At intermediate drug levels, drug resistance is guaranteed to emerge. At high drug levels, either the drug-resistant strain will dominate or, in the absence of longer-lived reservoirs of infected cells, both viral sub-populations will be cleared. In the latter case the immune system is maintained by a population of T cells which have absorbed sufficient quantities of the drug to prevent infection by even the drug-resistant strain. We provide estimates of a range of dosages and dosing schedules which would, if physiologically tolerable, theoretically eliminate free virus in this system. Our results predict that to control viral load, decreasing the interval between doses is more effective than increasing the dose.
Publisher: Springer Science and Business Media LLC
Date: 18-09-2007
DOI: 10.1007/S10654-007-9165-7
Abstract: Many long-term prospective studies have reported on associations of cardiovascular diseases with circulating lipid markers and/or inflammatory markers. Studies have not, however, generally been designed to provide reliable estimates under different circumstances and to correct for within-person variability. The Emerging Risk Factors Collaboration has established a central database on over 1.1 million participants from 104 prospective population-based studies, in which subsets have information on lipid and inflammatory markers, other characteristics, as well as major cardiovascular morbidity and cause-specific mortality. Information on repeat measurements on relevant characteristics has been collected in approximately 340,000 participants to enable estimation of and correction for within-person variability. Re-analysis of in idual data will yield up to approximately 69,000 incident fatal or nonfatal first ever major cardiovascular outcomes recorded during about 11.7 million person years at risk. The primary analyses will involve age-specific regression models in people without known baseline cardiovascular disease in relation to fatal or nonfatal first ever coronary heart disease outcomes. This initiative will characterize more precisely and in greater detail than has previously been possible the shape and strength of the age- and sex-specific associations of several lipid and inflammatory markers with incident coronary heart disease outcomes (and, secondarily, with other incident cardiovascular outcomes) under a wide range of circumstances. It will, therefore, help to determine to what extent such associations are independent from possible confounding factors and to what extent such markers (separately and in combination) provide incremental predictive value.
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2011
Abstract: Indoor residual spraying-spraying insecticide inside houses to kill mosquitoes-has been one of the most effective methods of disease control ever devised, being responsible for the near-eradication of malaria from the world in the third quarter of the twentieth century and saving tens of millions of lives. However, with malaria resurgence currently underway, it has received relatively little attention, been applied only in select physical locations and not always at regular intervals. We extend a time-dependent model of malaria spraying to include spatial heterogeneity and address the following research questions: 1. What are the effects of spraying in different geographical areas? 2. How do the results depend upon the regularity of spraying? 3. Can we alter our control strategies to account for asymmetric phenomena such as wind? We use impulsive partial differential equation models to derive thresholds for malaria control when spraying occurs uniformly, within an interior disc or under asymmetric advection effects. Spatial heterogeneity results in an increase in the necessary frequency of spraying, but control is still achievable.
Publisher: MDPI AG
Date: 18-05-2017
Publisher: Informa UK Limited
Date: 04-2011
Publisher: American Association for the Advancement of Science (AAAS)
Date: 05-02-2010
Abstract: Understanding the dynamics of drug-resistant strains of HIV and the key determinants affecting their evolution and spread is crucial for predicting future effects of drug treatment. Current models can only track one resistant strain, so Smith? et al. (p. 697 , published online 14 January) used empirical data from San Francisco to parameterize models that consider the transmission of single-, double-, and triple-resistant HIV strains. Many people who are infected with a resistant strain are capable of infecting more than one other person a scenario that could trigger an epidemic wave of drug-resistant virus. At a time when the World Health Organization's strategy for universal testing and treatment is being rolled out, the insights gained from this work are not restricted to HIV transmission and treatment in resource-rich countries, but are widely applicable.
Publisher: Elsevier BV
Date: 02-2023
Publisher: Springer Science and Business Media LLC
Date: 05-11-2013
DOI: 10.1007/S11538-013-9903-9
Abstract: The emergence of drug resistance is one of the most prevalent reasons for treatment failure in HIV therapy. This has severe implications for the cost of treatment, survival and quality of life. We use mathematical modelling to describe the interaction between T cells, HIV-1 and protease inhibitors. We use impulsive differential equations to examine the effects of different levels of protease inhibitors in a T cell. We classify three different regimes according to whether the drug efficacy is low, intermediate or high. The model includes two strains: the wild-type strain, which initially dominates in the absence of drugs, and the mutant strain, which is the less efficient competitor, but has more resistance to the drugs. Drug regimes may take trajectories through one, two or all three regimes, depending on the dosage and the dosing schedule. Stability analysis shows that resistance does not emerge at low drug levels. At intermediate drug levels, drug resistance is guaranteed to emerge. At high drug levels, either the drug-resistant strain will dominate or, in the absence of longer-lived reservoirs of infected cells, a region exists where viral elimination could theoretically occur. We provide estimates of a range of dosages and dosing schedules where the trajectories lie either solely within a region or cross multiple regions. Under specific circumstances, if the drug level is physiologically tolerable, elimination of free virus is theoretically possible. This forms the basis for theoretical control using combination therapy and for understanding the effects of partial adherence.
Publisher: Springer Science and Business Media LLC
Date: 15-04-2016
Publisher: Elsevier BV
Date: 02-2018
DOI: 10.1016/J.MBS.2017.12.002
Abstract: Mass-media reports on an epidemic or pandemic have the potential to modify human behaviour and affect social attitudes. Here we construct a Filippov model to evaluate the effects of media coverage and quarantine on the transmission dynamics of influenza. We first choose a piecewise smooth incidence rate to represent media reports being triggered once the number of infected in iduals exceeds a certain critical level [Formula: see text] . Further, if the number of infected cases increases and exceeds another larger threshold value [Formula: see text] ( [Formula: see text] ), we consider that the incidence rate tends to a saturation level due to the protection measures taken by in iduals meanwhile, we begin to quarantine susceptible in iduals when the number of susceptible in iduals is larger than a threshold value S
Publisher: Springer Science and Business Media LLC
Date: 11-12-2018
DOI: 10.1007/S11538-018-00544-2
Abstract: The issue of medical-resource constraints has the potential to dramatically affect disease management, especially in developing countries. We analyze a non-smooth epidemic model with nonlinear incidence rate and resource constraints, which defines a vaccination program with vaccination rate proportional to the number of susceptible in iduals when this number is below the threshold level and constant otherwise. To better understand the impact of this non-smooth vaccination policy, we provide a comprehensive qualitative analysis of global dynamics for the whole parameter space. As the threshold value varies, the target model admits multistability of three regular equilibria, bistability of two regular equilibria, that of one disease-free equilibrium and one generalized endemic equilibria, and that of one disease-free equilibrium and one crossing cycle. The steady-state regimes include healthy, low epidemic and high epidemic. This suggests the key role of the threshold value, as well as the initial infection condition in disease control. Our findings demonstrate that the case number can be contained at a satisfactorily controllable level or range if eradicating it proves to be impossible.
Publisher: The Royal Society
Date: 07-06-2005
Abstract: The basic reproductive ratio, R 0 , is defined as the expected number of secondary infections arising from a single in idual during his or her entire infectious period, in a population of susceptibles. This concept is fundamental to the study of epidemiology and within-host pathogen dynamics. Most importantly, R 0 often serves as a threshold parameter that predicts whether an infection will spread. Related parameters which share this threshold behaviour, however, may or may not give the true value of R 0 . In this paper we give a brief overview of common methods of formulating R 0 and surrogate threshold parameters from deterministic, non-structured models. We also review common means of estimating R 0 from epidemiological data. Finally, we survey the recent use of R 0 in assessing emerging diseases, such as severe acute respiratory syndrome and avian influenza, a number of recent livestock diseases, and vector-borne diseases malaria, dengue and West Nile virus.
Publisher: Elsevier BV
Date: 05-2005
Publisher: Elsevier BV
Date: 04-2012
Publisher: Elsevier BV
Date: 10-2004
Publisher: World Scientific Pub Co Pte Ltd
Date: 12-2018
DOI: 10.1142/S0218339018500262
Abstract: Successful immunologic control of HIV infection can be achieved in long-term non-progressors or HIV-1 controllers. Dendritic cells (DCs) are required for specific antigen presentation to naïve T lymphocytes and for antiviral, type I interferon secretion. To understand this mechanism, we develop a mathematical model that describes the role of direct presentation (replicating virus-infected DCs or other [Formula: see text] T cells directly) and cross presentation (DCs obtain antigen processed in other infected cells such as [Formula: see text] T lymphocytes) during HIV-1 infection. We find equilibria and determine stability in the case of no vaccination, and then, when vaccination is taken, we determine analytical thresholds for the strength and frequency of the vaccine to ensure the disease-free equilibrium remains stable. Our theoretical results suggest that the restoration of DC numbers may be predictive of immune restoration and may be a goal for immunotherapy to enhance viral control in a larger proportion of patients.
Publisher: Springer Science and Business Media LLC
Date: 04-03-2011
DOI: 10.1186/1471-2458-11-S2-S5
Abstract: Training is a key component of building capacity for public health surveillance and response, but has often been difficult to quantify. During fiscal 2009, the Armed Forces Health Surveillance Center, Division of Global Emerging Infections Surveillance and Response System (AFHSC-GEIS) supported 18 partner organizations in conducting 123 training initiatives in 40 countries for 3,130 U.S. military, civilian and host-country personnel. The training assisted with supporting compliance with International Health Regulations, IHR (2005). Training activities in pandemic preparedness, outbreak investigation and response, emerging infectious disease (EID) surveillance and pathogen diagnostic techniques were expanded significantly. By engaging local health and other government officials and civilian institutions, the U.S. military’s role as a key stakeholder in global public health has been strengthened and has contributed to EID-related surveillance, research and capacity-building initiatives specified elsewhere in this issue. Public health and emerging infections surveillance training accomplished by AFHSC-GEIS and its Department of Defense (DoD) partners during fiscal 2009 will be tabulated and described.
Publisher: Springer Science and Business Media LLC
Date: 09-2004
Publisher: MDPI AG
Date: 06-12-2021
DOI: 10.3390/V13122450
Abstract: Equine infectious anemia virus (EIAV) is a lentivirus similar to HIV that infects horses. Clinical and experimental studies demonstrating immune control of EIAV infection hold promise for efforts to produce an HIV vaccine. Antibody infusions have been shown to block both wild-type and mutant virus infection, but the mutant sometimes escapes. Using these data, we develop a mathematical model that describes the interactions between antibodies and both wild-type and mutant virus populations, in the context of continual virus mutation. The aim of this work is to determine whether repeated vaccinations through antibody infusions can reduce both the wild-type and mutant strains of the virus below one viral particle, and if so, to examine the vaccination period and number of infusions that ensure eradication. The antibody infusions are modelled using impulsive differential equations, a technique that offers insight into repeated vaccination by approximating the time-to-peak by an instantaneous change. We use impulsive theory to determine the maximal vaccination intervals that would be required to reduce the wild-type and mutant virus levels below one particle per horse. We show that seven boosts of the antibody vaccine are sufficient to eradicate both the wild-type and the mutant strains. In the case of a mutant virus infection that is given infusions of antibodies targeting wild-type virus (i.e., simulation of a heterologous infection), seven infusions were likewise sufficient to eradicate infection, based upon the data set. However, if the period between infusions was sufficiently increased, both the wild-type and mutant virus would eventually persist in the form of a periodic orbit. These results suggest a route forward to design antibody-based vaccine strategies to control viruses subject to mutant escape.
Publisher: Springer Science and Business Media LLC
Date: 07-01-2010
DOI: 10.1057/STH.2009.18
Publisher: Ovid Technologies (Wolters Kluwer Health)
Date: 18-11-2005
Publisher: Elsevier BV
Date: 04-2008
DOI: 10.1016/J.MBS.2008.02.001
Abstract: To stimulate the immune system's natural defenses, a post-infection HIV vaccination program to regularly boost cytotoxic T-lymphocytes has been proposed. We develop a mathematical model to describe such a vaccination program, where the strength of the vaccine and the vaccination intervals are constant. We apply the theory of impulsive differential equations to show that the model has an orbitally asymptotically stable periodic orbit, with the property of asymptotic phase. We show that, on this orbit, the vaccination frequency can be chosen so that the average number of infected CD4(+) T cells can be made arbitrarily low. We illustrate the results with numerical simulations and show that the model is robust with respect to both the parameter choices and the formulation of the model as a system of impulsive differential equations.
Publisher: American Medical Association (AMA)
Date: 11-11-2009
Publisher: American Society of Clinical Oncology (ASCO)
Date: 2021
DOI: 10.1200/JCO.20.01933
Abstract: As cancer surgery restarts after the first COVID-19 wave, health care providers urgently require data to determine where elective surgery is best performed. This study aimed to determine whether COVID-19–free surgical pathways were associated with lower postoperative pulmonary complication rates compared with hospitals with no defined pathway. This international, multicenter cohort study included patients who underwent elective surgery for 10 solid cancer types without preoperative suspicion of SARS-CoV-2. Participating hospitals included patients from local emergence of SARS-CoV-2 until April 19, 2020. At the time of surgery, hospitals were defined as having a COVID-19–free surgical pathway (complete segregation of the operating theater, critical care, and inpatient ward areas) or no defined pathway (incomplete or no segregation, areas shared with patients with COVID-19). The primary outcome was 30-day postoperative pulmonary complications (pneumonia, acute respiratory distress syndrome, unexpected ventilation). Of 9,171 patients from 447 hospitals in 55 countries, 2,481 were operated on in COVID-19–free surgical pathways. Patients who underwent surgery within COVID-19–free surgical pathways were younger with fewer comorbidities than those in hospitals with no defined pathway but with similar proportions of major surgery. After adjustment, pulmonary complication rates were lower with COVID-19–free surgical pathways (2.2% v 4.9% adjusted odds ratio [aOR], 0.62 95% CI, 0.44 to 0.86). This was consistent in sensitivity analyses for low-risk patients (American Society of Anesthesiologists grade 1/2), propensity score–matched models, and patients with negative SARS-CoV-2 preoperative tests. The postoperative SARS-CoV-2 infection rate was also lower in COVID-19–free surgical pathways (2.1% v 3.6% aOR, 0.53 95% CI, 0.36 to 0.76). Within available resources, dedicated COVID-19–free surgical pathways should be established to provide safe elective cancer surgery during current and before future SARS-CoV-2 outbreaks.
Publisher: Springer Science and Business Media LLC
Date: 10-02-2016
DOI: 10.1007/S00285-016-0971-Y
Abstract: Depopulation of birds has always been an effective method not only to control the transmission of avian influenza in bird populations but also to eliminate influenza viruses. We introduce a Filippov avian-only model with culling of susceptible and/or infected birds. For each susceptible threshold level [Formula: see text], we derive the phase portrait for the dynamical system as we vary the infected threshold level [Formula: see text], focusing on the existence of endemic states the endemic states are represented by real equilibria, pseudoequilibria and pseudo-attractors. We show generically that all solutions of this model will approach one of the endemic states. Our results suggest that the spread of avian influenza in bird populations is tolerable if the trajectories converge to the equilibrium point that lies in the region below the threshold level [Formula: see text] or if they converge to one of the pseudoequilibria or a pseudo-attractor on the surface of discontinuity. However, we have to cull birds whenever the solution of this model converges to an equilibrium point that lies in the region above the threshold level [Formula: see text] in order to control the outbreak. Hence a good threshold policy is required to combat bird flu successfully and to prevent overkilling birds.
Publisher: Springer Science and Business Media LLC
Date: 11-2009
Publisher: Elsevier BV
Date: 06-2016
DOI: 10.1016/J.MBS.2016.03.009
Abstract: There is an urgent need for more understanding of the effects of surveillance on malaria control. Indoor residual spraying has had beneficial effects on global malaria reduction, but resistance to the insecticide poses a threat to eradication. We develop a model of impulsive differential equations to account for a resistant strain of mosquitoes that is entirely immune to the insecticide. The impulse is triggered either due to periodic spraying or when a critical number of malaria cases are detected. For small mutation rates, the mosquito-only submodel exhibits either a single mutant-only equilibrium, a mutant-only equilibrium and a single coexistence equilibrium, or a mutant-only equilibrium and a pair of coexistence equilibria. Bistability is a likely outcome, while the effect of impulses is to introduce a saddle-node bifurcation, resulting in persistence of malaria in the form of impulsive periodic orbits. If certain parameters are small, triggering the insecticide based on number of malaria cases is asymptotically equivalent to spraying periodically.
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2018
DOI: 10.3934/MBE.2018060
Abstract: Hepatitis B virus (HBV) is responsible for an estimated 378 million infections worldwide and 620, 000 deaths annually. Safe and effective vaccination programs have been available for decades, but coverage is limited due to economic and social factors. We investigate the effect of immigration and infection age on HBV transmission dynamics, incorporating age-dependent immigration flow and vertical transmission. The mathematical model can be used to describe HBV transmission in highly endemic regions with vertical transmission and migration of infected HBV in iduals. Due to the effects of immigration, there is no disease-free equilibrium or reproduction number. We show that the unique endemic equilibrium exists only when immigration into the infective class is measurable. The smoothness and attractiveness of the solution semiflow are analyzed, and boundedness and uniform persistence are determined. Global stability of the unique endemic equilibrium is shown by a Lyapunov functional for a special case.
Publisher: Ovid Technologies (Wolters Kluwer Health)
Date: 04-03-2005
DOI: 10.1097/01.AIDS.0000161771.44276.92
Abstract: The following questions were addressed: would the introduction of vaginal microbicides substantially reduce the risk of female sex workers (FSWs) acquiring HIV? Which factor would it be most important to maximize, microbicide efficacy or microbicide use? What level of microbicide efficacy and use would be necessary to counterbalance a possible reduction in condom use? Mathematical modeling, with parameter estimations from available literature. Risk equations were developed and Monte Carlo simulations were performed to model a FSW's daily risk of HIV acquisition currently, and after, microbicide introduction. Uncertainty and sensitivity analyses were used as well as tornado plots for two ranges of microbicide efficacy (30-50%) and (50-80%). Risk was estimated for FSWs whose clients sometimes (10-50%) use condoms, and those whose clients never use condoms. An analytical threshold for which reducing condom use increases risk was estimated. For both groups of FSWs, daily risk would decrease by approximately 17% or approximately 28% using 30-50% or 50-80% effective microbicides, respectively. Increasing microbicide use would have greater impact on reducing risk than increasing microbicide efficacy. The microbicide efficacy and usage required to ensure that 'condom replacement' does not increase a FSW's risk of acquiring HIV was calculated. Microbicides could substantially reduce FSWs' risk of acquiring HIV absolute decrease in risk would be greatest in high-prevalence regions. The public health impact of microbicides will depend upon usage and efficacy. Even if the microbicides that become available are only low-to-moderately effective, the probability that risk in FSWs will increase (due to replacing condoms with microbicides) is low.
Publisher: Springer Science and Business Media LLC
Date: 07-08-2019
DOI: 10.1007/S12064-019-00297-Z
Abstract: A non-smooth epidemic model with piecewise incidence rate dependent on the derivative of the case number is proposed for the transmission dynamics of an infectious disease with media coverage, enhanced vaccination and treatment policy. This is an implicitly defined system, which is converted into an explicit system with three thresholds by employing the properties of the Lambert W function. We first analyze the dynamics of the proposed model for the limiting case, which induces two non-smooth but continuous models. The dynamic analysis of the model demonstrates that either one of the two generalized equilibria or the pseudo-equilibrium is globally asymptotically stable if the disease does not die out. This suggests that the case number can be contained either at an a priori level or at a high/low level, depending on the threshold, which governs whether the enhanced vaccination and treatment policies are implemented. Media coverage cannot help eradicate the disease, but it significantly delays the epidemic peak and lowers the peak case number. Hence, a good threshold policy and continuously updating the awareness of case numbers are required to combat the disease successfully.
Publisher: Elsevier BV
Date: 10-2016
Publisher: CMA Joule Inc.
Date: 07-12-2009
DOI: 10.1503/CMAJ.091704
Publisher: Oxford University Press
Date: 09-2011
Publisher: Springer Singapore
Date: 2020
Location: United States of America
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Frances Wensley.