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Mathematical Tools for Understanding Infectious Disease Dynamics
Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods.
Mathematical Tools for Understanding Infectious Disease Dynamicsfully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided.
Covers the latest research in mathematical modeling of infectious disease epidemiologyIntegrates deterministic and stochastic approachesTeaches skills in model construction, analysis, inference, and interpretationFeatures numerous exercises and their detailed elaborationsMotivated by real-world applications throughout
eBook
More Than Food: The Social Benefits of Localised Urban Food Systems
Localized urban food systems are gaining attention from policy makers, planners, and advocates for benefits that go well beyond food production and consumption. Recognizing that agriculture, and food systems more broadly, provide multiple, integrated services, this study measures the social, educational, civic, and nutritional impacts of four common types of local food system activity in an urban setting. Specifically, we examine the outcomes of two common types of urban agricultural production (home gardens and community gardens) and two common types of direct markets (farmers' markets and Community Supported Agriculture programs or CSAs) through a survey of 424 gardeners and 450 direct market shoppers in California's San Francisco Bay Area. Our comparative analysis focuses on four commonly discussed functions of agricultural production and direct marketing in urban areas: access to high-quality, fresh produce; food and agriculture education; social connections; and civic engagement. While impacts on nutrition were consistently high, some of the largest differences between types of local food system activity were in social interaction and civic engagement. For example, gardeners had a mean score of 3.77 on the social interaction scale compared to direct market participants, who had a mean score of 3.03. These findings confirm that different types of local production and direct marketing have distinct impacts on participants. Generally, gardens, which involve more sustained engagement with other people and the natural world, were sites of greater learning, connection, and civic participation than either type of direct marketing.
Journal Article
Waning and boosting: on the dynamics of immune status
The aim is to describe the distribution of immune status (as captured by antibody level) on the basis of a within-host submodel for continuous waning and occasional boosting. Inspired by Feller’s fundamental work and the more recent delay equation formulation of models for the dynamics of physiologically structured populations, we derive, for given force of infection, a linear renewal equation. The solution is obtained by generation expansion, with the generation number corresponding to the number of times the individual became infected. Our main result provides a precise characterization of the stable distribution of immune status.
Journal Article
Can a Species Keep Pace with a Shifting Climate?
Consider a patch of favorable habitat surrounded by unfavorable habitat and assume that due to a shifting climate, the patch moves with a fixed speed in a one-dimensional universe. Let the patch be inhabited by a population of individuals that reproduce, disperse, and die. Will the population persist? How does the answer depend on the length of the patch, the speed of movement of the patch, the net population growth rate under constant conditions, and the mobility of the individuals? We will answer these questions in the context of a simple dynamic profile model that incorporates climate shift, population dynamics, and migration. The model takes the form of a growth-diffusion equation. We first consider a special case and derive an explicit condition by glueing phase portraits. Then we establish a strict qualitative dichotomy for a large class of models by way of rigorous PDE methods, in particular the maximum principle. The results show that mobility can both reduce and enhance the ability to track climate change that a narrow range can severely reduce this ability and that population range and total population size can both increase and decrease under a moving climate. It is also shown that range shift may be easier to detect at the expanding front, simply because it is considerably steeper than the retreating back.
Journal Article
Separable mixing: The general formulation and a particular example focusing on mask efficiency
The aim of this short note is twofold. First, we formulate the general Kermack-McKendrick epidemic model incorporating static heterogeneity and show how it simplifies to a scalar Renewal Equation (RE) when separable mixing is assumed. A key general feature is that all information about the heterogeneity is encoded in one nonlinear real valued function of a real variable. Next, we specialize the model ingredients so that we can study the efficiency of mask wearing as a non-pharmaceutical intervention to reduce the spread of an infectious disease. Our main result affirms that the best way to protect the population as a whole is to protect yourself. This qualitative insight was recently derived in the context of an SIR network model. Here, we extend the conclusion to proportionate mixing models incorporating a general function describing expected infectiousness as a function of time since infection.
Journal Article
Controlling Methicillin-Resistant Staphylococcus aureus: Quantifying the Effects of Interventions and Rapid Diagnostic Testing
Control of nosocomial transmission of methicillin-resistant Staphylococcus aureus (MRSA) has been unsuccessful in most countries. Yet, some countries have maintained low endemic levels by implementing nationwide MRSA-specific infection control measures, such as \"search & destroy\" (S&D). These strategies, however, are not based on well designed studies, and their use in countries with high levels of endemicity is controversial. We present a stochastic three-hospital model and an analytical one-hospital model to quantify the effectiveness of different infection control measures and to predict the effects of rapid diagnostic testing (RDT) on isolation needs. Isolation of MRSA carriers identified by clinical cultures is insufficient to control MRSA. However, combined with proactive search (of high-risk patients on admission and/or contacts of index patients), it will maintain prevalence levels <1%. Concerted implementation of S&D in countries with high nosocomial endemicity reduces nosocomial prevalence to <1% within 6 years. Stepwise implementation of control measures can reduce isolation capacities needed. RDT can reduce isolation needs by >90% in low-endemic settings and by 20% in high-endemic settings. Surveillance of colonization and improved hand hygiene can markedly increase control efficacy. These findings strongly suggest that: (I) causality exists between S&D and low MRSA prevalence; (ii) isolating MRSA carriers identified by clinical cultures as a single measure is insufficient for control; (ii,) a combined approach of isolation and screening confers efficacy; and (iv) MRSA-prevalence levels can be reduced to <1% in high-endemic settings by S&D or a stepwise approach to interventions. RDT can markedly enhance feasibility.
Journal Article
Population genetics of dwarf eelgrass Zostera noltii throughout its biogeographic range
The marine angiosperm Zostera noltii (dwarf eelgrass), an important facilitator species and food source for invertebrates and waterfowl, predominantly inhabits intertidal habitats along eastern Atlantic shores from Mauritania to southern Norway/Kattegat Sea and throughout the Mediterranean, Black and Azov seas. We used 9 microsatellite loci to characterize population structure at a variety of spatial scales among 33 populations from 11 localities throughout the entire biogeographic range. Isolation by distance analysis suggested a panmictic genetic neighborhood of 100 to 150 km. At the global scale, a neighbor-joining tree based on Reynolds distances revealed strongly-supported groups corresponding to northern Europe, Mauritania and the Black/Azov Sea; separate Mediterranean and Atlantic-Iberian groups were poorly supported. Clones (genets with multiple ramets) were present in most populations but were generally small (ca. <3 m2). Exceptions were found in Mauritania (ca. 29 m in length), the Azov Sea (ca. 40 m in length) and the Black Sea (ca. 50 m in length). Although genetic diversity and allelic richness generally decreased from Mauritania to Denmark, the putative post-glacial recolonization route, both were unexpectedly high among populations from the German Wadden Sea.
Journal Article
Growing ‘good food’
With food security increasingly seen as an urban concern, urban agriculture (UA) has emerged as one strategy for improving access to healthy, affordable food within cities in the Global North. This research evaluates the contributions of three types of urban gardens in Santa Clara County, California, to food security. Survey, interview and harvest data were collected from home gardeners, community gardeners and gardeners participating in community food security (CFS) programs, which provide low-income families with the materials and training to grow their own vegetables. To assess food security we use a multi-dimensional framework that encompasses food availability, accessibility, nutritional adequacy and cultural acceptability as well as agency within the food system. Over the summer of 2015, median garden production ranged from 26 kg for participants in CFS programs to 56 kg for home gardeners. All garden types produced enough produce for at least one adult to consume the number of cups of vegetables recommended by federal nutritional guidelines. Gardening also increased some low-income gardeners’ access to healthy food, allowing them to have the diet they wanted—one high in organically grown vegetables—but could not otherwise afford to purchase. Interviews showed that gardeners do not think of cultural acceptability strictly in terms of the presence of certain types of cultural crops; they also articulated a broader set of values concerning the environmental and social conditions of food production. At all income levels, gardeners frequently described a set of food values related to knowledge, control, trust, freshness, flavor, organic production methods and sharing, which they were able to enact through gardening. Taken together, these findings demonstrate the nutritional contributions that urban gardens make but also highlight the importance that low-income gardeners place on having food that aligns with their cultural and ethical values and being able to exercise greater autonomy in making food choices. In conclusion, we suggest that more robust, holistic assessments of UA’s contributions to food security will include the subjective aspects of food as well as quantitative measures related to food production.
Journal Article
Population genetics of Zostera noltii along the west Iberian coast: Consequences of small population size, habitat discontinuity and near-shore currents
The effects of oceanographic patterns on marine genetic biodiversity along the SW Iberian Peninsula are poorly understood. We addressed the question of whether gene flow in this region depends solely on geographic distance between isolated patches of suitable habitat or if there are superimposed effects correlated with other factors such as current patterns. Zostera noltii, the dwarf eelgrass, is the keystone habitat-structuring seagrass species on intertidal mudflats along the Iberian west coast. We used 9 microsatellite loci to analyze population genetic diversity and differentiation for all existing 8 populations from NW Spain (Ria de Vigo) to SW Spain (Puerto Real, Cadiz). Populations are highly genetically differentiated as shown by high significant FST,Wright’s fixation index, (0.08 to 0.26) values. A neighbor-joining tree based on Reynold’s distances computed from allele frequencies revealed a split between northern and southern populations (bootstrap support of 84%). This pattern of differentiation can be explained by (1) ocean surface current patterns present during Z. noltii’s reproductive season which cause a dispersal barrier between the northern and southern populations of this region, (2) habitat isolation, due to large geographic distances between suitable habitats, preventing frequent gene flow, and (3) small effective population sizes, causing high drift and thus faster differentiation rates.
Journal Article