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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

The transmission heterogeneity of an epidemic is associated with a complex mixture of host, pathogen and environmental factors. And it may indicate superspreading events to reduce the efficiency of population-level control measures and to sustain the epidemic over a larger scale and a longer duration. Methods have been proposed to identify significant transmission heterogeneity in historic epidemics based on several data sources, such as contact history, viral genomes and spatial information, which may not be available, and more importantly ignore the temporal trend of transmission heterogeneity. Here we attempted to establish a convenient method to estimate real-time heterogeneity over an epidemic. Within the branching process framework, we introduced an instant-individualheterogenous infectiousness model to jointly characterize the variation in infectiousness both between individuals and among different times. With this model, we could simultaneously estimate the transmission heterogeneity and the reproduction number from incidence time series. We validated the model with data of both simulated and real outbreaks. Our estimates of the overall and real-time heterogeneities of the six epidemics were consistent with those presented in the literature. Additionally, our model is robust to the ubiquitous bias of under-reporting and misspecification of serial interval. By analyzing recent data from South Africa, we found evidence that the Omicron might be of more significant transmission heterogeneity than Delta. Our model based on incidence data was proved to be reliable in estimating the real-time transmission heterogeneity.

Adipocyte Turnover: Relevance to Human Adipose Tissue Morphology Erik Arner 1 , Pål O. Westermark 2 , Kirsty L. Spalding 3 , Tom Britton 4 , Mikael Rydén 1 , Jonas Frisén 3 , Samuel Bernard 5 and Peter Arner 1 1 Department of Medicine, Karolinska Institutet at Karolinska University Hospital, Stockholm, Sweden; 2 Institute for Theoretical Biology, Humboldt University Berlin and Charité, Berlin, Germany; 3 Department of Cell and Molecular Biology, Karolinska Institutet, Stockholm, Sweden; 4 Department of Mathematics, Stockholm University, Stockholm, Sweden; 5 Institut Camille Jordan, University of Lyon, Villeurbanne, France. Corresponding author: Peter Arner, peter.arner{at}ki.se . Abstract OBJECTIVE Adipose tissue may contain few large adipocytes (hypertrophy) or many small adipocytes (hyperplasia). We investigated factors of putative importance for adipose tissue morphology. RESEARCH DESIGN AND METHODS Subcutaneous adipocyte size and total fat mass were compared in 764 subjects with BMI 18–60 kg/m 2 . A morphology value was defined as the difference between the measured adipocyte volume and the expected volume given by a curved-line fit for a given body fat mass and was related to insulin values. In 35 subjects, in vivo adipocyte turnover was measured by exploiting incorporation of atmospheric 14 C into DNA. RESULTS Occurrence of hyperplasia (negative morphology value) or hypertrophy (positive morphology value) was independent of sex and body weight but correlated with fasting plasma insulin levels and insulin sensitivity, independent of adipocyte volume (β-coefficient = 0.3, P < 0.0001). Total adipocyte number and morphology were negatively related ( r = −0.66); i.e., the total adipocyte number was greatest in pronounced hyperplasia and smallest in pronounced hypertrophy. The absolute number of new adipocytes generated each year was 70% lower ( P < 0.001) in hypertrophy than in hyperplasia, and individual values for adipocyte generation and morphology were strongly related ( r = 0.7, P < 0.001). The relative death rate (∼10% per year) or mean age of adipocytes (∼10 years) was not correlated with morphology. CONCLUSIONS Adipose tissue morphology correlates with insulin measures and is linked to the total adipocyte number independently of sex and body fat level. Low generation rates of adipocytes associate with adipose tissue hypertrophy, whereas high generation rates associate with adipose hyperplasia. Footnotes The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. Received June 26, 2009. Accepted October 8, 2009. © 2010 American Diabetes Association

The real-time analysis of infectious disease surveillance data is essential in obtaining situational awareness about the current dynamics of a major public health event such as the COVID-19 pandemic. This analysis of e.g., time-series of reported cases or fatalities is complicated by reporting delays that lead to under-reporting of the complete number of events for the most recent time points. This can lead to misconceptions by the interpreter, for instance the media or the public, as was the case with the time-series of reported fatalities during the COVID-19 pandemic in Sweden. Nowcasting methods provide real-time estimates of the complete number of events using the incomplete time-series of currently reported events and information about the reporting delays from the past. In this paper we propose a novel Bayesian nowcasting approach applied to COVID-19-related fatalities in Sweden. We incorporate additional information in the form of time-series of number of reported cases and ICU admissions as leading signals. We demonstrate with a retrospective evaluation that the inclusion of ICU admissions as a leading signal improved the nowcasting performance of case fatalities for COVID-19 in Sweden compared to existing methods.

Many empirical studies have revealed considerable differences between nonparametric bootstrapping and Bayesian posterior probabilities in terms of the support values for branches, despite claimed predictions about their approximate equivalence. We investigated this problem by simulating data, which were then analyzed by maximum likelihood bootstrapping and Bayesian phylogenetic analysis using identical models and reoptimization of parameter values. We show that Bayesian posterior probabilities are significantly higher than corresponding nonparametric bootstrap frequencies for true clades, but also that erroneous conclusions will be made more often. These errors are strongly accentuated when the models used for analyses are underparameterized. When data are analyzed under the correct model, nonparametric bootstrapping is conservative. Bayesian posterior probabilities are also conservative in this respect, but less so.

Phylogenetic inference is an attractive means to reconstruct transmission histories and epidemics. However, there is not a perfect correspondence between transmission history and virus phylogeny. Both node height and topological differences may occur, depending on the interaction between within-host evolutionary dynamics and between-host transmission patterns. To investigate these interactions, we added a within-host evolutionary model in epidemiological simulations and examined if the resulting phylogeny could recover different types of contact networks. To further improve realism, we also introduced patient-specific differences in infectivity across disease stages, and on the epidemic level we considered incomplete sampling and the age of the epidemic. Second, we implemented an inference method based on approximate Bayesian computation (ABC) to discriminate among three well-studied network models and jointly estimate both network parameters and key epidemiological quantities such as the infection rate. Our ABC framework used both topological and distance-based tree statistics for comparison between simulated and observed trees. Overall, our simulations showed that a virus time-scaled phylogeny (genealogy) may be substantially different from the between-host transmission tree. This has important implications for the interpretation of what a phylogeny reveals about the underlying epidemic contact network. In particular, we found that while the within-host evolutionary process obscures the transmission tree, the diversification process and infectivity dynamics also add discriminatory power to differentiate between different types of contact networks. We also found that the possibility to differentiate contact networks depends on how far an epidemic has progressed, where distance-based tree statistics have more power early in an epidemic. Finally, we applied our ABC inference on two different outbreaks from the Swedish HIV-1 epidemic.

Spread of HIV typically involves uneven transmission patterns where some individuals spread to a large number of individuals while others to only a few or none. Such transmission heterogeneity can impact how fast and how much an epidemic spreads. Further, more efficient interventions may be achieved by taking such transmission heterogeneity into account. To address these issues, we developed two phylogenetic methods based on virus sequence data: 1) to generally detect if significant transmission heterogeneity is present, and 2) to pinpoint where in a phylogeny high-level spread is occurring. We derive inference procedures to estimate model parameters, including the amount of transmission heterogeneity, in a sampled epidemic. We show that it is possible to detect transmission heterogeneity under a wide range of simulated situations, including incomplete sampling, varying levels of heterogeneity, and including within-host genetic diversity. When evaluating real HIV-1 data from different epidemic scenarios, we found a lower level of transmission heterogeneity in slowly spreading situations and a higher level of heterogeneity in data that included a rapid outbreak, while R0 and Sackin's index (overall tree shape statistic) were similar in the two scenarios, suggesting that our new method is able to detect transmission heterogeneity in real data. We then show by simulations that targeted prevention, where we pinpoint high-level spread using a coalescence measurement, is efficient when sequence data are collected in an ongoing surveillance system. Such phylogeny-guided prevention is efficient under both single-step contact tracing as well as iterative contact tracing as compared to random intervention.

An important task in combating the current Covid-19 pandemic lies in estimating the effect of different preventive measures. Here, we focus on the preventive effect of enforcing the use of face masks. Several publications study this effect, however, often using different measures such as: the relative attack rate in case-control studies, the effect on incidence growth/decline in a specific time frame and the effect on the number of infected in a given time frame. These measures all depend on community-specific features and are hence not easily transferred to other community settings. We argue that a more universal measure is the relative reduction in the reproduction number, which we call the face mask effect, E FM. It is shown how to convert the other measures to E FM. We also apply the methodology to four empirical studies using different effect-measures. When converted to estimates of E FM, all estimates lie between 15 and 40%, suggesting that mandatory face masks reduce the reproduction number by an amount in this range, when compared with no individuals wearing face masks.