The transmission of the contagious COVID-19 is known to be highly dependent on individual viral dynamics. Since the cycle threshold (Ct) is the only semi-quantitative viral measurement that could reflect infectivity, we utilized Ct values to forecast COVID-19 incidences. Our COVID-19 cohort (n 9531), retrieved from a single representative cross-sectional virology test center in Lebanon, revealed that low daily mean Ct values are followed by an increase in the number of national positive COVID-19 cases. A subset of the data was used to develop a deep neural network model, tune its hyperparameters, and optimize the weights for minimal mean square error of prediction. The final model's accuracy is reported by comparing its predictions with an unseen dataset.

During the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic, polymerase chain reaction (PCR) tests were generally reported only as binary positive or negative outcomes. However, these test results contain a great deal more information than that. As viral load declines exponentially, the PCR cycle threshold (Ct) increases linearly. Hay et al. developed an approach for extracting epidemiological information out of the Ct values obtained from PCR tests used in surveillance for a variety of settings (see the Perspective by Lopman and McQuade). Although there are challenges to relying on single Ct values for individual-level decision-making, even a limited aggregation of data from a population can inform on the trajectory of the pandemic. Therefore, across a population, an increase in aggregated Ct values indicates that a decline in cases is occurring. Science , abh0635, this issue p. [eabh0635][1]; see also abj4185, p. [280][2] ### INTRODUCTION Current approaches to epidemic monitoring rely on case counts, test positivity rates, and reported deaths or hospitalizations. These metrics, however, provide a limited and often biased picture as a result of testing constraints, unrepresentative sampling, and reporting delays. Random cross-sectional virologic surveys can overcome some of these biases by providing snapshots of infection prevalence but currently offer little information on the epidemic trajectory without sampling across multiple time points. ### RATIONALE We develop a new method that uses information inherent in cycle threshold (Ct) values from reverse transcription quantitative polymerase chain reaction (RT-qPCR) tests to robustly estimate the epidemic trajectory from multiple or even a single cross section of positive samples. Ct values are related to viral loads, which depend on the time since infection; Ct values are generally lower when the time between infection and sample collection is short. Despite variation across individuals, samples, and testing platforms, Ct values provide a probabilistic measure of time since infection. We find that the distribution of Ct values across positive specimens at a single time point reflects the epidemic trajectory: A growing epidemic will necessarily have a high proportion of recently infected individuals with high viral loads, whereas a declining epidemic will have more individuals with older infections and thus lower viral loads. Because of these changing proportions, the epidemic trajectory or growth rate should be inferable from the distribution of Ct values collected in a single cross section, and multiple successive cross sections should enable identification of the longer-term incidence curve. Moreover, understanding the relationship between sample viral loads and epidemic dynamics provides additional insights into why viral loads from surveillance testing may appear higher for emerging viruses or variants and lower for outbreaks that are slowing, even absent changes in individual-level viral kinetics. ### RESULTS Using a mathematical model for population-level viral load distributions calibrated to known features of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) viral load kinetics, we show that the median and skewness of Ct values in a random sample change over the course of an epidemic. By formalizing this relationship, we demonstrate that Ct values from a single random cross section of virologic testing can estimate the time-varying reproductive number of the virus in a population, which we validate using data collected from comprehensive SARS-CoV-2 testing in long-term care facilities. Using a more flexible approach to modeling infection incidence, we also develop a method that can reliably estimate the epidemic trajectory in even more-complex populations, where interventions may be implemented and relaxed over time. This method performed well in estimating the epidemic trajectory in the state of Massachusetts using routine hospital admissions RT-qPCR testing data—accurately replicating estimates from other sources for the entire state. ### CONCLUSION This work provides a new method for estimating the epidemic growth rate and a framework for robust epidemic monitoring using RT-qPCR Ct values that are often simply discarded. By deploying single or repeated (but small) random surveillance samples and making the best use of the semiquantitative testing data, we can estimate epidemic trajectories in real time and avoid biases arising from nonrandom samples or changes in testing practices over time. Understanding the relationship between population-level viral loads and the state of an epidemic reveals important implications and opportunities for interpreting virologic surveillance data. It also highlights the need for such surveillance, as these results show how to use it most informatively. ![Figure][3] Ct values reflect the epidemic trajectory and can be used to estimate incidence. ( A and B ) Whether an epidemic has rising or falling incidence will be reflected in the distribution of times since infection (A), which in turn affects the distribution of Ct values in a surveillance sample (B). ( C ) These values can be used to assess whether the epidemic is rising or falling and estimate the incidence curve. Estimating an epidemic’s trajectory is crucial for developing public health responses to infectious diseases, but case data used for such estimation are confounded by variable testing practices. We show that the population distribution of viral loads observed under random or symptom-based surveillance—in the form of cycle threshold (Ct) values obtained from reverse transcription quantitative polymerase chain reaction testing—changes during an epidemic. Thus, Ct values from even limited numbers of random samples can provide improved estimates of an epidemic’s trajectory. Combining data from multiple such samples improves the precision and robustness of this estimation. We apply our methods to Ct values from surveillance conducted during the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic in a variety of settings and offer alternative approaches for real-time estimates of epidemic trajectories for outbreak management and response. [1]: /lookup/doi/10.1126/science.abh0635 [2]: /lookup/doi/10.1126/science.abj4185 [3]: pending:yes

Within epidemiological modeling, the majority of analyses assume a single epidemic process for generating ground-truth data. However, this assumed data generation process can be unrealistic, since data sources for epidemics are often aggregated across geographic regions and communities. As a result, state-of-the-art models for estimating epidemiological parameters, e.g.~transmission rates, can be inappropriate when faced with complex systems. Our work empirically demonstrates some limitations of applying epidemiological models to aggregated datasets. We generate three complex outbreak scenarios by combining incidence curves from multiple epidemics that are independently simulated via SEIR models with different sets of parameters. Using these scenarios, we assess the robustness of a state-of-the-art Bayesian inference method that estimates the epidemic trajectory from viral load surveillance data. We evaluate two data-generating models within this Bayesian inference framework: a simple exponential growth model and a highly flexible Gaussian process prior model. Our results show that both models generate accurate transmission rate estimates for the combined incidence curve at the cost of generating biased estimates for each underlying epidemic, reflecting highly heterogeneous underlying population dynamics. The exponential growth model, while interpretable, is unable to capture the complexity of the underlying epidemics. With sufficient surveillance data, the Gaussian process prior model captures the shape of complex trajectories, but is imprecise for periods of low data coverage. Thus, our results highlight the potential pitfalls of neglecting complexity and heterogeneity in the data generation process, which can mask underlying location- and population-specific epidemic dynamics.

Computed tomography (CT) equivalent information is needed for attenuation correction in PET imaging and for dose planning in radiotherapy. Prior work has shown that Gaussian mixture models can be used to generate a substitute CT (s-CT) image from a specific set of MRI modalities. This work introduces a more flexible class of mixture models for s-CT generation, that incorporates spatial dependency in the data through a Markov random field prior on the latent field of class memberships associated with a mixture model. Furthermore, the mixture distributions are extended from Gaussian to normal inverse Gaussian (NIG), allowing heavier tails and skewness. The amount of data needed to train a model for s-CT generation is of the order of 100 million voxels. The computational efficiency of the parameter estimation and prediction methods are hence paramount, especially when spatial dependency is included in the models. A stochastic Expectation Maximization (EM) gradient algorithm is proposed in order to tackle this challenge. The advantages of the spatial model and NIG distributions are evaluated with a cross-validation study based on data from 14 patients. The study show that the proposed model enhances the predictive quality of the s-CT images by reducing the mean absolute error with 17.9%. Also, the distribution of CT values conditioned on the MR images are better explained by the proposed model as evaluated using continuous ranked probability scores.