ABSTRACT
The large proportion of asymptomatic patients is the major cause leading to the COVID-19 pandemic which is still a significant threat to the whole world. A six-dimensional ODE system (SEIAQR epidemical model) is established to study the dynamics of COVID-19 spreading considering infection by exposed, infected, and asymptomatic cases. The basic reproduction number derived from the model is more comprehensive including the contribution from the exposed, infected, and asymptomatic patients. For this more complex six-dimensional ODE system, we investigate the global and local stability of disease-free equilibrium, as well as the endemic equilibrium, whereas most studies overlooked asymptomatic infection or some other virus transmission features. In the sensitivity analysis, the parameters related to the asymptomatic play a significant role not only in the basic reproduction number R0. It is also found that the asymptomatic infection greatly affected the endemic equilibrium. Either in completely eradicating the disease or achieving a more realistic goal to reduce the COVID-19 cases in an endemic equilibrium, the importance of controlling the asymptomatic infection should be emphasized. The three-dimensional phase diagrams demonstrate the convergence point of the COVID-19 spreading under different initial conditions. In particular, massive infections will occur as shown in the phase diagram quantitatively in the case R0>1. Moreover, two four-dimensional contour maps of Rt are given varying with different parameters, which can offer better intuitive instructions on the control of the pandemic by adjusting policy-related parameters.
ABSTRACT
There is an urgent need for automated methods to assist accurate and effective assessment of COVID-19. Radiology and nucleic acid test (NAT) are complementary COVID-19 diagnosis methods. In this paper, we present an end-to-end multitask learning (MTL) framework (COVID-MTL) that is capable of automated and simultaneous detection (against both radiology and NAT) and severity assessment of COVID-19. COVID-MTL learns different COVID-19 tasks in parallel through our novel random-weighted loss function, which assigns learning weights under Dirichlet distribution to prevent task dominance; our new 3D real-time augmentation algorithm (Shift3D) introduces space variances for 3D CNN components by shifting low-level feature representations of volumetric inputs in three dimensions; thereby, the MTL framework is able to accelerate convergence and improve joint learning performance compared to single-task models. By only using chest CT scans, COVID-MTL was trained on 930 CT scans and tested on separate 399 cases. COVID-MTL achieved AUCs of 0.939 and 0.846, and accuracies of 90.23% and 79.20% for detection of COVID-19 against radiology and NAT, respectively, which outperformed the state-of-the-art models. Meanwhile, COVID-MTL yielded AUC of 0.800 ± 0.020 and 0.813 ± 0.021 (with transfer learning) for classifying control/suspected, mild/regular, and severe/critically-ill cases. To decipher the recognition mechanism, we also identified high-throughput lung features that were significantly related (P < 0.001) to the positivity and severity of COVID-19.