The outbreak of novel coronavirus-caused pneumonia (COVID-19) in Wuhan has attracted worldwide attention. Here, we propose a generalized SEIR model to analyze this epidemic. Based on the public data of National Health Commission of China from Jan. 20th to Feb. 9th, 2020, we reliably estimate key epidemic parameters and make predictions on the inflection point and possible ending time for 5 different regions. According to optimistic estimation, the epidemics in Beijing and Shanghai will end soon within two weeks, while for most part of China, including the majority of cities in Hubei province, the success of anti-epidemic will be no later than the middle of March. The situation in Wuhan is still very severe, at least based on public data until Feb. 15th. We expect it will end up at the beginning of April. Moreover, by inverse inference, we find the outbreak of COVID-19 in Mainland, Hubei province and Wuhan all can be dated back to the end of December 2019, and the doubling time is around two days at the early stage.

During the study of epidemics, one of the most significant and also challenging problems is to forecast the future trends, on which all follow-up actions of individuals and governments heavily rely. However, to pick out a reliable predictable model/method is far from simple, a rational evaluation of various possible choices is eagerly needed, especially under the severe threat of COVID-19 epidemics which is spreading worldwide right now. In this paper, based on the public COVID-19 data of seven provinces/cities in China reported during the spring of 2020, we make a systematical investigation on the forecast ability of eight widely used empirical functions, four statistical inference methods and five dynamical models widely used in the literature. We highlight the significance of a well balance between model complexity and accuracy, over-fitting and under-fitting, as well as model robustness and sensitivity. We further introduce the Akaike information criterion, root mean square errors and robustness index to quantify these three golden means and to evaluate various epidemic models/methods. Through extensive simulations, we find that the inflection point plays a crucial role in the choice of the size of dataset in forecasting. Before the inflection point, no model considered here could make a reliable prediction. We further notice the Logistic function steadily underestimate the final epidemic size, while the Gomertz's function makes an overestimation in all cases. Since the methods of sequential Bayesian and time-dependent reproduction number take the non-constant nature of the effective reproduction number with the progression of epidemics into consideration, we suggest to employ them especially in the late stage of an epidemic. The transition-like behavior of exponential growth method from underestimation to overestimation with respect to the inflection point might be useful for constructing a more reliable forecast. Towards the dynamical models based on ODEs, it is observed that the SEIR-QD and SEIR-PO models generally show a better performance than SIR, SEIR and SEIR-AHQ models on the COVID-19 epidemics, whose success could be attributed to the inclusion of self-protection and quarantine, and a proper trade-off between model complexity and fitting accuracy.

Due to the intrinsic complexity and nonlinearity of chemical reactions, direct applications of traditional machine learning algorithms may face many difficulties. In this study, through two concrete examples with biological background, we illustrate how the key ideas of multiscale modeling can help to greatly reduce the computational cost of machine learning, as well as how machine learning algorithms perform model reduction automatically in a time-scale separated system. Our study highlights the necessity and effectiveness of an integration of machine learning algorithms and multiscale modeling during the study of chemical reactions.

The Onsager's reciprocal relation plays a fundamental role in the nonequilibrium thermodynamics. However, unfortunately, its classical version is valid only within a narrow region near equilibrium due to the linear regression hypothesis, which largely restricts its usage. In this paper, based on the conservation-dissipation formalism, a generalized version of Onsager's relations for the master equations and Fokker-Planck equations was derived. Nonlinear constitutive relations with nonsymmetric and positively stable operators, which become symmetric under the detailed balance condition, constitute key features of this new generalization. Similar conclusions also hold for many other classical models in physics and chemistry, which in turn make the current study as a benchmark for the application of generalized Onsager's relations in nonequilibrium thermodynamics.

Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a “thermodynamic” theory can also be developed based on Tsallis' generalized entropy $S^{\left(q\right)}={\sum }_{i=1}^N(p_i-p_i^q)/\left[q(q-1)\right]$ and Shiino's generalized free energy $F^{\left(q\right)}=[{\sum }_{i=1}^N{p}_i{(p_i/{\pi }_i)}^{q-1}-1]/\left[q(q-1)\right]$, where ${\pi }_i$ is the stationary distribution. $d{F}^{\left(q\right)}/dt=-f_d^{\left(q\right)}\le 0$ and it is zero if and only if the system is in its stationary state. $d{S}^{\left(q\right)}/dt-Q_{\text{ex}}^{\left(q\right)}=f_d^{\left(q\right)}$, where $Q_{\text{ex}}^{\left(q\right)}$ characterizes the heat exchange. For systems approaching equilibrium with detailed balance, $f_d^{\left(q\right)}$ is the product of Onsager's thermodynamic flux and force. However, it is discovered that the Onsager's force is nonlocal. This is a consequence of the particular transformation invariance for zero energy of Tsallis' statistics.

The partial equilibrium approximation (PEA) and the quasi-steady-state approximation (QSSA) are two classical methods for reducing complex macroscopic chemical reactions into simple computable ones. Previous studies have primarily focused on the accuracy of solutions before and after applying model reduction. In this paper, however, we adopt a thermodynamic view and aim to establish a quantitative connection on the essential thermodynamic quantities, such as entropy production rate, free-energy dissipation rate, and entropy flow rate, between the original chemical mass-action equations and the reduced models obtained by PEA or QSSA. Our findings reveal that the reduced models by PEA and QSSA may not preserve the thermodynamic structure of the original full model, particularly when algebraic relations are used instead of differential equations. This is evident in the loss of non-negativity of the free-energy dissipation rate. To validate our results, we apply them to the Michaelis-Menten reactions as a prototype, both analytically and numerically. We anticipate that our study will inspire a reevaluation of the effectiveness of various model reduction or approximation methods from the perspective of nonequilibrium thermodynamics. Published by the American Physical Society 2024