Quantitative Biology

COVID-19 has been impacting on the whole world critically and constantly Since December 2019. We have independently developed a novel statistical time delay dynamic model on the basis of the distribution models from CCDC. Based only on the numbers of confirmed cases in different regions in China, the model can clearly reveal that the containment of the epidemic highly depends on early and effective isolation. We apply the model on the epidemic in Japan and conclude that there could be a rapid outbreak in Japan if no effective quarantine measures are carried out immediately.

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.

Multicellular organisms comprise various types of cells, which are characterized by gene expression through interactions between chromosomal DNA and nuclear proteins. Many cutting-edge methods have been developed to reveal the three-dimensional organization of chromosomes. The detailed analyses of whole chromosomes have begun to uncover structural features specific to several cell types. Here, we show that cell types are instantly and highly accurately classified using conventional DNA staining and a convolutional neural network (CNN). A high-resolution single slice image of the nucleus is sufficient for the accurate classification of both live and fixed cells, including neurons and non-neural cells. These findings suggest that there may be cell-type-specific features decipherable by deep learning in a thin two-dimensional slice of the nucleus.

Early non-pharmaceutical interventions (NPIs) are crucial to prevent and control of COVID-19 pandemic. We established a stochastic non-classical SEIR NPIs model (ScEIQRsh) which can quantify the three kinds of NPIs measures simultaneously to mimic the clustered intra-family or intra-acquaintance spreading pattern of COVID-19 under the effective integrated NPIs in Mainland China. Model simulation demonstrated that measures to diminish contactable susceptible (Sc), such as home confinement, travel constraint, social distancing etc. and measures to avoid delay of diagnosis and hospitalized isolation ({eta}) were more effective but consumptive than contact tracing ({kappa}, {rho}). From fitted model by MCMC method, the proportion of asymptomatic infectors was 14.88% (IQR 8.17%, 25.37%). The association between air temperature and the fitted transmission rate ({beta}) of COVID-19 suggests that COVID-19 pandemic would be seasonal with the optimal temperature range of 5{degrees}C-14{degrees}C and peak of 10{degrees}C for spreading, and vaccine is indispensable to ultimate prevention COVID-19.

The rapid expansion of COVID-19 has caused a global pandemic. Although quarantine measures have been used widely, the critical steps among them to suppress the outbreak without a huge social-economic loss remain unknown. Hong Kong, unlike other regions in the world, had a massive number of travellers from Mainland China during the early expansion period, and yet the spread of virus has been relatively limited. Understanding the effect of control measures to reduce the transmission in Hong Kong can improve the control of the virus spreading. We have developed a susceptible-exposed-infectious-quarantined-recovered (SEIQR) meta-population model that can stratify the infections into imported and subsequent local infections, and therefore to obtain the control effects on transmissibility in a region with many imported cases. We fitted the model to both imported and local confirmed cases with symptom onset from 18 January to 29 February 2020 in Hong Kong with daily transportation data and the transmission dynamics from Wuhan and Mainland China. The model estimated that the reproductive number was dropped from 2.32 to 0.76 (95% CI, 0.66 to 0.86) after an infected case was estimated to be quarantined half day before the symptom onset, corresponding to the incubation time of 5.43 days (95% CI, 1.30-9.47). If the quarantine happened about one day after the onset, community spread would be likely to occur, indicated by the reproductive number larger than one. The results suggest that the early quarantine for a suspected case before the symptom onset is a key factor to suppress COVID-19.

We proposed using Poisson mixtures model that utilized data of deaths, recoveries, and total confirmed cases in each day since the outbreak. We demonstrated that our CFR estimates for Hubei Province and other parts of China were superior to the simple CFR estimators in the early stage of COVID-19 outbreak.

An outbreak of a novel coronavirus (SARS-CoV-2)-infected pneumonia (COVID-19) was first diagnosed in Wuhan, China, in December 2019 and then spread rapidly to other regions. We collected the time series data of the cumulative number of confirmed infected, dead, and cured cases from the health commissions in 31 provinces in mainland China. A descriptive model in a logistic form was formulated to infer the intrinsic epidemic rules of COVID-19, which illustrates robustness spatially and temporally. Our model is robust (R2>0.95) to depict the intrinsic growth rule for the cumulative number of confirmed infected, dead, and cured cases in 31 provinces in mainland China. Furthermore, we compared the intrinsic epidemic rules of COVID-19 in Hubei with that of severe acute respiratory syndrome (SARS) in Beijing, which was obtained from the Ministry of Public Health of China in 2003. We found that the infected case is the earliest to be saturated and has the lowest semi-saturation period compared with deaths and cured cases for both COVID-19 and SARS. All the three types of SARS cases are later to saturate and have longer semi-saturation period than that of COVID-19. Despite the virus caused SARS (SARS-CoV) and the virus caused COVID-19 (SARS-CoV-2) are homologous, the duration of the outbreak would be shorter for COVID-19.

In this study, we propose a novel statistical method to predict a long-term epidemic evolution based on a on-going data. We developed a Bayesian framework for the Susceptible-Infected-Removed model (Bayesian SIR), and estimated its underlying parameters based on day-by-day timeseries of the cumulative number of infectious individuals. The new Baysian framework extends the deterministic SIR model to a probabilistic form, which provides an accurate estimation of the underlying system by a short and noisy data. We applied it to the data reported on the Coronavirus Disease 2019 (COVID-19), and made a month long prediction on its evolution. Our simulated test using past timeseries to predict the current data gives a reasonable reliablity of the proposed method. Our analysis of the current data detected and warned a rising trend in the countries in Central Asia, Middle East, and South America, while United States or European countries, which have already experienced large numbers of infected cases, are predicted to slow down in the increase.

It is of great theoretical and application value to accurately forecast the spreading dynamics of COVID-19 epidemic. We first proposed and established a Bayesian model to predict the epidemic spreading behavior. In this model, the infection probability matrix is estimated according to the individual contact frequency in certain population group. This infection probability matrix is highly correlated with population geographic distribution, population age structure and so on. This model can effectively avoid the prediction malfunction by using the traditional ordinary differential equation methods such as SIR (susceptible, infectious and recovered) model and so on. Meanwhile, it would forecast the epidemic distribution and predict the epidemic hot spots geographically at different time. According to the results revealed by Bayesian model, the effect of population geographical distribution should be considered in the prediction of epidemic situation, and there is no simple derivation relationship between the threshold of group immunity and the virus reproduction number R0. If we further consider the virus mutation effect and the antibody attenuation effect, with a large global population spatial distribution, it will be difficult for us to eliminate Covid-19 in a short time even with vaccination endeavor. Covid-19 may exist in human society for a long time, and the epidemic caused by re-infection is characterized by a wild-geometric && low-probability distribution with no epidemic hotspots.

The outbreak of coronavirus disease 2019 (COVID-19) which originated in Wuhan, China, constitutes a public health emergency of international concern with a very high risk of spread and impact at the global level. We developed data-driven susceptible-exposed-infectious-quarantine-recovered (SEIQR) models to simulate the epidemic with the interventions of social distancing and epicenter lockdown. Population migration data combined with officially reported data were used to estimate model parameters, and then calculated the daily exported infected individuals by estimating the daily infected ratio and daily susceptible population size. As of Jan 01, 2020, the estimated initial number of latently infected individuals was 380.1 (95%-CI: 379.8[~]381.0). With 30 days of substantial social distancing, the reproductive number in Wuhan and Hubei was reduced from 2.2 (95%-CI: 1.4[~]3.9) to 1.58 (95%-CI: 1.34[~]2.07), and in other provinces from 2.56 (95%-CI: 2.43[~]2.63) to 1.65 (95%-CI: 1.56[~]1.76). We found that earlier intervention of social distancing could significantly limit the epidemic in mainland China. The number of infections could be reduced up to 98.9%, and the number of deaths could be reduced by up to 99.3% as of Feb 23, 2020. However, earlier epicenter lockdown would partially neutralize this favorable effect. Because it would cause in situ deteriorating, which overwhelms the improvement out of the epicenter. To minimize the epidemic size and death, stepwise implementation of social distancing in the epicenter city first, then in the province, and later the whole nation without the epicenter lockdown would be practical and cost-effective.

Our main aim is to estimate the end of the first wave epidemic of COVID-19 outbreak in mainland China. We developed mathematical models to predict reasonable bounds on the date of end of the COVID-19 epidemics in mainland China with strong quarantine and testing measures for a sufficiently long time. We used reported data in China from January 20, 2020 to April 9, 2020. We firstly used a deterministic approach to obtain a formula to compute the probability distribution of the extinction date by combining the models and continuous-time Markov processes. Then we present the individual based model (IMB) simulations to compare the result by deterministic approach and show the absolute difference between the estimated cumulative probability distribution computed by simulations and formula. We provide the predictions of the end of the first wave epidemic for different fractions f of asymptomatic infectious that become reported symptomatic infectious.

Coronavirus disease (COVID-19) broke out in Wuhan, Hubei province, China, in December 2019 and soon after Chinese health authorities took unprecedented prevention and control measures to curb the spreading of the novel coronavirus-related pneumonia. We develop a mathematical model based on daily updates of reported cases to study the evolution of the epidemic. With the model, on 95% confidence level, we estimate the basic reproduction number, R0 = 2.82 {+/-} 0.11, time between March 19 and March 21 when the effective reproduction number becoming less than one, the epidemic ending after April 2 and the total number of confirmed cases approaching 14408 {+/-} 429 on the Chinese mainland excluding Hubei province.

As COVID-19 evolves rapidly, the issues the governments of affected countries facing are whether and when to take public health interventions and what levels of strictness of these interventions should be, as well as when the COVID-19 spread reaches the stopping point after interventions are taken. To help governments with policy-making, we developed modified auto-encoders (MAE) method to forecast spread trajectory of Covid-19 of countries affected, under different levels and timing of intervention strategies. Our analysis showed public health interventions should be executed as soon as possible. Delaying intervention 4 weeks after March 8, 2020 would cause the maximum number of cumulative cases of death increase from 7,174 to 133,608 and the ending points of the epidemic postponed from Jun 25 to Aug 22.

As of February 11, 2020, all prefecture-level cities in mainland China have reported confirmed cases of 2019 novel coronavirus (2019-nCoV), but the city-level epidemical dynamics is unknown. The aim of this study is to model the current dynamics of 2019-nCoV at city level and predict the trend in the next 30 days under three possible scenarios in mainland China. We developed a spatially explicit epidemic model to consider the unique characteristics of the virus transmission in individual cities. Our model considered that the rate of virus transmission among local residents is different from those with Wuhan travel history due to the self-isolation policy. We introduced a decay rate to quantify the effort of each city to gradually control the disease spreading. We used mobile phone data to obtain the number of individuals in each city who have travel history to Wuhan. This city-level model was trained using confirmed cases up to February 10, 2020 and validated by new confirmed cases on February 11, 2020. We used the trained model to predict the future dynamics up to March 12, 2020 under different scenarios: the current trend maintained, control efforts expanded, and person-to-person contact increased due to work resuming. We estimated that the total infections in mainland China would be 72172, 54348, and 149774 by March 12, 2020 under each scenario respectively. Under the current trend, all cities will show the peak point of daily new infections by February 21. This date can be advanced to February 14 with control efforts expanded or postponed to February 26 under pressure of work resuming. Except Wuhan that cannot eliminate the disease by March 12, our model predicts that 95.4%, 100%, and 75.7% cities will have no new infections by the end of February under three scenarios. The spatial pattern of our prediction could help the government allocate resources to cities that have a more serious epidemic in the next 30 days.

BackgroundIn computational biology, embedding known physical laws into deep learning models to construct "Physics-Informed Neural Networks" (PINNs) is a mainstream paradigm for enhancing model interpretability and extrapolation capability. However, in complex multi-physics coupling problems, there is a risk of competitive imbalance between the physical term and the flexible artificial intelligence (AI) residual term, causing the model to degenerate into a "black-box" fit and lose the original purpose of being physics-driven. MethodsIn this study, targeting the problem of predicting protein liquid-liquid phase separation (LLPS) behavior in response to environmental factors (temperature, salt concentration), we identified physical distortions, gradient vanishing, and numerical instability in the initial physics-AI hybrid model. Three core correction strategies were proposed: (1) Weight Allocation Logic Reconstruction: Force the physical trunk weight to 1.0 at the output layer, suppressing the AI residual term to the perturbation level of 0.05~0.1, ensuring physics dominance; (2) Robust Physics Formula Construction: Abandon the unstable power function and introduce a combination of Softplus and logarithmic functions to stably simulate the nonlinear effects of charge shielding; (3) Gain Compensation Alignment: Apply gain compensation to the weak signal branch (temperature) to ensure its effective participation in optimization. ResultsThe optimized model maintained a fitting accuracy of R2{approx}0.62 on the test set, while physical consistency was significantly enhanced. The model successfully restored the monotonic increase in solubility with temperature characteristic of UCST-type phase diagrams and correctly captured the nonlinear charge shielding features in the salt concentration response. The weights of key physical parameters (e.g., hydrophobic contribution w_h, net charge contribution w_ncpr) increased from <10-3 to the 10-2 magnitude, demonstrating the reactivation of the physical branch. ConclusionsThe weight control, formula stabilization, and signal gain alignment strategies proposed in this study effectively address the classic problem of "AI hijacking" physics in physics-AI hybrid models. This work provides a universal solution for constructing biophysical predictive models that combine high fitting accuracy with strong physical interpretability.

Nuclear speckles are nuclear bodies consisting of populations of small and irregularly shaped droplet-like molecular condensates that contain various splicing factors. Recent experiments have shown the following morphological features of nuclear speckles: (I) Each molecular condensate contains SON and SRRM2 proteins, and MALAT1 non-coding RNA surrounds these condensates; (II) In the normal interphase of the cell cycle, these condensates are broadly distributed throughout the nucleus in multicellular organisms. In contrast, the fusion of condensates leads to the formation of strongly condensed spherical droplets when cell transcription is suppressed; (III) SON is dispersed spatially in MALAT1 knocked-down cells, whereas MALAT1 is dispersed in SON knocked-down cells by the collapse of nuclear speckles. However, the detailed interactions among molecules that reveal the mechanisms of this rich variety of morphologies remain unknown. In this study, a coarse-grained molecular dynamics model of the nuclear speckle was developed considering the dynamics of SON, SRRM2 or SRSF2, MALAT1, and pre-mRNA as representative components of condensates. The simulations reproduced the abovementioned morphological changes, by which the interaction strength among the representative components of the condensates was predicted.

ImportanceRemoving the epidemic waves and reducing the instability level of an endemic critical point of COVID-19 dynamics are fundamental to the control of COVID-19 in the US. ObjectiveTo develop new mathematic models and investigate when and how will the COVID-19 in the US be evolved to endemic. Design, Setting, and ParticipantsTo solve the problem of whether mass vaccination against SARS-CoV-2 will ultimately end the COVID-19 pandemic, we defined a set of nonlinear ordinary differential equations as a mathematical model of transmission dynamics of COVID-19 with vaccination. Multi-stability analysis was conducted on the data for the daily reported new cases of infection from January 12, 2021 to December 12, 2022 across 50 states in the US using the developed dynamic model of COVID-19 and limit cycle theory. Main Outcomes and MeasuresEigenvalues and the reproduction number under the disease-free equilibrium point and endemic equilibrium point were used to assess the stability of the disease-free equilibrium point and endemic equilibrium point. Both analytic analysis and numerical methods were used to determine the instability level of new cases of COVID-19 in the US under the different types of equilibrium points and to investigate how the system moves back and forth between stable and unstable states of the system and how the pandemic COVD-19 will evolve to endemic in the US. ResultsMulti-stability analysis identified two types of critical equilibrium points, disease-free endemic equilibrium points in the COVID-19 transmission dynamic system. The transmissional, recovery, vaccination rates and vaccination effectiveness during the major transmission waves of COVID-19 across 50 states in the US were estimated. These parameters in the model varied over time and across the 50 states. The eigenvalues and the reproduction numbers R0 and [Formula] in the disease-free equilibrium point and endemic equilibrium point were estimated to assess stability and classify equilibrium points. They also varied from state to state. The impacts of the transmission and vaccination parameters on the stability of COVID-19 were simulated, and stability attractor regions of these parameters were found and ranked for all 50 states in the US. The US experienced five major epidemic waves, endemic equilibrium points of which across 50 states were all in unstable states. However, the combination of re-infection and vaccination (hybrid immunity) may provide strong protection against COVID-19 infection, and stability analysis showed that these unstable equilibrium points were toward stable points. Theoretical analysis and real data analysis showed that additional epidemic waves may be possible in the future, but COVID-19 across all 50 sates in the US is rapidly moving toward stable endemicity. Conclusions and RelevanceBoth stability analysis and observed epidemic waves in the US indicated that the pandemic might not end with the disappearance of the virus. However, after enough people gained immune protection from vaccination and from natural infection, COVID-19 would become an endemic disease, as the stability analysis showed. Educating the population about multiple epidemic waves of the transmission dynamics of COVID-19 and designing optimal vaccine rollout are crucial for controlling the pandemic of COVID-19 and its evolving to endemic. Key PointsO_ST_ABSQuestioC_ST_ABSThe US has already experienced five waves of the epidemic. We urgently need to know when and how will COVID-19 be evolved into endemic. FindingsTo solve the problem, we developed a mathematical model of transmission dynamics of COVID-19 with vaccination and performed a multi-stability analysis of COVID-19 transmission dynamics in the US. We found that COVID-19 dynamics of all 50 states in the US were getting closer and closer to endemic and stable states. MeaningCOVID-19 dynamics of all 50 states in the US are toward stable states and will be evolved to endemic in the near future.

COVID-19 has become a global pandemic. However, the impact of the public health interventions in China needs to be evaluated. We established a SEIRD model to simulate the transmission trend of China. In addition, the reduction of the reproductive number was estimated under the current forty public health interventions policies. Furthermore, the infection curve, daily transmission replication curve, and the trend of cumulative confirmed cases were used to evaluate the effects of the public health interventions. Our results showed that the SEIRD curve model we established had a good fit and the basic reproductive number is 3.38 (95% CI, 3.25-3.48). The SEIRD curve show a small difference between the simulated number of cases and the actual number; the correlation index (H2) is 0.934, and the reproductive number (R) has been reduced from 3.38 to 0.5 under the current forty public health interventions policies of China. The actual growth curve of new cases, the virus infection curve, and the daily transmission replication curve were significantly going down under the current public health interventions. Our results suggest that the current public health interventions of China are effective and should be maintained until COVID-19 is no longer considered a global threat.

Throughout history, Influenza A viruses (IAVs) have caused significant harm and catastrophic pandemics. The presence of host barriers results in viral host tropism, where infected hosts are subject to strict restrictions due to the hindered spread of viruses across hosts. Therefore, the identification of host tropism of IAVs, particularly in humans, is crucial to preventing the cross-host transmission of avian viruses and their outbreaks in humans. Nevertheless, efficiently and effectively identifying host tropism, especially for early host susceptibility warnings based on viral genome sequences during outbreak onset, remains challenging. To address this challenge, we propose Flu-CNN, a deep neural network model based on classical character-level convolutional networks. By analyzing the genomic segments of IAVs, Flu-CNN can accurately identify the host tropism, with a particular focus on avian influenza viruses that may infect humans. According to our experimental evaluations, Flu-CNN achieved an accuracy of 99% in identifying virus hosts via only a single genomic segment, even for subtypes with a relatively small number of viral strains such as H5N1, H7N9, and H9N2. The superiority of Flu-CNN demonstrates its effectiveness in screening for critical amino acid mutations, which is important to host adaptation, and zoonotic risk prediction of viral strains. Flu-CNN is a valuable tool for identifying evolutionary characterization, monitoring potential outbreaks, and preventing epidemical spreads of IAVs, which contribute to the effective surveillance of influenza A viruses.

A novel corona virus (2019-nCoV) was identified in Wuhan, China and has been causing an unprecedented outbreak in China. The spread of this novel virus can eventually become an international emergency. During the early outbreak phase in Wuhan, one of the most important public health tasks is to prevent the spread of the virus to other cities. Therefore, full-scale border control measures to prevent the spread of virus have been discussed in many nearby countries. At the same time, lockdown in Wuhan cityu (border control from leaving out) has been imposed. The challenge is that many people have traveled from Wuhan to other cities before the border control. Thus, it is difficult to forecast the number of imported cases at different cities and estimate their risk on outbreak emergence. Here, we have developed a mathematical framework incorporating city-to-city connections to calculate the number of imported cases of the novel virus from an outbreak source, and the cumulative number of secondary cases generated by the imported cases. We used this number to estimate the arrival time of outbreak emergence using air travel frequency data from Wuhan to other cities, collected from the International Air Transport Association database. In addition, a meta-population compartmental model was built based on a classical SIR approach to simulate outbreaks at different cities. We consider the scenarios under three basic reproductive number (R0) settings using the best knowledge of the current findings, from high (2.92), mild (1.68), to a much lower numbers (1.4). The mean arrival time of outbreak spreading has been determined. Under the high R0, the critical time is 17.9 days after December 31, 2019 for outbreak spreading. Under the low R0, the critical time is between day 26.2 to day 35 after December 31, 2019. To make an extra 30 days gain, under the low R0 (1.4), the control measures have to reduce 87% of the connections between the source and target cities. Under the higher R0 (2.92), the effect on reducing the chance of outbreak emergence is generally low until the border control measure was enhanced to reduce more than 95% of the connections.