Combining the dynamic model and deep neural networks to identify the intensity of interventions during COVID-19 pandemic.

During the COVID-19 pandemic, control measures, especially massive contact tracing following prompt quarantine and isolation, play an important role in mitigating the disease spread, and quantifying the dynamic contact rate and quarantine rate and estimate their impacts remain challenging. To precisely quantify the intensity of interventions, we develop the mechanism of physics-informed neural network (PINN) to propose the extended transmission-dynamics-informed neural network (TDINN) algorithm by combining scattered observational data with deep learning and epidemic models. The TDINN algorithm can not only avoid assuming the specific rate functions in advance but also make neural networks follow the rules of epidemic systems in the process of learning. We show that the proposed algorithm can fit the multi-source epidemic data in Xi'an, Guangzhou and Yangzhou cities well, and moreover reconstruct the epidemic development trend in Hainan and Xinjiang with incomplete reported data. We inferred the temporal evolution patterns of contact/quarantine rates, selected the best combination from the family of functions to accurately simulate the contact/quarantine time series learned by TDINN algorithm, and consequently reconstructed the epidemic process. The selected rate functions based on the time series inferred by deep learning have epidemiologically reasonable meanings. In addition, the proposed TDINN algorithm has also been verified by COVID-19 epidemic data with multiple waves in Liaoning province and shows good performance. We find the significant fluctuations in estimated contact/quarantine rates, and a feedback loop between the strengthening/relaxation of intervention strategies and the recurrence of the outbreaks. Moreover, the findings show that there is diversity in the shape of the temporal evolution curves of the inferred contact/quarantine rates in the considered regions, which indicates variation in the intensity of control strategies adopted in various regions.

Linking Spontaneous Behavioral Changes to Disease Transmission Dynamics: Behavior Change Includes Periodic Oscillation.

Behavior change significantly influences the transmission of diseases during outbreaks. To incorporate spontaneous preventive measures, we propose a model that integrates behavior change with disease transmission. The model represents behavior change through an imitation process, wherein players exclusively adopt the behavior associated with higher payoff. We find that relying solely on spontaneous behavior change is insufficient for eradicating the disease. The dynamics of behavior change are contingent on the basic reproduction number R a corresponding to the scenario where all players adopt non-pharmaceutical interventions (NPIs). When R a < 1 , partial adherence to NPIs remains consistently feasible. We can ensure that the disease stays at a low level or maintains minor fluctuations around a lower value by increasing sensitivity to perceived infection. In cases where oscillations occur, a further reduction in the maximum prevalence of infection over a cycle can be achieved by increasing the rate of behavior change. When R a > 1 , almost all players consistently adopt NPIs if they are highly sensitive to perceived infection. Further consideration of saturated recovery leads to saddle-node homoclinic and Bogdanov-Takens bifurcations, emphasizing the adverse impact of limited medical resources on controlling the scale of infection. Finally, we parameterize our model with COVID-19 data and Tokyo subway ridership, enabling us to illustrate the disease spread co-evolving with behavior change dynamics. We further demonstrate that an increase in sensitivity to perceived infection can accelerate the peak time and reduce the peak size of infection prevalence in the initial wave.

Hormetic and synergistic effects of cancer treatments revealed by modelling combinations of radio - or chemotherapy with immunotherapy.

BACKGROUND: Radio/chemotherapy and immune systems provide examples of hormesis, as tumours can be stimulated (or reduced) at low radio/chemical or antibody doses but inhibited (or stimulated) by high doses. METHODS: Interactions between effector cells, tumour cells and cytokines with pulsed radio/chemo-immunotherapy were modelled using a pulse differential system. RESULTS: Our results show that radio/chemotherapy (dose) response curves (RCRC) and/or immune response curves (IRC) or a combination of both, undergo homeostatic changes or catastrophic shifts revealing hormesis in many parameter regions. Some mixed response curves had multiple humps, posing challenges for interpretation of clinical trials and experimental design, due to a fuzzy region between an hormetic zone and the toxic threshold. Mixed response curves from two parameter bifurcation analyses demonstrated that low-dose radio/chemotherapy and strong immunotherapy counteract side-effects of radio/chemotherapy on effector cells and cytokines and stimulate effects of immunotherapy on tumour growth. The implications for clinical applications were confirmed by good fits to our model of RCRC and IRC data. CONCLUSIONS: The combination of low-dose radio/chemotherapy and high-dose immunotherapy is very effective for many solid tumours. The net benefit and synergistic effect of combined therapy is conducive to the treatment and inhibition of tumour cells.

Humanized mouse models for inherited thrombocytopenia studies.

Inherited thrombocytopenia (IT) is a group of hereditary disorders characterized by a reduced platelet count as the main clinical manifestation, and often with abnormal platelet function, which can subsequently lead to impaired hemostasis. In the past decades, humanized mouse models (HMMs), that are mice engrafted with human cells or genes, have been widely used in different research areas including immunology, oncology, and virology. With advances of the development of immunodeficient mice, the engraftment, and reconstitution of functional human platelets in HMM permit studies of occurrence and development of platelet disorders including IT and treatment strategies. This article mainly reviews the development of humanized mice models, the construction methods, research status, and problems of using humanized mice for the in vivo study of human thrombopoiesis.

Humanized mouse models (HMMs) refer to immunodeficient mice that have been used for the investigation of human hematopoiesis and immunity for years. With engrafted human hematopoietic stem cells (HSCs), the differentiation process of HSCs and re-construction of platelets can be monitored in the mice. Until now, several strains of HMMs have been used in the studies of inherited thrombocytopenia (IT), a genetic disorder associated with low platelet count in the blood. In this study, we reviewed the development of these HMMs in IT studies, compared the different sources of HSCs transplanted into HMMs and summarize the strategies of HSC transplantation in HMMs. The Kit^−/− immunodeficient mice showed effectively long-term and stable implantation of human HSC without irradiation and higher implantation levels, and they also support multilinear differentiation of human HSC, such as platelets and red blood cells. The source and count of HSCs and the transplantation strategy may also impact the result. This study provides a basis information for HMMs used in IT and will help other investigators in this field choosing the right research plan.

Threshold conditions for curbing COVID-19 with a dynamic zero-case policy derived from 101 outbreaks in China.

By 31 May 2022, original/Alpha, Delta and Omicron strains induced 101 outbreaks of COVID-19 in mainland China. Most outbreaks were cleared by combining non-pharmaceutical interventions (NPIs) with vaccines, but continuous virus variations challenged the dynamic zero-case policy (DZCP), posing questions of what are the prerequisites and threshold levels for success? And what are the independent effects of vaccination in each outbreak? Using a modified classic infectious disease dynamic model and an iterative relationship for new infections per day, the effectiveness of vaccines and NPIs was deduced, from which the independent effectiveness of vaccines was derived. There was a negative correlation between vaccination coverage rates and virus transmission. For the Delta strain, a 61.8% increase in the vaccination rate (VR) reduced the control reproduction number (CRN) by about 27%. For the Omicron strain, a 20.43% increase in VR, including booster shots, reduced the CRN by 42.16%. The implementation speed of NPIs against the original/Alpha strain was faster than the virus's transmission speed, and vaccines significantly accelerated the DZCP against the Delta strain. The CRN ([Formula: see text]) during the exponential growth phase and the peak time and intensity of NPIs were key factors affecting a comprehensive theoretical threshold condition for DZCP success, illustrated by contour diagrams for the CRN under different conditions. The DZCP maintained the [Formula: see text] of 101 outbreaks below the safe threshold level, but the strength of NPIs was close to saturation especially for Omicron, and there was little room for improvement. Only by curbing the rise in the early stage and shortening the exponential growth period could clearing be achieved quickly. Strengthening China's vaccine immune barrier can improve China's ability to prevent and control epidemics and provide greater scope for the selection and adjustment of NPIs. Otherwise, there will be rapid rises in infection rates and an extremely high peak and huge pressure on the healthcare system, and a potential increase in excess mortality.

Optimal strategies for coordinating infection control and socio-economic activities.

It becomes challenging to identify feasible control strategies for simultaneously relaxing the countermeasures and containing the Covid-19 pandemic, given China's huge population size, high susceptibility, persist vaccination waning, and relatively weak strength of health systems. We propose a novel mathematical model with waning of immunity and solve the optimal control problem, in order to provide an insight on how much detecting and social distancing are required to coordinate socio-economic activities and epidemic control. We obtain the optimal intensity of countermeasures, i.e., the dynamic nucleic acid screening and social distancing, under which the health system is functioning normally and people can engage in a certain level of socio-economic activities. We find that it is the isolation capacity or the restriction of the case fatality rate (CFR) rather than the hospital capacity that mainly determines the optimal strategies. And the solved optimal controls under quarterly CFR restrictions exhibit oscillations. It is worth noticing that, if without considering booster or very low booster rate, the optimal strategy is a "on-off" mode, alternating between lock down and opening with certain social distancing, which reflects the importance and necessity of China's static management on a certain area during Covid-19 outbreak. The findings suggest some feasible paths to smoothly transit from the Covid-19 pandemic to an endemic phase.

The impact of supplementary immunization activities on measles transmission dynamics and implications for measles elimination goals: A mathematical modelling study.

BACKGROUND: Measles has re-emerged globally due to the accumulation of susceptible individuals and immunity gap, which causes challenges in eliminating measles. Routine vaccination and supplementary immunization activities (SIAs) have greatly improved measles control, but the impact of SIAs on the measles transmission dynamics remains unclear as the vaccine-induced immunity wanes. METHODS: We developed a comprehensive measles transmission dynamics model by taking into account population demographics, age-specific contact patterns, seasonality, routine vaccination, SIAs, and the waning vaccine-induced immunity. The model was calibrated by the monthly age-specific cases data from 2005 to 2018 in Jiangsu Province, China, and validated by the dynamic sero-prevalence data. We aimed to investigate the short-term and long-term impact of three-time SIAs during 2009-2012 (9.68 million and 4.25 million children aged 8 months-14 years in March 2009 and September 2010, respectively, and 140,000 children aged 8 months-6 years in March 2012) on the measles disease burden and explored whether additional SIAs could accelerate the measles elimination. RESULTS: We estimated that the cumulative numbers of measles cases from March 2009 to December 2012 (in the short run) and to December 2018 (in the long run) after three-time SIAs (base case) were 6,699 (95% confidence interval [CI]: 2,928-10,469), and 22,411 (15,146-29,675), which averted 45.0% (42.9%-47.0%) and 34.3% (30.7%-37.9%) of 12,226 (4,916-19,537) and 34,274 (21,350-47,199) cases without SIAs, respectively. The fraction of susceptibles for children aged 8-23 months and 2-14 years decreased from 8.3% and 10.8% in March 2009 to 5.8% and 5.8% in April 2012, respectively. However, the fraction of susceptibles aged 15-49 years and above 50 years increased gradually to about 15% in 2018 irrespective of SIAs due to the waning immunity. The measles elimination goal would be reached in 2028, and administrating additional one-off SIAs in September 2022 to children aged 8-23 months, or young adolescents aged 15-19 years could accelerate the elimination one year earlier. CONCLUSIONS: SIAs have greatly reduced the measles incidence and the fraction of susceptibles, but the benefit may wane over time. Under the current interventions, Jiangsu province would reach the measles elimination goal in 2028. Additional SIAs may accelerate the measles elimination one year earlier.

Determining travel fluxes in epidemic areas.

Infectious diseases attack humans from time to time and threaten the lives and survival of people all around the world. An important strategy to prevent the spatial spread of infectious diseases is to restrict population travel. With the reduction of the epidemic situation, when and where travel restrictions can be lifted, and how to organize orderly movement patterns become critical and fall within the scope of this study. We define a novel diffusion distance derived from the estimated mobility network, based on which we provide a general model to describe the spatiotemporal spread of infectious diseases with a random diffusion process and a deterministic drift process of the population. We consequently develop a multi-source data fusion method to determine the population flow in epidemic areas. In this method, we first select available subregions in epidemic areas, and then provide solutions to initiate new travel flux among these subregions. To verify our model and method, we analyze the multi-source data from mainland China and obtain a new travel flux triggering scheme in the selected 29 cities with the most active population movements in mainland China. The testable predictions in these selected cities show that reopening the borders in accordance with our proposed travel flux will not cause a second outbreak of COVID-19 in these cities. The finding provides a methodology of re-triggering travel flux during the weakening spread stage of the epidemic.

Controlling Multiple COVID-19 Epidemic Waves: An Insight from a Multi-scale Model Linking the Behaviour Change Dynamics to the Disease Transmission Dynamics.

COVID-19 epidemics exhibited multiple waves regionally and globally since 2020. It is important to understand the insight and underlying mechanisms of the multiple waves of COVID-19 epidemics in order to design more efficient non-pharmaceutical interventions (NPIs) and vaccination strategies to prevent future waves. We propose a multi-scale model by linking the behaviour change dynamics to the disease transmission dynamics to investigate the effect of behaviour dynamics on COVID-19 epidemics using game theory. The proposed multi-scale models are calibrated and key parameters related to disease transmission dynamics and behavioural dynamics with/without vaccination are estimated based on COVID-19 epidemic data (daily reported cases and cumulative deaths) and vaccination data. Our modeling results demonstrate that the feedback loop between behaviour changes and COVID-19 transmission dynamics plays an essential role in inducing multiple epidemic waves. We find that the long period of high-prevalence or persistent deterioration of COVID-19 epidemics could drive almost all of the population to change their behaviours and maintain the altered behaviours. However, the effect of behaviour changes fades out gradually along the progress of epidemics. This suggests that it is essential to have not only persistent, but also effective behaviour changes in order to avoid subsequent epidemic waves. In addition, our model also suggests the importance to maintain the effective altered behaviours during the initial stage of vaccination, and to counteract relaxation of NPIs, it requires quick and massive vaccination to avoid future epidemic waves.

Potential biomarkers for inherited thrombocytopenia 2 identified by plasma proteomics.

Inherited thrombocytopenia 2 (THC2) is difficult to diagnose due to the lack of specific clinical characteristics and diagnostic methods. To identify potential plasma protein biomarkers for THC2, we collected the plasma samples from a THC2 family (9 THC2 and 15 non-THC2 members), enriched the medium and low abundant proteins using Proteominer and analyzed the protein profiles using the liquid chromatography-mass spectrometry in data independent acquisition mode. Initially, we detected 784 proteins in the plasma samples of this family and identified 27 up-regulated and 36 down-regulated in the THC2 group compared to the non-THC2 group (|log2 ratio| >1 and p-value <0.05). To improve the predictive power, top eight dysregulated proteins (B7Z2B4, LTF, HP, ERN1, IGHV1-8, A0A0X9V9C4, VH6DJ, and D3JV41) were selected by an area under the curve-based random forest process to construct a clinical model. Multivariate analysis with random forest and support vector machine showed that the prediction model provided high discrimination ability for THC2 diagnosis (AUC: 1.000 and 0.967, respectively). The potential plasma protein biomarkers will be tested in more THC2 patients and other thrombocytopenia patients to further validate their specificity and sensitivity.

EloA promotes HEL polyploidization upon PMA stimulation through enhanced ERK1/2 activity.

Megakaryocytes (MKs) are the unique non-pathological cells that undergo polyploidization in mammals. The polyploid formation is critical for understanding the MK biology, and transcriptional regulation is involved in the differentiation and maturation of MKs. However, little is known about the functions of transcriptional elongation factors in the MK polyploidization. In this study, we investigated the role of transcription elongation factor EloA in the polyploidy formation during the MK differentiation. We found that EloA was highly expressed in the erythroleukemia cell lines HEL and K562. Knockdown of EloA in HEL cell line was shown to impair the phorbol myristate acetate (PMA) induced polyploidization process, which was used extensively to model megakaryocytic differentiation. Selective over-expression of EloA mutants with Pol II elongation activity partially restored the polyploidization. RNA-sequencing revealed that knockdown of EloA decelerated the transcription of genes enriched in the ERK1/2 cascade pathway. The phosphorylation activity of ERK1/2 decreased upon the EloA inhibition, and the polyploidization process of HEL was hindered when ERK1/2 phosphorylation was inhibited by PD0325901 or SCH772984. This study evidenced a positive role of EloA in HEL polyploidization upon PMA stimulation through enhanced ERK1/2 activity.

Analysis of a diffusive epidemic system with spatial heterogeneity and lag effect of media impact.

We considered an SIS functional partial differential model cooperated with spatial heterogeneity and lag effect of media impact. The wellposedness including existence and uniqueness of the solution was proved. We defined the basic reproduction number and investigated the threshold dynamics of the model, and discussed the asymptotic behavior and monotonicity of the basic reproduction number associated with the diffusion rate. The local and global Hopf bifurcation at the endemic steady state was investigated theoretically and numerically. There exists numerical cases showing that the larger the number of basic reproduction number, the smaller the final epidemic size. The meaningful conclusion generalizes the previous conclusion of ordinary differential equation.

CRIF1 as a potential target to improve the radiosensitivity of osteosarcoma.

Resistance to ionizing radiation (IR), which is a conventional treatment for osteosarcoma that cannot be resected, undermines the efficacy of this therapy. However, the mechanism by which IR induces radioresistance in osteosarcoma is not defined. Here, we report that CR6-interacting factor-1 (CRIF1) is highly expressed in osteosarcoma and undergoes nuclear-cytoplasmic shuttling of cyclin-dependent kinase 2 (CDK2) after IR. Osteosarcoma cells lacking CRIF1 show increased sensitivity to IR, which is associated with delayed DNA damage repair, inactivated G1/S checkpoint, and mitochondrial dysfunction. CRIF1 interacts with the DNA damage checkpoint regulator CDK2, and CRIF1 and CDK2 colocalize in the nucleus after IR. Nuclear localization of CDK2 is associated with phosphorylation changes that promote DNA repair and activation of the G1/S checkpoint. CRIF1 knockdown synergized with IR in an in vivo osteosarcoma model, leading to tumor regression. Based on these findings, we identify CRIF1 as a potential therapeutic target in osteosarcoma that can increase the efficacy of radiotherapy. More broadly, our findings may provide insights into the mechanism for other types of radioresistant cancers and be exploited for therapeutic ends.

Complex dynamics of an epidemic model with saturated media coverage and recovery.

During the outbreak of emerging infectious diseases, media coverage and medical resource play important roles in affecting the disease transmission. To investigate the effects of the saturation of media coverage and limited medical resources, we proposed a mathematical model with extra compartment of media coverage and two nonlinear functions. We theoretically and numerically investigate the dynamics of the proposed model. Given great difficulties caused by high nonlinearity in theoretical analysis, we separately considered subsystems with only nonlinear recovery or with only saturated media impact. For the model with only nonlinear recovery, we theoretically showed that backward bifurcation can occur and multiple equilibria may coexist under certain conditions in this case. Numerical simulations reveal the rich dynamic behaviors, including forward-backward bifurcation, Hopf bifurcation, saddle-node bifurcation, homoclinic bifurcation and unstable limit cycle. So the limitation of medical resources induces rich dynamics and causes much difficulties in eliminating the infectious diseases. We then investigated the dynamics of the system with only saturated media impact and concluded that saturated media impact hardly induces the complicated dynamics. Further, we parameterized the proposed model on the basis of the COVID-19 case data in mainland China and data related to news items, and estimated the basic reproduction number to be 2.86. Sensitivity analyses were carried out to quantify the relative importance of parameters in determining the cumulative number of infected individuals at the end of the first month of the outbreak. Combining with numerical analyses, we suggested that providing adequate medical resources and improving media response to infection or individuals' response to mass media may reduce the cumulative number of the infected individuals, which mitigates the transmission dynamics during the early stage of the COVID-19 pandemic.

Linking the disease transmission to information dissemination dynamics: An insight from a multi-scale model study.

During the outbreak of emerging infectious diseases, information dissemination dynamics significantly affects the individuals' psychological and behavioral changes, and consequently influences on the disease transmission. To investigate the interaction of disease transmission and information dissemination dynamics, we proposed a multi-scale model which explicitly models both the disease transmission with saturated recovery rate and information transmission to evaluate the effect of information transmission on dynamic behaviors. Considering time variation between information dissemination, epidemiological and demographic processes, we obtained a slow-fast system by reasonably introducing a sufficiently small quantity. We carefully examined the dynamics of proposed system, including existence and stability of possible equilibria and existence of backward bifurcation, by using the fast-slow theory and directly investigating the full system. We then compared the dynamics of the proposed system and the essential thresholds based on two methods, and obtained the similarity between the basic dynamical behaviors of the slow system and that of the full system. Finally, we parameterized the proposed model on the basis of the COVID-19 case data in mainland China and data related to news items, and estimated the basic reproduction number to be 3.25. Numerical analysis suggested that information transmission about COVID-19 pandemic caused by media coverage can reduce the peak size, which mitigates the transmission dynamics during the early stage of the COVID-19 pandemic.

Effects of New York's Executive Order on Face Mask Use on COVID-19 Infections and Mortality: A Modeling Study.

There is growing evidence on the effect of face mask use in controlling the spread of COVID-19. However, few studies have examined the effect of local face mask policies on the pandemic. In this study, we developed a dynamic compartmental model of COVID-19 transmission in New York City (NYC), which was the epicenter of the COVID-19 pandemic in the USA. We used data on daily and cumulative COVID-19 infections and deaths from the NYC Department of Health and Mental Hygiene to calibrate and validate our model. We then used the model to assess the effect of the executive order on face mask use on infections and deaths due to COVID-19 in NYC. Our results showed that the executive order on face mask use was estimated to avert 99,517 (95% CIs 72,723-126,312) COVID-19 infections and 7978 (5692-10,265) deaths in NYC. If the executive order was implemented 1 week earlier (on April 10), the averted infections and deaths would be 111,475 (81,593-141,356) and 9017 (6446-11,589), respectively. If the executive order was implemented 2 weeks earlier (on April 3 when the Centers for Disease Control and Prevention recommended face mask use), the averted infections and deaths would be 128,598 (94,373-162,824) and 10,515 (7540-13,489), respectively. Our study provides public health practitioners and policymakers with evidence on the importance of implementing face mask policies in local areas as early as possible to control the spread of COVID-19 and reduce mortality.

Effects of medical resource capacities and intensities of public mitigation measures on outcomes of COVID-19 outbreaks.

BACKGROUND: The COVID-19 pandemic is complex and is developing in different ways according to the country involved. METHODS: To identify the key parameters or processes that have the greatest effects on the pandemic and reveal the different progressions of epidemics in different countries, we quantified enhanced control measures and the dynamics of the production and provision of medical resources. We then nested these within a COVID-19 epidemic transmission model, which is parameterized by multi-source data. We obtained rate functions related to the intensity of mitigation measures, the effective reproduction numbers and the timings and durations of runs on medical resources, given differing control measures implemented in various countries. RESULTS: Increased detection rates may induce runs on medical resources and prolong their durations, depending on resource availability. Nevertheless, improving the detection rate can effectively and rapidly reduce the mortality rate, even after runs on medical resources. Combinations of multiple prevention and control strategies and timely improvement of abilities to supplement medical resources are key to effective control of the COVID-19 epidemic. A 50% reduction in comprehensive control measures would have led to the cumulative numbers of confirmed cases and deaths exceeding 590,000 and 60,000, respectively, by 27 March 2020 in mainland China. CONCLUSIONS: Multiple data sources and cross validation of a COVID-19 epidemic model, coupled with a medical resource logistic model, revealed the key factors that affect epidemic progressions and their outbreak patterns in different countries. These key factors are the type of emergency medical response to avoid runs on medical resources, especially improved detection rates, the ability to promote public health measures, and the synergistic effects of combinations of multiple prevention and control strategies. The proposed model can assist health authorities to predict when they will be most in need of hospital beds and equipment such as ventilators, personal protection equipment, drugs, and staff.

Investigating the relationship between reopening the economy and implementing control measures during the COVID-19 pandemic.

OBJECTIVES: The COVID-19 pandemic has resulted in an enormous burden on population health and the economy around the world. Although most cities in the United States have reopened their economies from previous lockdowns, it was not clear how the magnitude of different control measures-such as face mask use and social distancing-may affect the timing of reopening the economy for a local region. This study aimed to investigate the relationship between reopening dates and control measures and identify the conditions under which a city can be reopened safely. STUDY DESIGN: This was a mathematical modeling study. METHODS: We developed a dynamic compartment model to capture the transmission dynamics of COVID-19 in New York City. We estimated model parameters from local COVID-19 data. We conducted three sets of policy simulations to investigate how different reopening dates and magnitudes of control measures would affect the COVID-19 epidemic. RESULTS: The model estimated that maintaining social contact at 80% of the prepandemic level and a 50% face mask usage would prevent a major surge of COVID-19 after reopening. If social distancing were completely relaxed after reopening, face mask usage would need to be maintained at nearly 80% to prevent a major surge. CONCLUSIONS: Adherence to social distancing and increased face mask usage are keys to prevent a major surge after a city reopens its economy. The findings from our study can help policymakers identify the conditions under which a city can be reopened safely.

When to lift the lockdown in Hubei province during COVID-19 epidemic? An insight from a patch model and multiple source data.

After diagnosed in Wuhan, COVID-19 spread quickly in mainland China. Though the epidemic in regions outside Hubei in mainland China has maintained a degree of control, evaluating the effectiveness and timeliness of intervention strategies, and predicting the transmission risk of work resumption as well as lifting the lockdown in Hubei province remain urgent. A patch model reflecting the mobility of population between Hubei and regions outside Hubei is formulated, and parameterized based on multiple source data for Hubei and regions outside Hubei. The effective reproduction numbers for Hubei and regions outside Hubei are estimated as 3.59 and 3.26 before Jan 23rd, 2020, but decrease quickly since then and drop below 1 after Jan 31st and Jan 28th, 2020. It is predicted that the new infections in Hubei province will decrease to very low level in mid-March, and the final size is estimated to be about 68,500 cases. The simulations reveal that contact rate after work resumption or lifting the lockdown in Hubei plays a critical role in affecting the epidemic. If the contact rate could be kept at a relatively low level, work resumption starting as early as on March 2nd in Hubei province may not induce the secondary outbreak, and the daily new infectious cases can be controlled at a low level if the lockdown in Hubei is liftted after March 9th, otherwise both work resumption and lifting the lockdown in Hubei should be postponed.

Estimation of the reproduction number and identification of periodicity for HFMD infections in northwest China.

Repeated outbreaks of Hand, foot and mouth disease (HFMD) infections have been observed in recent decades and dominated by various enteroviral serotypes. In particular, enterovirus 71 (EV-A71), coxsackievirus A16 (CV-A16) and coxsackievirus A6 (CV-A6) dominated the prevalence of HFMD infections alternatively in recent years with various outbreak sizes in Baoji, a city of Shaanxi Province in Northwest China. Estimating the reproduction number for various enteroviruses serotypes in northwest China (north temperate zone) and identification of cyclicity of HFMD infections are therefore an issue of great importance for future epidemics prediction and control. The basic/effective reproduction numbers for EV-A71, CV-A16 and CV-A6 were estimated based on daily new cases in 2010, 2011 and 2018, respectively, in which the corresponding pathogen dominated the epidemic. Two different methods based on serial interval were adopted and the basic reproduction number were estimated to be in the range of (1.33, 1.46) for CV-A16, (1.20, 1.29) for EV-A71, and (1.38, 1.59) for CV-A6, respectively. The estimated daily effective reproduction numbers significantly fluctuated before June or after July but varied mildly in (0.5,2) in around June to July for three serotypes. The weekly effective reproduction number for HFMD was estimated based on weekly new cases from year 2010 to 2018, and in most years it peaked in the range of (1.6,2.0) in February to March as well as in the range of (1.0,1.2) in September to October. The wavelet analysis based on the time series of HFMD cases from 2008 to 2018 showed obvious annual and semi-annual cyclicity, while the inter-annual cycles are infeasible. In this study we found that CV-A6 shows the greatest transmission ability among these three pathogens while EV-A71 exhibits the weakest ability of transmission, and moreover, the estimated values of basic reproduction number in northwest China are lower than those in Singapore, Hongkong and Guangdong, which may be due to different climatic circumstances.