In this paper, the relative controllability and the relative U-controllability of a class of fractional neutral differential control systems with multiple delays are studied. Firstly, the new expression for the solution of the system is obtained by using Laplace transform. Further, the sufficient and necessary conditions for the system to be relatively controllable are obtained by the Grammian matrix. Finally, the sufficient and necessary conditions for the nonlinear fractional neutral differential control system to be relative U-controllable to are given.

In this paper, based on Nesterov-Todd direction, and by introducing a measure for the central path and a primal-dual logarithmic barrier function, a long step primal-dual path-following lgorithm for convex quadratic semidefinite programming is presented. The algorithm ensures that the step size 1 is accepted when the iterative point falls into the neighborhood of the central path. An ε-optimal solution is obtained after at most O(n|ln εε|) iterations. Some preliminary numerical results are reported.

The m-dimensional vectorial Sturm-Liouville problem with discontinuous conditions inside a finite interval is considered. We mainly obtain some conclusions about multiplicity of the eigenvalues based on the estimation of solutions. It is proved that, under certain conditions on potential matrix, the problem can only have a finite number of eigenvalues with multiplicity m. As an application, Ambarzumyan’s theorem is proved for the problem.

Two-dimensional discrete-time quantum walk is the extension of quantum walk on the line. With the help of evolutionary operator, the walker can move according to a certain rule. In this paper, we take the Hadamard operator as the coin operator controlling the direction of the walker, and combine it with the conditional transfer operator controlling the position of the walker to form a complete evolutionary operator. After transforming the time domain space of the walker into frequency domain space through Fourier transform, the amplitude of the position (x,y) of the walker after t steps and the probability estimation at this time are obtained by using the stationary phase method of the Fourier integral.

The existence of nontrivial solutions is obtained by topological degree method for semi-positone (k,n-k) boundary value problem subject to nonlocal boundary conditions with Stieltjes integrals in which the nonlinearity f may not be nonnegative but bounded below. Two corollaries are given for the existence of positive solutions that are the extension of previous results when f is nonnegative. Two examples are presented to illustrate the main results that have mixed boundary conditions involving multi-point with sign-changing coefficients and integral with sign-changing kernel.

In this paper, the generalized compound option with random execution time is defined. The pricing formula of generalized compound option is derived under different circumstances.Considering the compound option investment with guaranteed income, the generalized compound option with threshold is defined and the option pricing formula is derived. Discuss the properties and application value of these two options,and further generalize the compound option.

In this paper, we discuss a special four-species stochastic predator-prey model with double delays. We first prove that the stochastic predator-prey model has a unique global positive solution to the positive initial conditions. Then, by constructing the appropriate Lyapunov function and combining the application of Ito's formula, the stochastic model is discussed from the gradual progress of the solution near the equilibrium point. Finally, numerical simulation of ordinary differential equation is used to verify the main conclusions in the theorem of this paper.

In this paper, by constructing a new Lyapunov function, using linear matrix inequality (LMI) and generalized Gronwall inequality, the finite-time stabilizability of fractional-order linear singular differential system is studied. Considering the influence of singular and disturbance on the stabilizability of the system, some sufficient conditions under a state feedback which makes the fractional linear singular differential system stable in finite time are derived. Two examples are given to check the feasibility of the conditions of the theorems.

Using a result of Zalcman concerning normal families, we investigate the problem of the order of solution of two types of systems of complex higher-order differential equations. At the same time, using the Nevanlinna value distribution theory, we discuss the growth of transcendental entire solutions of two types of complex differential-difference equations, and obtain some results, which due to some results in references are in proved and generalized. Examples show that our results are precise.

M. Klešč and J. Petrillová characterized graphs G₁ and G₂ for which the crossing number of its Cartesian product G₁□G₂ is two if G₁ is a cycle. Based on this result, we study the necessary and sufficient conditions of G₂ for which cr(G₁□G₂)=2 if G₁=P₄ or if G₁=P₃ and Δ(G₂)=4.

Stochastic optimization has wide applications in a lot of areas, such as economic, management, engineering, and national defense. As a kind of stochastic optimization problem to solve the distributed information fuzzy, distributionally robust optimization has become a research hotspot in academics in recent years, but it can be computationally complex when the recourse decisions are modeled as decision rules, i.e., functions of the random variable. It had been argued that stochastic programs can quite generally be made tractable by restricting the space of decision rules to those that exhibit a linear data dependence. In this paper, it is based on the φ-divergence uncertain set and linear decision method to research the modeling and calculation of distributionally robust stochastic optimization problem. We apply the linear decision rules to both original and dual versions of the distributionally robust optimization, which is developed the main idea to distributionally robust optimization in Kuhn D, Wiesemann W, Georghiou A. Primal and dual linear decision rules in stochastic and robust optimization. Mathematical Programming, 2011, 130(1): 177-209. By employing the optimal theorems and methods, we construct the upper and lower bounds problem which make the distributionally robust stochastic optimization be easily calculated. The experiments of the numerical value demonstrate the validity of the model analysis.

In this paper, aiming at the practical application of a transmission-dynamic model of emerging infectious disease like COVID-19, the quantity of contact associated with real-time data on confirmed cases is proposed and then the model is optimized and its practical value is enhanced. The real-time data information is applied to the parameter estimation of the dynamical model, which is applied to estimate the peak, the final size and the peak time of COVID-19 in Guangzhou and Wuhan, respectively. Such quantity of contact can also be applied to other emerging infectious diseases to reveal the transmission risk in the different periods of their outbreaks.

Coronavirus significantly affects China and many other countries. In the early stages of the outbreak, the number of infected patients is unclear due to insufficient medical resources in some areas. Then, efficient estimation of the number of infected patients will provide important support for the decision-making of the government. In this paper, the sampling technique in Statistics is used for estimating the number of infected patients in the areas of acute outbreak. For example, for estimating the infected ratio in Wuhan city, we use the infected ratio of the persons in Wenzhou city who came from Wuhan after the outbreak of COVIA-19. The estimation can be verified by the infected data in Singapore and the other provinces in China. It is shown that this estimation method is simple and efficient. The data in this paper are derived from the open data.

Based on Wuhan's COVID-19 reported cases by National Health Commission of the People's Republic of China from January 23 to February 20, 2020, the relationship between transmission of COVID-19 in Wuhan and soft quarantine intensity in susceptible population is investigated. Dividing the population into six categories:quarantined susceptible-exposed susceptible-exposed-infectious but not yet symptomatic (pre-symptomatic)-infectious with symptoms-recovered, we propose a generalized S_qSEAIR model to analyze this epidemic. We estimate key epidemic parameters by Monte Carlo method. Data fitting and numerical simulation are carried out for the model. We obtain effective reproduction number, peak arrival time, peak value, epidemic time, and final size after the implementation of soft quarantine measures. The effects of quarantine rate and exposure rate of susceptible population on COVID-19 transmission are evaluated.

This paper establishes a multi-stage and multi-scale SEIR epidemic patch model with deterministic and random diffusions. The modeling approach is incorporated with the Eulerian diffusion and the Lagrangian diffusion, and built upon multi-source training data with time-dependent parameters, so that the model has strong adaptability and effectiveness, and can flexibly be applied to study and predict different stages of emerging diseases (Sporadic, Outbreak, Epidemic, Endemic, Pandemic) and the transmission patterns at different spatial scales.
We use the proposed multi-stage and multi-scale SEIR epidemic patch model to analyze the spatial spread of the novel coronavirus between Wuhan and Beijing, and some quantitative numerical simulation results are presented here. The basic reproduction number in Beijing dropped from 3.58 before January 30 to 0.18 after February 3; Wuhan's basic reproduction number decreased from 4.3 before January 30 to 0.47 after February 6. If the lockdown of Wuhan were postponed for 3 days and 6 days instead of January 23, the cumulative number of infected cases in Beijing on March 1 would become approximately 2.14 times and 3.16 times as in normal, respectively, and the cumulative number of cases in Wuhan on March 1 became 1.80 times and 4.22 times as in normal.

The range of incubation period is crucial to the definition of epidemiological cases and can be used to determine the appropriate isolation time. In addition, understanding of the incubation period helps assess the effectiveness of immigration screening and contact tracing.In this study, we used the epidemiological data compiled according to the information publicly reported by the Chinese provincial centers for disease control and other institutions, and estimated the parameter distribution of the incubation period of novel coronavirus under the data structure of doubly interval censoring. According to our calculation, the median incubation period is estimated to be about 5.5 days, and under the lognormal distribution hypothesis, the incubation period falls at[2.01,15.36] with with 95% confidence. The method in this paper can make full use of the data structure of the epidemiological investigation of COVID-19 and provide a reliable basis for the formulation of epidemic prevention and control policies.

The unprecedented stringent public health intervention measures implemented in China and specially in the Hubei province has significantly halted the COVID-19 epidemic that the focus has been shifted to treatment of patients with critical or severe symptoms. The National Health Commission of China has officially included the convalescent plasma therapy as one of the treatment measures. In the absence of effective treatment and in consideration of the global spread, the effectiveness of this therapy and the anticipated challenge for its large scale use in the population needs to be addressed through simulations. Here, based on the epidemic characteristic and implemented public health interventions for COVID-19 in the Hubei province, we develop a mathematical model with treatment-donation-stockpile dynamics for the convalescent plasma therapy, estimate unknown model parameters by using the publicly reported data, conduct sensitivity analyses to estimate the number of patients who could be saved by the convalescent plasma therapy and to examine complication in the logistic realization of this therapy in large population. Our results show that plasma donation probability of the potential donors has major impacts on the treatment outcome. Under the assumed case that the convalescent plasma therapy could reduce the death ratio by 80% and only 10% of the recovered patients satisfy the condition of plasma donation, the reduced number of deaths could increase from 879 to 1382 if the donation probability increases from 10% to 40%. While, if 25% of the recovered patients satisfy the condition of plasma donation, the reduced number of deaths could increase to more than 2000 if the donation probability reaches 40%. Our simulations suggest the importance of enhancing the recruitment of potential donors.

The outbreak of novel coronavirus disease (COVID-19) in Wuhan in late 2019 has entered the "global pandemic" state. Based on the data on the first 425 confirmed cases in Wuhan from December 10, 2019 to January 4, 2020, this paper uses Maximum Likelihood Estimate method to obtain the basic reproduction number of COVID-19 outbreaks, which is 2.42, and the mean serial interval, which is 8.85 days. In order to characterize the regional differences in the transient transmission capacity of the disease, the daily report data of cities in Hubei Province and the other provinces and cities in China were used to obtain an estimated daily basic reproduction number of each region in February 2020 on the basis of the statistical model. Further, this paper defines a new epidemic control effectiveness formula based on the instantaneous reproduction number, and qualitatively evaluates the influence of the control strategies adopted in each region on the real-time transmission capacity of COVID-19. The results indicate that the risk of recurrence of the domestic epidemic is still high due to the imported cases at this stage, and there are obvious regional differences in the spread of COVID-19, but the factors that cause the differences deserve further follow-up.

Since the outbreak of novel Coronavirus pneumonia (COVID-19), many researchers have investigated the development trend of COVID-19 infection, transmission risk and etc. Based on open epidemic data and classic SEIR model, providing important decision basis for early COVID-19 epidemic prediction and early warning. Firstly, this paper discusses how the mathematical models of infectious diseases can help the prevention and control of epidemic situation, and what kind of important role it can play in the major public health emergencies. Then we focus on the formulation of COVID-19 models with contact tracking and quarantine measures during the COVID-19 epidemic, focusing on the similarities and differences between symptomatic infected individual and confirmed individual-driven contact tracing and quarantine measures in terms of mathematical modelling approach, and finally obtain the confirmed individual-driven COVID-19 non-autonomous model with time delay. The main conclusions reveal that the confirmation delay not only can effectively delay the peak, but also can generate multiple outbreaks for the number of exposed (infected) cases, even induce the relatively large final size, but the stringent mitigation strategies can effectively slow down the adverse impact of the confirmation delay. This finding provides a new and important model reference for the analysis of complex epidemic data.

Using mobile phone positioning big data to infer the characteristics of population activities, identify and monitor high-risk groups of new coronary pneumonia is not only an innovation of epidemiological investigation methods, but also an important support for epidemic prevention and control.This paper focuses on constructing a capture and recapture model based on mobile phone positioning big data, estimating the total number of high-risk groups of COVID-19 infection in a specific region. Taking Tianjin positioning big data with apps as an example, the method is verified to be effective in practice.Results from data analysis show that from January 24 to January 31, 2020, the scale of daily high-risk groups in Tianjin was about 13,500.The value of the research lies in the fact that it not only clarifies the key directions for the identification and monitoring of high-risk contagious people in the current epidemic prevention and control, and resumes production,, but also provides big data method support for the future construction of a major epidemic prevention and control system in China.The research in this paper provides big data method support for the identification and monitoring of high-risk groups infectious in the current epidemic prevention and control and resumption of production.

In this paper, we try to solve the challenge of COVID-19 epidemic prevention and control brought by infectivity in incubation period and asymptomatic infections. A COVID-19 epidemic prevention and control model is developed by using health-code blockchain. The spatial association matrix is used to assess the difficulty and effectiveness of epidemic prevention and control. Combined with the model and simulation, there are three findings:first, it is found that the closed city in the epidemic will have a square effect (plane superposition effect) on the economic and social development, or even a three-dimensional superposition effect, which will bring a major blow to economic and social activities. Second, it is found that the protective effect is very obvious, which can effectively reduce the number of infectious persons caused by asymptomatic infections. It is believed that with the help of the health-code blockchain, we can find asymptomatic infections. Third, it is found that the prevention and control strategies of different regions can be optimized. It is believed that the higher the node degree, the more strict the prevention and control measures should be implemented in the regions, and different prevention and control strategies should be adopted in the rural areas, central towns and central urban areas.

Since December 2019, the outbreak of the disease of novel coronavirus pneumonia, hereafter named COVID-19, has rapidly evolved into a magnitude outburst public health incident. It has posed great challenges to related prevention and control work of COVID-19 because of the strong infectious and bad consequences that cause severe symptoms and even death. Considering that the incubation and suspected period distributions play important roles in setting the quarantine and modelling the prediction in prevention of COVID-19, this paper collects and analyzes the data of 2172 confirmed cases in 29 provinces(The data are taken from the public websites of the Health Commission), and estimates the incubation and suspected period distributions with Weibull distribution. The 95th quantile of the incubation period distribution is 15.05 days. We suggest that one may use the related results of areas or provinces of different economic level in China in forecasting the epidemic situation of the other countries. It is expected that the current results have the potential to help the further studies of COVID-19.

Since the first case appeared in Wuhan, China in December 2019, the number of confirmed cases of the 2019 novel coronavirus (referred to as Corona Virus Disease 2019, or COVID-19) has swept the country at an unprecedented rate and spread to more than 160 countries and regions in the world. As of March 18, the domestic battle against COVID-19 had come to an end. Apart from imported cases abroad, there are only a few newly confirmed cases in the main land of China for several days. Under the new situation, work resumption becomes an urgent task. However, with the spread of the epidemic in Italy, Spain and other European countries, as well as Iran, South Korea, and United States, we are reminded once again that the spread of the virus is extremely powerful, and the prevention and control of the epidemic is still urgent. We first adopted a mathematical model based on the confirmed case data from January 25 to February 23, analyzed and predicted the epidemic trends and key time points in domestic provinces and major cities. A comparative analysis of those predictions and the status of the epidemic on March 18 proved that this forecast is in line with the trend of the epidemic situation and is capable to make predictions about the future epidemic situation. Therefore, based on the domestic and foreign epidemic data released in real time, we established an early warning system for the epidemic COVID-19, showing the regional spreading trends of the global epidemic from multiple aspects and monitoring of possible regional pandemic trends in real-time.

In this paper, we constructed a multi-patch endemic model to characterize the geographic spread of the coronavirus disease (COVID-19). Since Hubei was the epicenter of this COVID-19 outbreak in China and Chongqing is a neighbor municipality sharing direct airway, high-speed railway, highway, and waterway transportation, we applied 2-patch model to describe the spatial spread of COVID-19 between these two provinces and to calibrate the reported infected cases data from these two provinces. By preforming the sensitivity analysis of the basic reproduction number in terms of model parameters, we examined the effects of various control strategies such as closing the border, quarantining the exposed individuals, isolating and treating the infected individuals, and so on. It is found that closing the border alone is not enough to control the outbreak and a comprehensive strategy that combines several measures is required to eliminate this infectious disease.

Based on publicly available data online, this article uses the principal component analysis method to study the relationship between the cumulative number of confirmed diagnoses and close contacts and suspects in China. At present, the number of imported diseases has increased significantly, and prevention of imported diseases has become the focus of epidemic prevention and control in China. This paper uses cluster analysis to study the severity of the 2019 novel coronavirus pneumonia epidemic in various countries, and divides foreign countries with novel coronavirus pneumonia epidemic into three categories:major epidemic areas, key epidemic areas, and scattered epidemic area, of which Italy belongs to the main epidemic area, Iran, Spain, France, Germany, and The United States belong to key epidemic area, Japan, Malaysia and other countries are scattered epidemic areas. According to the risk level, China's border inspection can conduct batch inspection and strictly detect of entry and exit personnel, and do a good job of tracking and managing imported cases. Through the study of overseas epidemics, the risk levels of various countries are predicted in order to provide a basis for China's epidemic prevention and control work.

In this paper, we develop an SEIR model which distinguishes general population and healthcare staff, to evaluate the effects of healthcare staff on the transmission of COVID-19. Our finds suggest that the number of healthcare staff are crucial in prevention and control of COVID-19. Our results also show that when the healthcare staff are under protection, the disease will be prevalent only if the total number of susceptible people is below the critical value. When the prevention of healthcare staff is sufficient, an increasing proportion of healthcare staff to the total number of susceptible individuals will decrease the risk of disease transmission. Furthermore, when the proportion of healthcare staff exceeds a threshold, the risk of transmission is low which can also avoid a second outbreak.

The coronavirus disease 2019 (COVID-19) outbreak started in Wuhan, Hubei province, China in the end of 2019 and swiftly spread to the whole country and overseas, and became the first pandemic caused by a coronavirus in human history. By March, 2020, the outbreak in China has largely been under control with tremendous efforts and losses, while other regions, e.g., Europe and Middle East, are in extreme difficulty. The lesson learnt in Wuhan, Hubei shall be very valuable for battles in other regions. In this paper we propose a compartmental model to study the transmission dynamics of COVID-19. Our model incorporates different isolation strategies for mild and severe cases and is fitted to the cumulative number of confirmed cases in Wuhan from January 1 to 31, 2020, for COVID-19 epidemic to estimate some parameters. We find that the COVID-19 could have increased exponentially if strict measures were not properly implemented. We estimate the basic reproduction number to be 2.80, which could vary from 0.97 to 3.24 depending on human host susceptibility and transmissibility. Numerical simulations indicate that reducing transmission rate is the key factor for effective use simple word control of the outbreak. These results suggest that timely hospitalization/isolation of suspected and confirmed cases as well as quarantine of people who had close contact with infected cases in epidemic areas are vital to mitigate the spread of COVID-19.

Since the outbreak of novel coronavirus disease (COVID-19) has been spread in mainland China, the Chinese government has implemented a series of intervention policies to curb the epidemic of infectious disease. Constructing mathematical models for the prediction of possible courses of COVID-19 can help countries develop appropriate control polices. Based on the cumulative confirmed cases, the cumulative recovered cases, the cumulative deaths and the existing potential cases published daily by the National Health Commission of the People's Republic of China, we proposed a P-SIHR probabilistic graphical model to estimate the number of infectious individuals without isolation and time-varying reproduction number, so that the effects of policies could be reasonably reflected and estimated. Our results indicated that the enterprises could gradually reopen at the end of February in the severe epidemic areas outside Hubei province, where the epidemic of COVID-19 could be under the control during early March. Guangdong, as one of the most severe areas in China, there was intensive pressure to prevent and control the epidemic, due to its large population of migrants from Hubei province at an early stage. However, the intervention policies were implemented properly and timely, leading to the epidemic situation was quickly controlled.

In the past several months, the widely spreading diseases caused by the novel coronavirus (COVID-19) have severely threatened the global public health security and the global economics as well. Although the studies using the traditional compartmental epidemic models have rendered a series of profound and significant results on retrospect and prediction of epidemic process, the limitations of these studies indicate several directions for further improving the current investigations, including consideration of detailed influences from surroundings (such as real road networks, ports of entry, and loci of hospitals) and investigation of epidemic spreading dynamics induced by different indoor or/and outdoor conditions. In this article, along these suggested directions, we introduce an agent-based model and design a computational simulator, mimicking the tempo-spatial spreading dynamics of infectious diseases on a real megapolis map. Our model as well as the simulator involves real-world objects and operation rules, updating the agents' states based on their dynamic interactions with the surroundings in the map. In particular, the computational results obtained by our simulator reveal major differences of the COVID-19 spreading dynamics with and without interventions. Also, our simulator is applicable to computing those parameters related crucially to the public health, including the time-varying controlled reproduction number, in a more realistic environment. Additionally, our model establishes an elementary framework for a finite Markov decision process, allowing further broad extensions, e.g. applying reinforcement learning to train reward functions for designing optimal intervention strategies. We anticipate that our model, together with the simulator and the future extensions, could be potentially beneficial to achieving precise prediction and efficient prevention of epidemic spreading in megapolis.

According to the public data of Coronavirus (COVID-19) form National Health Committee of the People's Republic of China, we comprehensively quantified the number of confirmed patients and the status of suspected cases, and finally proposed the confidence index to fight the epidemic. The use of this index objectively reflects people's confidence in defeating the pneumonia outbreak of new coronavirus infection. On this basis, with an error target as the requirement, we modeling of Bernstein basis functions by simulation of the Coronavirus (COVID-19) epidemic. Combining with the concept of rate in the physical sense, the proposed trends of new coronavirus-infected pneumonia were thoroughly analyzed and analyzed, and good results were achieved.

There has been an outbreak of coronavirus disease (COVID-19) in Wuhan city, Hubei province, China since December 2019. In the early stage of the outbreak, cases imported from the epicenter Wuhan to other parts of China and the whole world became the main source of COVID-19 transmission. The information of imported cases can be used to infer the actual number of patients in Wuhan. We provide estimates of the daily trend in the size of the epidemic in Wuhan based on the detailed information of 10,940 confirmed cases outside Hubei province retrieved from publicly availiable records and predict the development of this epidemic in Wuhan. In this modelling study, we estimate the epidemic size and reporting rate in Wuhan from January 10, 2020, to March 19, 2020, based on the confirmed cases outside Hubei province that left Wuhan by January 23, 2020. We also estimate the date when the first patient was infected. Since some confirmed cases have no information on whether they visited Wuhan before, ordinary statistical inference could be biased. We implement the double robust method to the missing data to obtain more accurate results. The results indicate that the introduction of clinical diagnosis in Wuhan in February 2020 is an effective complement to the confirmation method at that time. As of March 19, 2020, the transmission of COVID-19 in Wuhan has been controlled.

In December 2019, a novel coronavirus is discovered in China, and named "COVID-19" after. Nowadays, multiple research are focused on modeling the confirmed case data of COVID-19. However, inadequate analysis is being done on epidemiological data, which contains additional information about the contact history of each infected case. While epidemiological data provides a deeper insight regarding the transimission characteristics of the virus, they are likely to contain missing data, which is common in real practice and brings challenge to the modeling and data analysis. We construct a transimission model that accounts for the heterogeneity from branching process theory. EM algorithm is used to process the incomplete data. By simulation, we verify the effectiveness of EM algorithm. Finally, we apply the new method on realistic data to acquire new features of the transmission of COVID-19.

In this paper, a stochastic model which captures the unique transmission dynamics of COVID-19 and the effects of intervention measures is implemented to predict the epidemic development and control time, and to estimate clinical features overseas.This model fully takes into account the influence of transmissibility during incubation, asymptomatic infection, medical tracking and other containment measures on the epidemic, overcomes the shortage of traditional dynamic model, and hence effectively predicts the occurrence and development trend of the epidemic. We find that the numbers of cases in the US, UK, Germany, Italy and Spain are expected to rise to millions in the absence of additional controls; under mild control measures, the outbreak would take more time to get controlled; while under effective measures, the outbreak would be well controlled. We also find that the UK and Spain have the relatively highest controlled reproduction number at present which suggests the risk of further spreading of the epidemic is alarmingly high in both countries. Based on the current trends and control policies, Spain could possibly overtake Italy as one of the new epicenter of COVID 19 within two weeks. Combining with the current situation of imported cases, provided that the overseas' prevention and control policies and China's border control policies remain unchanged, the number of imported cases to China would reach more than 3,000 in the next two weeks.

This paper proposes a simple, flexible and widely applied dynamic growth rate model to analyze the characteristics and the trend of global outbreak of COVID-19. Firstly, based on the ordinary differential equation for infectious diseases, the dynamic growth rate model is derived and further discussed. Secondly, this paper selects a two-parameter power function as the proper fitting function of the dynamic growth rate by using epidemic data of COVID-19 in China, and test the generality of the model by using epidemic data of SARS in China. Thirdly, this paper divides the global COVID-19 outbreak into three stages and contrast epidemic situation of foreign countries with that of China. Finally, the dynamic model is utilized to predict the inflection points of countries facing serious outbreak and forecast the future trend of existing infected case number, based on which a concise analysis of epidemic peak and end phase is provided. The results show that whether the prevention and control measures are timely and effective determines the epidemic trend, while most countries have not made good use of the precious period that China has strived for the world. Moreover, if the status maintained, it is not optimistic to expect the inflection points of those countries to come in several weeks or even months.

The data used in this paper are from the public data published in China Statistical Yearbook and National Health Commission of the People's Republic of China, as well as Baidu migration big data (desensitization data). The novel coronavirus pneumonia outbreak in Wuhan in late 2019 attracted worldwide attention. How to effectively prevent and control it has become a topic of concern in the world. First of all, the two coping mechanisms of public health emergencies are analyzed. Secondly, the data of population migration before the closure of Wuhan and the data of epidemic situation in China are obtained by using the technology of web crawler, and the epidemic prevention and control ability of 30 provinces and 15 regions in Hubei Province are calculated. Finally, the problems in the process of epidemic prevention and control are summarized, and the epidemic prevention and control are put forward Opinions on the construction of control mechanism. The research conclusion shows that there are decision-making difficulties in adopting "sentinel mode". The "sentinel mode" of fault tolerance and exemption for "Whistler" and "actuarial mode" based on big data technology are effective methods to prevent public health emergencies in the future. Accelerating the construction of big data platform and changing from "closed control" to "accurate intelligent control" are the direction of future development.

In this paper, based on the transmission mechanism of COVID-19 and public health intervention measures such as follow-up isolation of close contacts and treatment, we develop a non-autonomous dynamical model to predict the development of epidemic in Hubei Province and evaluate the effectiveness of corresponding control strategies. Firstly, using the data published by Health Commission of Hubei Province, and utilizing the methods of least square and MCMC, we estimate the model parameter values. Then, based on the estimated parameter values, we verify model prediction and estimate peak timing, peak scale and total cases during the epidemic in the Hubei Province. In addition, we reveal that quarantined exposed and existing confirmed individuals can account for a large proportion of the total cases in Hubei Province. Hence, speeding up the screening of the quarantined population and the treatment of the confirmed population can contain epidemic more quickly. Finally, a sensitivity analysis of effective reproduction number reveals that even in the later stage of the epidemic, strengthening the follow-up isolation of close contacts is still the most effective measure.

A hybrid conjugate gradient method is a new and improved conjugate gradient method with better numerical performance. Base on the hybrid conjugate gradient method proposed by Jia, a new hybrid conjugate gradient algorithm with sufficient descent property is presented, and the algorithm possesses the global convergence under the strong Wolfe line search. Numerical results show that the new algorithm was effective.

With the development of science and technology, the study of the Oscillation of dynamic equations on time scales has important applications in biological population dynamics models, Keller oscillation models in electronic engineering, quantum dynamics, and aerospace science and engineering. In recent years, there have been many results on the study of the second-order dynamic equations on the time scales, and the results of the third-order dynamic equations are not perfect, so it is of great significance to study the third-order dynamic equations. In this paper, we study the oscillation and asymptotic behavior for a class of third-order Emden-Fowler neutral delay dynamic equations on time scales. Using Riccati transformation and inequality techniques, the Leighton-type, Kemenev-type and Philos-type vibration criteria for this kind of equations are established, and some conclusions obtained in this paper generalize the known results. And some concrete examples are given to illustrate the main conclusions of this paper.

In this paper, we consider the optimal consumption, life insurance and investment problem with habit formation. We assume that the individual invests his wealth in a risk-free asset and a risky asset, and he purchases life insurance before retirement. His goal is to maximize the utility which consists of the utility from consumption before retirement or death, wealth at the retirement and heritage. From the dynamic programming principle, the problem is reduced to solve HJB equation. We obtain the explicit solutions of optimal strategy for the CRRA case. The result is that when the habit formation is included, the individual's investment amount is smaller than that without habit formation. Furthermore, the low bound of the optimal consumption depends on time, while it's zero in the classic case. If the individual's relative risk aversion is greater than 1, we also found that both the volatility of optimal consumption and the optimal insurance purchase are smaller than that in the classic case. Then we use the data in China to carry out numerical simulation in order to analyze how habit formation influences the optimal strategy. We found that when the habit formation level becomes higher, the difference of consumption between early and late periods become more significant, and the investment and the insurance purchase become less. The stronger the adaptability of the individual is, the smoother the consumption would be and the individual has stronger ability to take risks which lead to more investment in risk asset.