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The spread of online games has become more and more serious in recent years, which not only endangers the healthy growth of young people, but also has a certain potential harm to society. Therefore, how to effectively control the spread of games has become an urgent problem to be solved. To solve this problem, a new fractional model of online game addiction is developed in this paper. In the aspect of qualitative analysis, the non-negativity and boundedness of the model solutions are demonstrated. All equilibria and basic reproduction number are solved. The global asymptotic stability of all equilibria are proved by constructing ingenious Lyapunov functions. In terms of quantitative analysis, different from previous fractional order literature, we use a new method to fit the real data of game users in China from 2010 to 2021, and obtain the optimal fractional order α = 0. 98942 and model parameters. The estimated results show that the value of the basic reproduction number during this period is R 0 = 7. 1045. By setting different values of the parameters, the effects of all parameters on the model are shown. With the Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) techniques, the influence of all parameters in the basic reproduction number R 0 are quantified and the means to control the spread of the game were generalized: isolation and treatment. Finally, the Fractional Euler Method (FEM) and the fractional Forward Backward Sweep Method (FBSM) are used together to solve the fractional optimal control problem and the optimal control strategy is determined. The results of this paper provide a new research idea for parameter estimation of fractional equation, and a more reliable result for controlling the spread of online games. • In Caputo sense, a new fractional model of online game addiction is developed. • The nonlinear dynamics of the new model are investigated. • Through a new parameter estimation method, the estimates are much closer to the real data are obtained. • An efficient algorithm combining Fractional Euler Method (FEM) and Forward Backward Sweep Method (FBSM) is shown. [ABSTRACT FROM AUTHOR]

In these days, as the recycling of household appliances becomes increasingly popular, the recycling network tends to be perfect in television industry. This paper focuses on the game among two recyclers and a processor in a Duopoly market of color TV recycling. We find that if the adjustment coefficients of the decision variables are changed abruptly, the system will fall into chaotic state. In order to avoid hazard of falling into a chaotic state, we adopt the method of delay control, providing the manufacturers with effective measures about chaos control. This paper analyzes the system's reactions to government decision, finding that when the parameters become beneficial for manufacturers, consumers and the environment, the system will fall into chaos and system's regional stability will reduce. Resulting from our analysis, this paper gives advice on the improvement of the environment and enhance in social welfare. Tested through the data we collected, this study is practical in both its theory and its applicability. [ABSTRACT FROM AUTHOR]

Abstract: An integrated ecological evaluation of the Beijing economy was presented in the paper based on the emergy accounting with the data in 2004. Through calculating environmental and economic inputs within and outside the Beijing economy, this paper discusses the Beijing’s resource structure, economic situation and trade status based on a series of emergy indicators. Through the comparison of the systematic indicators of Beijing with those of the selected Chinese cities, the general status of the Beijing economy in China is identified. The results also show that most indicators of Beijing are located at middle levels among the selected Chinese cities. Particularly, the environmental impacts, expressed by the ratio of waste to the renewable emergy, and the ratio of waste to the total emergy use, are 84.2 and 0.26, respectively in Beijing in 2004, which indicate that the Beijing economy is greatly reliant on the imported intensive fuels, goods and services with high empower density and environmental loading. [Copyright &y& Elsevier]

Abstract: This paper provides an integrated study on the ecological account for the Chinese economy in 2004 based on emergy synthesis theory. The detailed flows of the Chinese economy is diagramed, accounted and analyzed in categories using the biophysically based ecological accounting. Through calculating environmental and economic inputs within and outside the Chinese economy, this paper discusses the Chinese international exchange, describes the resource structure, and assesses its sustainability as a whole. Also, the comparison of systematic indicators, such as emergy/dollar ratio, environmental load ratio, and emergy self-support ratio, with those of the other countries is tabled and explored to illustrate the general status of the Chinese economy in the world. Take, for example, the environmental load ratio, which was 9.29 in China 2004, it reveals that the Chinese economy put high pressure on the local environment compared with those of the environment-benign countries, such as Brazil (0.75), Australia (0.86) and New Zealand (0.81). In addition, in this paper, the accounting method of tourism is adjusted based on the previous researches. [Copyright &y& Elsevier]

Antiretroviral therapy and long-range diffusion of HIV-infected individuals in heterogeneous environments can greatly impact the transmission and distribution of HIV/AIDS in a population. In this paper, we present a nonlocal dispersal HIV/AIDS epidemic model incorporating spatial heterogeneity as well as antiretroviral therapy to study the spatial and temporal dynamics of HIV/AIDS in China. To overcome the difficulty about a lack of compactness of the semiflow and the challenge about the existence and uniqueness of the principal eigenvalue of an eigenvalue problem without obvious compactness, we apply the operator semigroup and dissipative system theories. We establish the well-posedness and the existence of the global attractor for the system. Then we derive the basic reproduction number R 0 which is defined as the spectral radius of the next generation operator by the renewal equation. Afterwards, we obtain the global dynamics of the system in terms of R 0. Our numerical simulations suggest that: (1) the dynamics of HIV/AIDS transmission largely depends on the nonlocal dispersal kernel function; (2) it is necessary to monitor and design/refine rules for the mobility of HIV-infected population between remote and metropolitan areas to control the HIV/AIDS transmission; (3) antiretroviral therapy benefits not only each treated individual but also the entire community, and increasing the therapy coverage rate is one of the most effective ways to prolong the longevity of HIV-infected population. Moreover, spatial dispersal is also an important factor that cannot be ignored for designing antiretroviral therapy strategies. [ABSTRACT FROM AUTHOR]

Brucellosis is a zoonotic disease, which has gave rise to massive financial burden to animal husbandry in China. Jilin province is one of the worst-hit areas of brucellosis and thus understanding the transmission mechanism of brucellosis is of great significance for successful containment. In this paper, we leverage a discrete-time human-sheep coupled model constructed by employing backward Euler method to investigate the effects of different control measures on the brucellosis transmission in Jilin province. Firstly, we introduce the basic reproduction number R 0 which completely determines the threshold dynamics. Secondly, the parameters values of the transmission dynamics are estimated based on the confirmed human brucellosis cases and the trend of newly infected human brucellosis cases are simulated for the next few years in Jilin province, and the simulated results elucidate that brucellosis will not disappear in a short time. Lastly, we reveal that enlarging the frequency and effectiveness of disinfection, the efficacy of propaganda and education, and the elimination rate can reduce the prevalent time and final scale of brucellosis in Jilin Province. Specifically speaking, when the disinfection frequency τ = 0. 0666 and the effective disinfection rate δ = 0. 3 , the incidence of brucellosis can be dropped to less than 1 per 100,000 eleven years ahead of baseline model. When the effectiveness of propaganda and education is 60%, the control target will be attained eight years in advance. When the elimination rate μ increases by 20%, brucellosis can reach the control target ten years ahead. However, when the new born number of sheep exceeds 12075 or the elimination rate is below 0.00234, the brucellosis will outbreak promptly. Overall, the obtained results may be conductive to suppress the spread of brucellosis. • A discrete model is posed to investigate the dynamics of brucellosis transmission. • Threshold dynamics is completely proved for the discrete model. • We evaluate the effectiveness of control measures based on the model and data. [ABSTRACT FROM AUTHOR]

Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models and developing novel models, relatively limited attention has been paid to the relationship among diverse models and the modelling mechanism. The current paper proposes a unified framework and reconstructs the unified model from an integro-differential equation perspective. First, we propose a methodological framework that subsumes various nonlinear grey system models as special cases, providing a cumulative sum series-orientated modelling paradigm. Then, by introducing an integral operator, the unified model is reduced to an equivalent integro-differential equation; on this basis, the structural parameters and initial value are estimated simultaneously via the integral matching approach. The modelling procedure comparison further indicates that the integral matching-based integro-differential equation provides a direct modelling paradigm. Next, large-scale Monte Carlo simulations are conducted to compare the finite sample performance, and the results show that the reduced model has higher accuracy and robustness to noise. Applications of forecasting the municipal sewage discharge and water consumption in the Yangtze River Delta of China further illustrate the effectiveness of the reconstructed nonlinear grey models. • Propose a unified form to cover the existing nonlinear grey system models • Deduce an integro-differential equation to provide a direct modelling paradigm • Estimate structural parameters and initial conditions simultaneously • Conduct Monte Carlo simulations to compare the finite sample performance of models [ABSTRACT FROM AUTHOR]

Abstract: For urban economies, an ecological endowment embodiment analysis has to be supported by endowment intensities at both the international and domestic scales to reflect the international and domestic imports of increasing importance. A three-scale input–output modeling for an urban economy to give nine categories of embodiment fluxes is presented in this paper by a case study on the carbon dioxide emissions by the Beijing economy in 2007, based on the carbon intensities for the average world and national economies. The total direct emissions are estimated at 1.03E+08t, in which 91.61% is energy-related emissions. By the modeling, emissions embodied in fixed capital formation amount to 7.20E+07t, emissions embodied in household consumption are 1.58 times those in government consumption, and emissions in gross capital formation are 14.93% more than those in gross consumption. As a net exporter of carbon emissions, Beijing exports 5.21E+08t carbon embodied in foreign imported commodities and 1.06E+08t in domestic imported commodities, while emissions embodied in foreign and domestic imported commodities are 3.34E+07 and 1.75E+08t respectively. The algorithm presented in this study is applicable to the embodiment analysis of other environmental resources for regional economies characteristic of multi-scales. [Copyright &y& Elsevier]

Abstract: A 135-sector inventory and embodiment analysis for carbon emissions and resources use by Chinese economy 2007 is presented in this paper by an ecological input–output modeling based on the physical entry scheme. Included emissions and resources belong to six categories as: (1) greenhouse gas (GHG) in terms of CO2, CH4, and N2O; (2) energy in terms of coal, crude oil, natural gas, hydropower, nuclear power, and firewood; (3) water in terms of freshwater; (4) exergy in terms of coal, crude oil, natural gas, grain, bean, tuber, cotton, peanut, rapeseed, sesame, jute, sugarcane, sugar beet, tobacco, silkworm feed, tea, fruits, vegetables, wood, bamboo, pulp, meat, egg, milk, wool, aquatic products, iron ore, copper ore, bauxite, lead ore, zinc ore, pyrite, phosphorite, gypsum, cement, nuclear fuel, and hydropower; (5) and (6) solar and cosmic emergies in terms of sunlight, wind power, deep earth heat, chemical power of rain, geopotential power of rain, chemical power of stream, geopotential power of stream, wave power, geothermal power, tide power, topsoil loss, coal, crude oil, natural gas, ferrous metal ore, non-ferrous metal ore, non-metal ore, cement, and nuclear fuel. Accounted based on the embodied intensities are carbon emissions and resources use embodied in the final use as rural consumption, urban consumption, government consumption, gross fixed capital formation, change in inventories, and export, as well as in the international trade balance. The resulted database is basic to environmental account of carbon emissions and resources use at various levels. [Copyright &y& Elsevier]

Abstract: Ecological systems modelling based on the unified biophysical measure of cosmic emergy in terms of embodied cosmic exergy is illustrated in this paper with ecological accounting, simulation and scenario analysis, by a case study for the regional socio-economic ecosystem associated with the municipality of Beijing. An urbanized regional ecosystem model with eight subsystems of natural support, agriculture, urban production, population, finance, land area, potential environmental impact, and culture is representatively presented in exergy circuit language with 12 state variables governing by corresponding ecodynamic equations, and 60 flows and auxiliary variables. To characterize the regional socio-economy as an ecosystem, a series of ecological indicators based on cosmic emergy are devised. For a systematic ecological account, cosmic exergy transformities are provided for various dimensions including climate flows, natural resources, industrial products, cultural products, population with educational hierarchy, and environmental emissions. For the urban ecosystem of Beijing in the period from 1990 to 2005, ecological accounting is carried out and characterized in full details. Taking 2000 as the starting point, systems modelling is realized to predict the urban evolution in a one hundred time horizon. For systems regulation, scenario analyses with essential policy-making implications are made to illustrate the long term systems effects of the expected water diversion and rise in energy price. [Copyright &y& Elsevier]

Abstract: Considering the importance of supporting system for the urban ecosystem development, the urban ecological carrying capacity (UECC) representing the supporting functions of biophysical environment for urban development is introduced into the analysis of urban ecosystem degradation. It is proposed in this paper that the urban ecosystem degradation can be attributed to the imbalance between supply and demand of UECC, i.e. the conflict between the infinite demand of urban development and finite supply of biophysical supporting system, which can be mainly described by the dominant limiting factors of UECC. Through the shortage indices of various factors that denoted by the ratio of the gap between the demand and supply to the demand, the limiting factors of UECC can be identified and graded with different levels. The urban ecosystem degradation can thus be regulated by adjusting the relationship of supply and demand in terms of limiting factors from both the layers of technical practice and goal-based government management. As for Ningbo City, the shortage of water resources quantity, the pressure of SO2 emission, insufficiency of sewage treatment and green area are the prominent limiting factors and corresponding regulation scheme is thereafter suggested to adjust the relationship between supply and demand of UECC. [Copyright &y& Elsevier]

Abstract: This paper aims to present a biophysical understanding of the agricultural ecological engineering by emergy analysis for a farm biogas project in China as a representative case. Accounting for the resource inputs into and accumulation within the project, as well as the outputs to the social system, emergy analysis provides an empirical study in the biophysical dimension of the agricultural ecological engineering. Economic benefits and ecological economic benefits of the farm biogas project indicated by market value and emergy monetary value are discussed, respectively. Relative emergy-based indices such as renewability (R%), emergy yield ratio (EYR), environmental load ratio (ELR) and environmental sustainability index (ESI) are calculated to evaluate the environmental load and local sustainability of the concerned biogas project. The results show that the farm biogas project has more reliance on the local renewable resources input, less environmental pressure and higher sustainability compared with other typical agricultural systems. In addition, holistic evaluation and its policy implications for better operation and management of the biogas project are presented. [Copyright &y& Elsevier]

Abstract: Presented in this paper is an overview of energy consumption in rural China in view of temporal and spatial variations. Characterized by steadily decreased proportion of biomass use and increased percentage of coal and electricity use, coal and biomass are still the major energy sources in rural areas, accounting for nearly 80% of the total rural energy consumption. Moreover, the energy consumption varies significantly across provinces both in total sum and by fuel types due to diversities of geographic features, economic development levels and local energy source availability. Three statistical groups are clustered associated with quantitative change and structural change, exhibiting evident transition from noncommercial energy pattern to commercial energy pattern. Much more work need to be done to cope with the forthcoming dramatic changes associated with booming rural economy and newly released policy from the points of both energy security and environmental pressure in China. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to incorporate the water resources into the unified resources accounting based on scientific objectivity so as to present a brief portrait of the significance of water for the resource conversion and management of the national-scale society in a systems ecological perspective. The water resources in sustaining the human society are incorporated into the total exergy budget and national-scale social exergy accounting framework, not only by accounting the conventionally usable water flowing through society regarding seawater as reference environment, but also by introducing the evaporation exergy of freshwater as essential investment from the hydrological cycle. A case study of the Chinese society 2001–2005 is conducted, with the societal system broken down into seven sectors, i.e., extraction, conversion, agriculture, industry, transportation, tertiary and households sectors, to explore the resource utilization structure based on the proposed accounting method. Typical results for China 2005 showed that the total net input of the societal conventional resource exergy was 87.9EJ, of which 75.4EJ was from mineral resources and 22.6EJ from other resources, while the water resource exergy input amounted to 105.1EJ, which contributed 54.5% of the total resources exergy investment to the total society. Finally, the exergetic resource use intensities (RUIs) for six sectors were calculated, with the results that RUIs of agriculture and conversion sectors are much higher than those derived from conventional resource accounting. [Copyright &y& Elsevier]

Abstract: Freshwater inflow requirements (FIRs for short), which considered the requirements for protection of drinking water sources as well as the first-grade state protection wildlife (Acipenser sinensis) in larval periods, were analyzed in this paper for the Yangtze River Estuary, China. Based on the different levels of salinity objectives and the relationship between salinity and the freshwater inflows, the FIRs for the Yangtze River Estuary were determined. The estuary FIRs were determined based on the habitat ecosystem health from April to November with minimum and medium levels, from March to December with high level; and on the requirement of protection of drinking water sources in other months of the year, accordingly. Combined the salinity objectives of drinking water sources and critical habitat in the Yangtze River Estuary, the FIRs for the estuary are calculated to be 938.2×109, 729.4×109 and 615.5×109 m3 in the whole year with different levels, which is equal to 100.8%, 78.4% and 66.2% of the average annual river discharge for the Yangtze River Estuary, respectively. Annual river discharges can satisfy the medium and minimum levels of FIRs for the estuary. However, the temporal variation of the actual runoff has distinct difference from the FIRs for the estuary in critical periods (May, July and August) for the habitat ecosystem, 5% of the FIRs for the estuary should be maintained from December to February for protection of drinking water sources. [Copyright &y& Elsevier]

Abstract: Power suppliers with market power intend to bid high-price to obtain excessive profit when intensions in the balance of electricity supply and demand emerge. New index is thus necessary to be defined to assess the economic withholding behavior associated with both bidding prices and corresponding bidding capacity. Stages of low price section, economic withholding section and reasonable adventure section were classified in this paper. Based on bidding prices and capacity, absolute index and relative index were proposed to measure the economic withholding degree, with the former used for estimation of the total power system while the latter for comparisons amongst different units. A case study on Zhejiang electricity market indicated that these two proposed indices can accurately assess the economic withholding behavior in the electricity market. Finally, upper limit was suggested to be set for the relative index to suppress the behavior of excessive bidding prices in short of capacity. [Copyright &y& Elsevier]

Abstract: In many cities, the inconsistency between water supply and water demand has become a critical problem because of deteriorating water shortage and increasing water demand. Uniform price of residential water cannot promote the efficient water allocation. In China, block water price will be put into practice in the future, but the outcome of such regulation measure is unpredictable without theory support. In this paper, the residential water is classified by the volume of water usage based on economic rules and block water is considered as different kinds of goods. A model based on extended linear expenditure system (ELES) is constructed to simulate the relationship between block water price and water demand, which provide theoretical support for the decision-makers. Finally, the proposed model is used to simulate residential water demand under block rate pricing in Beijing. [Copyright &y& Elsevier]

Abstract: The study on probability density function and distribution function of electricity prices contributes to the power suppliers and purchasers to estimate their own management accurately, and helps the regulator monitor the periods deviating from normal distribution. Based on the assumption of normal distribution load and non-linear characteristic of the aggregate supply curve, this paper has derived the distribution of electricity prices as the function of random variable of load. The conclusion has been validated with the electricity price data of Zhejiang market. The results show that electricity prices obey normal distribution approximately only when supply-demand relationship is loose, whereas the prices deviate from normal distribution and present strong right-skewness characteristic. Finally, the real electricity markets also display the narrow-peak characteristic when undersupply occurs. [Copyright &y& Elsevier]

Abstract: Cities as superorganisms confront disturbances from their metabolic processes, including large metabolic fluxes, low stocks of resources and products, and a low efficiency of the urban material metabolism. Based on ecological thermodynamics, an indicator system is established in this paper to evaluate the fluxes, stocks, and effiency of the urban material metabolism using emergy analysis. Also, a new model for the urban material metabolism is proposed to define the production possibility curve using a wealth index (WI) and an ecological effiency index (EEI). Then, six large Chinese cities including Beijing, Shanghai, Tianjin, Chongqing, Guangzhou, and Shenzhen are selected as typical cases to validate the proposed model. The results show that Shenzhen has the highest metabolic capacity, followed by Beijing, Shanghai, Guangzhou, Tianjin, and Chongqing. It is also reflected that different urban material metabolisms of the six cities are resulted from the varied regional metabolic capacities, thus providing insights into how cities improve their metabolic capacities. Meanwhile, Shenzhen has the highest WI and EEI, Chongqing has the lowest WI and EEI, and Beijing, Shanghai, Tianjin, and Guangzhou has low WI and high EEI. It is also shown that the sustainable operation of the urban material metabolism reflects the mutualism and symbiosis between socioeconomic development and ecological environment protection. [Copyright &y& Elsevier]

Abstract: Based on GIS technology, eco-suitability evaluation method integrating economic, social and ecological factors is employed to optimize the locations of the sewage treatment plants and outfalls in this paper. The ecological indices considering eco-sensitivity areas as key elements of the integrated evaluation system are allotted to the water subsystem, riparian zone subsystem, and land subsystem. A novel integrated eco-suitability evaluation index system encompassing ten criteria and fifteen indices is established to generate the distributed eco-suitability map of the concerned areas and determine the possible locations of sewage treatment plants and sewage outfalls according to the eco-suitability levels. With the case study of Nansha District in Guangzhou City, China, 212km2 areas of land are found to be suitable for locating the sewage treatment plants, 87km2 areas of water suitable for sewage release, and 6km2 area of riparian zone unsuitable for sewage outfalls. [Copyright &y& Elsevier]

Abstract: Due to the increasingly serious ecological degradation of river systems, the river health research has attracted more and more attention of the researchers and decision-makers. This paper aims to integrate the fuzzy assessment method with analytic hierarchy process to establish the integrative fuzzy hierarchical assessment model, thus combing qualitative analysis and quantitative assessment and overcoming the disadvantages of subjectivity of the previous evaluation methods. The results show that the proposed assessment method is able to reveal how the river system is disturbed by human activities. Finally, the integrative fuzzy hierarchical method is validated and applied to the case study of Yong River in Ningbo City, China. [Copyright &y& Elsevier]

Abstract: Ecosystem health has been a hot topic of ecosystem management research for years. Considering the urban area as a complex ecosystem consisted of natural, societal and economic entities, urban ecosystem health assessment is necessary to be conducted for the scientific management and proper ecological restoration. Combining with the ecosystem service function of the urban ecosystem, theoretical framework and methodology of the urban ecosystem health assessment based on emergy are proposed and the temporal variation of the health level of the city are also outlined in this paper. Following the principle of ecosystem health assessment, four major factors, including vigor (V), organizational structure (O), resilience (R) and function maintenance (F), are integrated to construct a novel emergy-based urban ecosystem health index (EUEHI). Based on the EUEHI and comparing with those of five other typical Chinese cities, the case study of Baotou city shows that its urban ecosystem health level is steadily arising despite the year 2001 as a turning point. Due to the emphasis on the resource structure adjustment and utilization efficiency, Baotou has obtained a better organizational structure and service function for the total urban ecosystem. [Copyright &y& Elsevier]

Abstract: The rapid agricultural development of the Yellow River basin in China has caused serious potential water pollution to the vicinal areas. In this paper, a compact scheme is developed and employed to simulate the unsteady transportation of three representative water quality variables including ammonia nitrogen, nitrite nitrogen and nitrate nitrogen in the downstream Yellow River. As an extension of Ref. [Yang ZF, Chen GQ. The compact fourth-order finite difference scheme for the unsteady convection–diffusion equation involving source term. Chin Sci Bull 1993;38(2):113–6 [in Chinese]], the scheme is applied to the more general convection–diffusion equation with complicated terms reflecting the mutual action of water and sediment, which conforms to the characteristic of high sediment concentration of the Yellow River. The simulation results indicate that the error yielded from the proposed method is smaller than that of the referenced scheme (five-point hybrid scheme) in solving the water quality equation. [Copyright &y& Elsevier]

Abstract: Ecological treatment engineering has been widely accepted as an artificially designed work to deal with the deteriorating ecological environment with low energy and resource consumption. To measure the energy and resource consumption and environmental support contained in the constructed wetland as a kind of ecological treatment engineering, emergy as embodied solar energy based assessment is performed and relative emergy-based indices including emergy yield ratio (EYR), emergy load ratio (ELR), emergy sustainability index (ESI), net economic benefit index (Np), and renewable percentage index (Pr), are also modified to evaluate the local sustainability of the constructed wetland in this paper. A case study on Longdao River constructed wetland compared with those of some earlier conventional treatment systems indicate that more local renewable resources and less ecological cost are involved, thus promoting the economic benefit due to less energy and resource consumption and simultaneously lowering the environmental stress of the treatment system on the local areas. [Copyright &y& Elsevier]

Abstract: Presented in this paper is an integrated cost and efficiency analysis of a pilot vertical subsurface-flow constructed wetland (CW) built up in 2004 near the Longdao River in Beijing, China. The CW has been monitored over one year and proved to be a good solution to treat the polluted water and restored the ecosystem health of the Longdao River. The modified CW system in accordance with local conditions costs less in construction, operation and maintenance than traditional wastewater treatment system and occupies less land than conventional CW. Also, derived from the efficiency analysis, the Longdao River CW provides better elimination effects for nutrient substances in the polluted river water and has stable performances in cold seasons. [Copyright &y& Elsevier]

• A novel composite forecasting framework is successfully developed. • The new-information based buffer operator is employed to process raw data with stochastic disturbances. • The optimized nonlinear grey Bernoulli model is put forward by designing the novel initial condition. • The proposed model with buffer operator strikingly outperforms any of other benchmarks. To accurately predict the time series having limited data with stochastic disturbances and nonlinearity, this paper proposed a composite forecasting model by adaptive data preprocessing and optimized nonlinear grey Bernoulli model. Specifically, improvements in the proposed model lie in the following aspects: firstly, the new-information-based buffer operator is utilized to eliminate stochastic disturbance effects and thereby enhance the smoothness of the system series, which can effectively extract the potential patterns of recent development. Secondly, based on the preprocessed data, the nonlinear grey Bernoulli model provided with the newly-designed initial condition that abides by the principle of new information priority without data lapses enables the forecasting precision and applicability enhancement. Thirdly, due to the nonlinear relationships between the prediction errors and the parameters introduced by the above optimization paths, the Particle Swarm Optimization algorithm is employed to ascertain the optimal parameters simultaneously, whose efficacy and robustness have been validated by experimental comparison and sensitivity analysis. On the foundation of the above functional improvements, the novel composite forecasting framework successfully overcomes the limitations of conventional grey models to obtain more accurate and robust forecasts, which are substantiated by the applications for predicting the sales of new energy vehicles in China and Norway. Experimental results and discussions demonstrate that the new-information-based buffer operator can be regarded as an excellent alternative tool for data preprocessing. Besides, the grey models with buffered preprocessing can deliver much more accurate forecasts than their corresponding versions without buffered preprocessing. Furthermore, the proposed model with buffered preprocessing outperforms any of the other competitors and can be considered as the most promising technique for prognosticating NEVs sales. [ABSTRACT FROM AUTHOR]

• A new reaction-diffusion HFMD model with nonsmooth saturation treatment function is introduced. • The stability of equilibria, and the existence of Turing instability, Hopf bifurcation for our model are analyzed. • Simulations demonstrate the validity of theoretical results. • The model is used to fit the accumulated cases of HFMD in Guangxi Province, China from January, 2016 to May, 2019. In this paper, we propose a new reaction-diffusion model to investigate the spatial spread of hand, foot and mouth disease (HFMD). To reflect the actual factors which are limited medical resources for treatment and intensive treatment strategies which depend on a certain threshold, we also consider a continuous and nonsmooth treatment function in our model. First, existences of equilibria are determined by discussing the relation of parameters. Second, for the local stability of equilibria, the effect of the spatial diffusion including the variation of the size of the space domain and the diffusion coefficients of susceptible and infectious individuals on the stability is studied and Turing instability is demonstrated. Third, spatially homogeneous Hopf bifurcation and spatially homogeneous Hopf bifurcation are also studied by analyzing the corresponding characteristic equation. Finally, we use the model to fit the reported cases of HFMD in Guangxi Province, China from January, 2016 to May, 2019. Our results containing theoretical analysis and numerical simulations show that reducing the threshold I c with respect to intensive treatment and reducing the range of activities of infectious individuals can effectively control the spread of HFMD. [ABSTRACT FROM AUTHOR]

• Mathematical model for coronavirus disease that fits well the spread in China. • New θ -SEIHRD model taking into account undetected infections. • Validation of the model with the reported data on China. • Estimation of errors when identifying parameters at early stages of the pandemic. • Different scenarios to show the impact of undetected cases on the pandemic. In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 (COVID-19). It is a new θ -SEIHRD model (not a SIR, SEIR or other general purpose model), which takes into account the known special characteristics of this disease, as the existence of infectious undetected cases and the different sanitary and infectiousness conditions of hospitalized people. In particular, it includes a novel approach that considers the fraction θ of detected cases over the real total infected cases, which allows to study the importance of this ratio on the impact of COVID-19. The model is also able to estimate the needs of beds in hospitals. It is complex enough to capture the most important effects, but also simple enough to allow an affordable identification of its parameters, using the data that authorities report on this pandemic. We study the particular case of China (including Chinese Mainland, Macao, Hong-Kong and Taiwan, as done by the World Health Organization in its reports on COVID-19), the country spreading the disease, and use its reported data to identify the model parameters, which can be of interest for estimating the spread of COVID-19 in other countries. We show a good agreement between the reported data and the estimations given by our model. We also study the behavior of the outputs returned by our model when considering incomplete reported data (by truncating them at some dates before and after the peak of daily reported cases). By comparing those results, we can estimate the error produced by the model when identifying the parameters at early stages of the pandemic. Finally, taking into account the advantages of the novelties introduced by our model, we study different scenarios to show how different values of the percentage of detected cases would have changed the global magnitude of COVID-19 in China, which can be of interest for policy makers. [ABSTRACT FROM AUTHOR]