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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]

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]

• 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]