Evaluation of the Number of Visits to Chinese Medical Institutions Using a Logistic Differential Equation Model

In this study, we established a two-dimensional logistic differential equation model to study the number of visits in Chinese PHCIs and hospitals based on the behavior of patients. We determine the model's equilibrium points and analyze their stability and then use China medical services data to fit the unknown parameters of the model. Finally, the sensitivity of model parameters is evaluated to determine the parameters that are susceptible to influence the system. The results indicate that the system corresponds to the zero-equilibrium point, the boundary equilibrium point, and the positive equilibrium point under different parameter conditions. We found that, in order to substantially increase visits to PHCIs, efforts should be made to improve PHCI comprehensive capacity and maximum service capacity.

Application of fuzzy mathematics calculation in quantitative evaluation of students’ performance of basketball jump shot

In order to improve the modelling efficiency in dynamic system prediction, this paper proposes a predictive model based on high-order normal differential equations to model high-order differential data to obtain an explicit model. The high-order constant differential equation model is reduced, and the numerical method is used to solve the predictive value. The results show that the method realises the synchronisation of model establishment and parameter optimisation, and greatly enhances the modelling efficiency.

Differential equation model of financial market stability based on Internet big data

In the context of Internet big data, the market characteristics of the financial market can be used to feed back its stability with the help of differential equation models. China's financial market is roughly divided into three main markets: stocks, currency and foreign exchange. The interaction of the three has promoted the development of the financial market. With this as a background, the paper aims at these three financial markets and selects relevant indicators that can reflect the indications of the financial market to construct differential equations to analyse the relationship between the three. The paper uses the nonlinear characteristics of ordinary differential equations and related algorithms to solve the three types of market models. It uses an example to demonstrate that the differential equation model proposed in this paper can feed back the evolutionary characteristics of the three, and this model can help investors produce more correct investment decisions.

User online consumption behaviour based on fractional differential equation

User consumption behaviour is a subject worthy of study. Because consumers’ consumption behaviours are dynamic and with individual differences, various factors need to be considered when establishing a fractional differential equation model of users’ online consumption behaviour. The two elements, namely advertising and price are more evident in influencing consumer behaviour. Therefore, the paper establishes a product diffusion fractional differential equation model of price and advertising presence or absence to study the impact of these two factors on consumer behaviour. It turns out that ignoring the advertisement and the cost of the product is related to the characteristics of the consumer network. When there are advertising and price factors, product awareness is related to price constraints.

Nonlinear Differential Equations in the Teaching Model of Educational Informatisation

This article takes the nonlinear differential equation model as an example and uses information technology to create a new course teaching model. The computing software Maple is effectively applied to the precise solution of nonlinear differential equations through the analysis of examples. The overall goal and specific implementation of the teaching plan to integrate ordinary differential equations and information technology have been completed. The study found that the teaching plan proposed in the article is assisted by information technology, with teachers and students participating in an interactive and exploratory teaching method. This method is worthy of further promotion.

Parameter estimation of a susceptible–infected–recovered–dead computer worm model

Computer worms are serious threats to Internet security and have caused billions of dollars of economic losses during the past decades. In this study, we implemented a susceptible–infected–recovered–dead (SIRD) model of computer worms and analyzed the characteristics and mechanisms of worm transmission. We applied the ordinary differential equation model to simulate the transmission process of computer worms and estimated the unknown parameters of the SIRD model through the methods of least squares, Markov chain Monte Carlo, and ensemble Kalman filtering (ENKF). The results reveal that the proposed SIRD model is more accurate than the susceptible–exposed–infected–recovered–susceptible model with respect to parameter estimation.