Abstract
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.
Highlights
E above studies mainly used statistical methods to analyze historical data or used common prediction models to forecast the number of future patient visits
In contrast to previous studies, the research purpose and innovations of this paper are mainly reflected in the following aspects: (1) We use a logistic differential equation model to study the development trend of the number of visits to medical institutions in the absence of strong government intervention. e differential equation model is an excellent method of describing the process of a system, and it can transform complex social problems into an intuitive mathematical model
Since the outbreak of pneumonia in the novel coronavirus infection, many scientists have established models to analyze and predict the development trend of infectious diseases and have achieved promising results [28,29,30,31,32,33,34]. is model has been applied in the fields of sustainable science [35], economics [36], and in other areas, but few studies have focused on the study of the study of visits to medical institutions. e differential equation model of this paper is similar to the plaque model of the cross-regional transmission of infectious diseases [37]
Summary
China’s medical system is a complex, nonlinear system. we establish a two-dimensional differential equation model based on the present situation to analyze the process of change of the number of visits in PHCIs and hospitals over time. Taking into account that deaths occur in the population and some people give up treatment due to difficulties in seeking medical treatment, this reduces the number of visits to medical institutions, so we use d1 and d2 to represent the churn rate of visits to PHCIs and hospitals, which positively correlates with the above situations. We use m to represent this leapfrog medical treatment rate that is related to patient behavior, and mx represents the number of visits from PHCIs to hospitals per unit time. E initial conditions are x0, y0 > 0, r1,2, k1,2, d1,2, m, n > 0
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