Modeling the effect of health education and individual participation on the increase of sports population and optimal design

Pan Tang; Ning Wang; Tong Zhang; Longxing Qi; Pan Tang; Ning Wang; Tong Zhang; Longxing Qi

doi:10.3934/mbe.2023579

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12990-13014. doi: 10.3934/mbe.2023579

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Modeling the effect of health education and individual participation on the increase of sports population and optimal design

1.
Department of Public Sports and Art Teaching, Hefei University, Hefei 230601, China
2.
School of Mathematical Sciences, Anhui University, Hefei 230601, China

Academic Editor: Xiaodi Li

Received: 29 December 2022 Revised: 25 April 2023 Accepted: 07 May 2023 Published: 05 June 2023

Health education plays an important role in cultivating people's awareness of participating in physical exercise. In this paper, a new differential equation model is established to dynamically demonstrate the different impact of mass communication and interpersonal communication in health education on people's participation in physical exercise. Theoretical analysis shows that health education does not affect the system threshold, but individual participation does. The combination of the two leads to different equilibria and affects the stability of equilibria. When mass communication, interpersonal communication and individual participation satisfy different conditions, the system will obtain different positive equilibrium with different number of sports population. If the interpersonal transmission rate of information is bigger, there is a positive equilibrium with a large number of sports population in the system. Sensitivity and optimal design analysis show some interesting results. First, increasing interpersonal communication and mass communication can both increase the number of conscious non-sports population and sports population. For increasing the number of conscious non-sports population, the effect of mass communication is better than that of interpersonal communication. For increasing the number of sports population, the effect of interpersonal communication is better than that of mass communication. However, individual participation has the best effect on increasing the sports population. Second, increasing the daily fixed amount of new information will be more helpful for media information dissemination. Finally, the three control measures need to be implemented simultaneously for a period of time at first, and then health education and participation of sports people need to be implemented periodically in order to maximize the sports population.
- sports population,
- mathematical model,
- periodic health education,
- individual participation
Citation: Pan Tang, Ning Wang, Tong Zhang, Longxing Qi. Modeling the effect of health education and individual participation on the increase of sports population and optimal design[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12990-13014. doi: 10.3934/mbe.2023579

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Abstract

Health education plays an important role in cultivating people's awareness of participating in physical exercise. In this paper, a new differential equation model is established to dynamically demonstrate the different impact of mass communication and interpersonal communication in health education on people's participation in physical exercise. Theoretical analysis shows that health education does not affect the system threshold, but individual participation does. The combination of the two leads to different equilibria and affects the stability of equilibria. When mass communication, interpersonal communication and individual participation satisfy different conditions, the system will obtain different positive equilibrium with different number of sports population. If the interpersonal transmission rate of information is bigger, there is a positive equilibrium with a large number of sports population in the system. Sensitivity and optimal design analysis show some interesting results. First, increasing interpersonal communication and mass communication can both increase the number of conscious non-sports population and sports population. For increasing the number of conscious non-sports population, the effect of mass communication is better than that of interpersonal communication. For increasing the number of sports population, the effect of interpersonal communication is better than that of mass communication. However, individual participation has the best effect on increasing the sports population. Second, increasing the daily fixed amount of new information will be more helpful for media information dissemination. Finally, the three control measures need to be implemented simultaneously for a period of time at first, and then health education and participation of sports people need to be implemented periodically in order to maximize the sports population.

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