Modeling the influence of health education on individual behavior in the process of disease transmission

Health education directly affects the different behaviors of individuals who visit and do not visit after illness by reporting the number of patients and their changing rate. As a result, visiting and non-visiting patients have different infection rates, cure rates, and disease-related mortality. In response to this impact, this article establishes a model to further analyze the impact of health education on the spread of diseases. We divide patients into visiting and non-visiting patients and introduce a weighting function that depends on the number of visiting patients and their changing rate. We constructs an implicit differential equations and use the properties of Lambert W function and its inverse function to transform it into piecewise smooth systems with explicit definitions. According to the analysis method of switched system, the two subsystems are analyzed qualitatively. The results show that health education cannot affect the basic reproduction number of disease transmission, but it causes the system to produce many types of equilibria. In addition, the difference in the healing rate and self-healing rate between visiting and non-visiting patients will affect the number of visiting and non-visiting patients and the stability of the equilibria. Moreover, the system will generate fold branch. In addition, the patient's healing/self-healing rate and the implementation of health education will affect the appearance of virtual or false equilibrium. Numerical simulation and sensitivity analysis further confirm that the total number of visiting and non-visiting patients will decrease with the increase of health education. Finally, our research results show that health education can reduce the infection rate only if there are enough susceptible people receiving health education.