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Background: Health education plays a vital role in the prevention and control of schistosomiasis in China and throughout the world. However, the coverage of health education varies from place to place for various reasons. Moreover, people with different levels of health education migrate between different regions. Methods: In order to analyze the effects of different coverages of health education on schistosomiasis transmission, a schistosomiasis mathematical model with people's inter-regional migration is constructed in two regions with different coverages of health education. The basic reproduction number is calculated, the global stability of the system is analyzed qualitatively, and a numerical simulation is carried out. Results: (1) The transmission trend of schistosomiasis could be reduced by increasing the migration of the susceptible population from the region with a high coverage of health education to the region with low coverage, or by increasing the migration of the infected population between the two regions. Schistosomiasis can even be eliminated if the migration of the susceptible or infected population from the region with a high coverage of health education to the region with a low coverage is sufficiently large. This is quite different from the prevention and control of other epidemics in which the movement of people should be restricted. (2) A low coverage of health education will have an impact on the number of patients and infected snails in both of the two regions. This result indicates that increasing the coverage of health education can reduce the risk of schistosomiasis not only in the local population but also in the surrounding regions to which people migrate. Conclusions: There is no need to restrict the migration of the infected population between the two regions nor the migration of the susceptible population from the region with a high coverage of health education to the region with a low coverage. However, there is a need to restrict the migration of the susceptible population from the region with a low coverage of health education to the region with a high coverage. These are some suggestions to prevent and control schistosomiasis. [ABSTRACT FROM AUTHOR]

In this paper, a class of respiratory disease model is established by taking into account simultaneously two situations that susceptible individuals directly got sick by inhaling air pollutants and indirectly fallen ill from infection by patients with respiratory diseases. The sufficient conditions for equilibria existence of the system and locally asymptotically stability of endemic equilibria are obtained. The existence of saddle‐node bifurcation is derived by using the Sotomayor theorem. The stability of periodic solution of Hopf bifurcation is determined by calculating the first Lyapunov number. The direct conversion rate and indirect infection rate in the system are selected as bifurcation parameters; the existence of Bogdanov–Takens bifurcation of codimension 2 of the system is proved by calculating the universal unfolding near the cusp. This research shows that direct and indirect ways of getting sick have a significant influence on dynamical behaviors of the respiratory disease system. [ABSTRACT FROM AUTHOR]