The selection pressures induced non-smooth infectious disease model and bifurcation analysis

• A non-smooth infectious disease model to describe selection pressure is developed.
• The effect of selection pressure on infectious disease transmission is addressed.
• The key factors which are related to the threshold value are determined.
• The stabilities and bifurcations of model have been revealed in more detail.
• Strategies for the prevention of emerging infectious disease are proposed.

Mathematical models can assist in the design strategies to control emerging infectious disease. This paper deduces a non-smooth infectious disease model induced by selection pressures. Analysis of this model reveals rich dynamics including local, global stability of equilibria and local sliding bifurcations. Model solutions ultimately stabilize at either one real equilibrium or the pseudo-equilibrium on the switching surface of the present model, depending on the threshold value determined by some related parameters. Our main results show that reducing the threshold value to a appropriate level could contribute to the efficacy on prevention and treatment of emerging infectious disease, which indicates that the selection pressures can be beneficial to prevent the emerging infectious disease under medical resource limitation.