Propagation dynamics for a time-periodic reaction-diffusion two group SIR epidemic model

The paper was devoted to studying the spreading speed and traveling wave solutions for a time-periodic reaction-diffusion two group susceptible-infective-recovered (SIR) epidemic model. With regard to the basic reproduction number $ R_0 $ of the corresponding periodic ordinary differential system and the minimal wave speed $ c^* $, spreading properties of the corresponding solution of the model when $ R_0>1 $ were established, which implied that the minimal wave speed $ c^* $ was equal to spreading speed of system (2). On the basis of it, the full information about the existence and nonexistence of traveling wave solutions of the system related with $ R_0 $ nd $ c^* $ can be studied. More specifically, we proved that when $ R_{0} > 1 $ and $ c \geq c^* $, the system admitted a nontrivial time-periodic traveling wave solution with wave speed $ c $, and for $ c<c^* $ there were no such traveling waves satisfying the system. In addition, when $ R_{0} < 1 $, the system admitted no nontrivial traveling waves.