Entire solutions in a bistable reaction–diffusion system modeling man–environment–man epidemics

This paper is concerned with entire solutions of a bistable reaction–diffusion system modeling man–environment–man epidemics, i.e., solutions defined for all times t∈Rt∈R and for all points x∈Rx∈R. It is known that the system has an increasing traveling wave solution with nonzero wave speed under some reasonable conditions. Using the comparison argument and sub-super-solution method, we construct some new entire solutions for the system which behave like two increasing traveling wave solutions propagating from both sides of the xx-axis and annihilating at a finite time.