An impulsive predator–prey model with communicable disease in the prey species only

A system of impulsive differential equations describing predator–prey dynamics with impulsive effect is proposed and analyzed with the assumption that a transmissible disease is spreading among the prey species only. At first, the “semi-trivial” periodic solution (S(t),0,0)(S(t),0,0) is given. After that, the existence of “infection-free” periodic solution (S(t),0,P(t))(S(t),0,P(t)) and the “predator-free” periodic solution have been obtained via bifurcation. Finally, the method of coincidence degree has been used to derive a set of sufficient conditions for the existence of at least one strictly positive periodic solution. Numerical simulations and a brief discussion conclude the paper.