On a common fixed point theorem in vector-valued b-metric spaces: Its consequences and application

We introduce a Ciric type contraction principle in a vector-valued b-metric space that generalizes Perov's contraction principle. We investigate the possible conditions on the mappings W, E : G -> G (G is a non-empty set), for which these mappings admit a unique common fixed point in G subject to a nonlinear operator F : P-m -> R-m. We illustrate the hypothesis of our findings with examples. We consider an infectious disease model represented by the system of delay integrodifferential equations and apply the obtained fixed point theorem to show the existence of a solution to this model.