Oscillation in a discrete partial delay survival red blood cells model

In this paper, we shall consider the discrete partial delay survival red blood cells model Pm+1,n + Pm,n+1 − Pm,n = −δPm,n + qe−aPm − σ, n −τ where Pm,n represents the number of the red blood cells at time m and site n, δ, a, and q are positive constants and δ and τ are nonnegative integers. We shall show that (∗) has a unique positive steady state P∗, prove that every positive solution of (∗) which does not oscillate about P∗ converges to P∗ as m, n → ∞, and present necessary and sufficient conditions for oscillation of all positive solutions of (∗) about P∗.