This thesis aims to study the oscillatory behavior of solutions of the modified Lasota–Wazewska model, which is used to describe the survival dynamics of red blood cells in humans. The model was generalized by considering the probabilities of red blood cell production and death as variable functions. The study also considered the presence of time delays in the model, analyzed its equilibrium points, and selected an appropriate equilibrium value around which the oscillatory behavior of solutions was investigated.

The thesis investigated the model in both differential and difference forms with delays. Two mathematical transformations, namely the linear transformation and the nonlinear logarithmic transformation, were employed to derive sufficient conditions that guarantee the oscillation of solutions around the equilibrium point. The theoretical results were illustrated through several examples .

The researcher was awarded a (Distinction).