Human red blood cells (RBCs) are responsible to transport oxygen and carbon dioxide for human bodies. The physiological functions of RBCs are greatly influenced by their mechanical properties. When RBC is infected by Malaria parasite called Plasmodium falciparum, it shows progressive changes in mechanical properties and loses its deformability. The infected red blood cells (IRBCs) develop properties of cytoadherence (stickiness) and rosetting (the binding of non-infected RBCs to parasitized RBCs). In this paper to analyze the mechanical properties and deformability of the IRBC, we applied stress-stretch ratio relation of its biomembrane .To express this constitutive relation, we proposed a mathematical model (Neo-Hookean model) based on membrane theory. On this model, we present continuous stress-stretch ratio curves for the relation derived from the model for different intracellular developmental stages of the parasite, to determine the mechanical properties of IRBC. The analytical results obtained from the mathematical model are more closed with the experimental data [1] which demonstrates the validity of the model. By restricting our attention to spherically symmetric deformation in the final schizont stage of parasite development, the pressure-extension ratio relation curve also adapted from the proposed strain energy function. The change in osmotic pressure versus volumetric ratio has been also considered for IRBC before hemolysis

Sickle cell disease (SCD) is a disease of abnormal rheology. The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In SCD, the intracellular polymerization of sickle hemoglobin upon deoxygnation leads to marked increase in intracellular viscosity and elastic stiffness and also having indirect effects on cell membrane .To examine mathematically, the abnormal cell rheology behavior due to polymerization process and that due membrane abnormalities , we mechanically modeled the whole cell deformability as viscoelastic solid and proposed a Voigt-model of nonlinear viscoelastic solid constitutive relation as " mixture''of an elastic and viscous dissipative parts, with parameters of elastic and viscous moduli. The elastic part used to express stress-strain relations via strain energy function of the material and the viscous part derivation depends on strain -rate of deformation. The combination of both constitutive expressions is used to predict the viscoelastic properties of normal and sickle erythrocyte. Furthermore, sickle hemoglobin polymerization also leads to alter the osmotic behavior of the cell and to investigate such osmotic effect; we employ the van't Hoff law of osmotic pressure versus volume relation. The analysis of both formulations presented well the abnormal rheological /mechanical characterization of sickle erythrocyte membrane as we understood and concluded from our results.