We study the effects of EGFR inhibition in wild-type and mutant cell lines upon tyrosine kinase inhibitor TKI treatment through a systems level deterministic and spatially homogeneous model to help characterize the hypersensitive response of the cancer cell lines harboring constitutively active mutant kinases to inhibitor treatment. By introducing a molecularly resolved branched network systems model (the molecular resolution is introduced for EGFR reactions and interactions in order to distinguish differences in activation between wild-type and mutants), we are able to quantify differences in (1) short-term signaling in downstream ERK and Akt activation, (2) the changes in the cellular inhibition EC50 associated with receptor phosphorylation (i.e., 50% inhibition of receptor phosphorylation in the cellular context), and (3) EC50 for the inhibition of activated downstream markers ERK-(p) and Akt-(p), where (p) denotes phosphorylated, upon treatment with the inhibitors in cell lines carrying both wild-type and mutant forms of the receptor. Using the branched signaling model, we illustrate a possible mechanism for preferential Akt activation in the cell lines harboring the oncogenic mutants of EGFR implicated in non-small-cell lung cancer and the enhanced efficacy of the inhibitor erlotinib especially in ablating the cellular Akt-(p) response. Using a simple phenomenological model to describe the effect of Akt activation on cellular decisions, we discuss how this preferential Akt activation is conducive to cellular oncogene addiction and how its disruption can lead to dramatic apoptotic response and hence remarkable inhibitor efficacies. We also identify key network nodes of our branched signaling model through sensitivity analysis as those rendering the network hypersensitive to enhanced ERK-(p) and Akt-(p); intriguingly, the identified nodes have a strong correlation with species implicated in oncogenic transformations in human cancers as well as in drug resistance mechanisms identified for the inhibitors in non-small-cell lung cancer therapy.