Viruses cause human diseases by entering in to human cells. Many drugs have been developed that act at various stages of viral infection, but they fail due to their toxic side effects and high mutation rates of viruses. Recently, a new class of drugs called entry inhibitors has been developed which acts on the early stages of viral infection. These drugs have been developed by studying the entry process of viruses in to host cells. The success of these drugs, however, is still limited and research is being done to quantify the optimum dosage of these drugs and find new drugs targets. We developed a mathematical model based on chemical reaction kinetics to estimate the threshold number of complexes between viral and target cell surface proteins necessary for HIV-1 entry into target cells. Our model quantitatively describes data of HIV entry in the presence of several entry inhibitors and presents an avenue for identifying optimal drug levels for restricting HIV entry. Majority of viruses enter into host cells by either endocytosis of fusion. But when virus enters through endocytosis and when through fusion is still not clear. We developed a theory that predicts the virus entry pathway based on the underlying biophysical properties like membrane bending modulus, viral and cellular receptor concentration and the energy released by the formation of protein complexes. Through this theory of viruses we presented the entry of viruses through fusion or endocytosis on a phase diagram. We validated the phase diagram by comparing it with known pathways of existing viruses. This study may aid in unraveling the entry pathways of new viruses and may also help in identifying new drug targets.