Infection by many viruses begins with fusion of viral and cellular lipid membranes, followed by entry of viral contents into the target cell and ultimately, after many biochemical steps, integration of viral DNA into that of the host cell. The early steps of membrane fusion and viral capsid entry are mediated by adsorption to the cell surface, and receptor and coreceptor binding. HIV-1 specifically targets CD4+ helper T-cells of the human immune system and binds to the receptor CD4 and coreceptor CCR5 before fusion is initiated. Previous experiments have been performed using a cell line (293-Affinofile) in which the expressions of CD4 and CCRS concentration were independently controlled. After exposure to HIV-1 of various strains, the resulting infectivity was measured through the fraction of infected cells. To design and evaluate the effectiveness of drug therapies that target the inhibition of the entry processes, an accurate functional relationship between the CD4/CCR5 concentrations and infectivity is desired in order to more quantitatively analyze experimental data. We propose three kinetic models describing the possible mechanistic processes involved in HIV entry and fit their predictions to infectivity measurements, contrasting and comparing different outcomes. Our approach allows interpretation of the clustering of infectivity of different strains of HIV-1 in the space of mechanistic kinetic parameters. Our model fitting also allows inference of nontrivial stoichiometries of receptor and coreceptor binding and provides a framework through which to quantitatively investigate the effectiveness of fusion inhibitors and neutralising antibodies.