In this work, a superinfection model of two HIV strains was proposed. The proposed model was solved and interpreted using the Elzaki Transform Method (ETM). The proposed model presented some non-linear terms which are difficult to resolve using the ETM. Hence, we employed the Adomian Decomposition Method (ADM) to resolve the nonlinear terms. We derived an iterative scheme that was used to predict the behavior of the model. Results of data simulation showed that the population of healthy CD4+ T cells declined with respect to time in the presence of HIV strains. The viral loads for both viral strains are observed to be on a steady increase. The study reveals that ETM can be used to solve Superinfection models of HIV. The method is easier, more efficient, and more effective, and it converges faster to the solution when compared to other transform methods. We recommend that ETM can be applied to superinfection and co-infection models of other infectious diseases.