The goal of this study is to try to understand multi-strain diseases with the presence of cross-immunity by using mathematical models and other mathematical tools. Cross-immunity occurs when a host who is exposed to one disease, or one strain of a disease, develops resistance or partial resistance to related diseases or strains. It is an important factor in the epidemiology of diseases prone to mutation. This work includes modelling influenza in both presence and absence of controls. It also includes modelling malaria when cross-species immunity is present. In addition, vector-bias of mosquitoes to infected humans is also studied in the single-strain malaria model.