Tuberculosis (TB), AIDS (Acquired Immune Deficiency Syndrome), measles, malaria and CCHF (Crimean-Congo Hemorrhagic Fever) are the main epidemic diseases that persist as major global health problems. Estimating the number of affected people from epidemic diseases is of importance to reduce/minimize the probable negative outcomes. Therefore applicable and appropriate mathematical modelling is very useful and necessary to analyse, forecast and prevent the evolution of the diseases. A variety of mathematical models are used to detect losses from many epidemic diseases seen in the world. Some of these are SI, SIS, SIR, MSIRS, etc. Among the models, we studied SI (Susceptible-Infective) and SIS (Susceptible-Infective-Susceptible) models to decide the best appropriate/fitting model and to predict the effects of these epidemic diseases in some countries, namely, Norway for TB, malaria for Nigeria, HIV/AIDS for Ghana, CCHF for Bulgaria and measles for Afghanistan. We showed the relative predictive power of each model and in general models were found to confirm the reliability and robustness. After the analysis of the numerical results, we concluded that the SI and SIS models are very good at predicting the number of infected individuals, sensitive to fluctuations in real data and can follow the trend of exact data. Moreover, they give results in a short time.