The purpose of this research is to establish a suitable mathematical model for the study of epidemiology, showing the role of the epidemic threshold which cannot be distinguished from the data for use by infectious disease experts and public health. There has been a growing interest in recent epidemiological models of epidemiology because of their health and economic effects. Epidemiology (from a mathematical point of view) is a section of general epidemiology that deals with mathematical modeling in relation to the need to predict and spread infectious diseases.