The process of modeling and classifications of viruses that belong to a specific family is an important for biologist and for many biological applications. There are many ways for Viruses families' classification. The degree of similarity or diversity among the structure of the viruses capsid proteins is very useful in studying the Viruses families' classification and their genetic evolution . It also important propose if we construct a mathematical model of the virus life cycle to be able to fully understand the life cycle of Viruses families' activities . In this paper we introduce a proposed mathematical model for some Herpesvirus family viruses simple life cycle and comprehensive study for its classification using sequence alignment algorithms in order to demonstrate their genetic evolution according to the structure of their capsid protein. Herpesvirus family is considered one of the most important family in the families of the enveloped DNA viruses as it contain many dangerous viruses for human health. This family contain one of newly discovered viruses called Epstein-Barr virus (EBV), also called human herpesvirus 4 (HHV-4), which is one of the most common viruses in human. Infection with EBV occurs by the oral transfer of saliva [1] and genital secretions.