A new theoretical approach is proposed to investigate the effect of intra-individual variability in behavior on the spread of directly transmitted diseases within host populations. The classical hawk-dove game is used to describe interactions between individuals on a fast time scale (the day). Individuals may exhibit both tactics according to their own experience, to environment conditions, and to the opponent. They are not able to recognize the epidemiological state of their opponents. This fast-time part of the model is coupled to a classical compartmental epidemic model describing the demography of the population and the transmission of the disease from an infected individual to a healthy one on a slow time scale (the year). The model is applied to the case of feline immunodeficiency virus (FIV)-domestic cat population system. Our model gives rise to different predictions according to values of cost and gain due to fights: extinction of the epidemic, FIV endemicity at low, intermediate and high prevalence. These predictions are in good agreement with results from domestic cat populations living in different environmental conditions.