Anthrax is a rapidly fatal, infectious disease which occurs in many animal species, particularly herbivore mammals, and is one of the main causes of population decline in several national parks worldwide. As the infected animals face inevitable death and each infected carcass contributes spores to the surrounding environment, infected carcasses and the infected animals are the main sources of new infections. Thus any control measure should focus on vaccinating susceptible animals and the proper disposal of infected carcasses. In this paper, a system of ordinary differential equations modeling an anthrax epizootic in a wildlife reserve is formulated. Two controls representing vaccination of the susceptible animals and disposal of the infected carcasses are investigated in order to minimize the number of infected animals, the number of infected carcasses and the cost of vaccination and carcass disposal. Model parameters are estimated by using outbreak data from Malilangwe Wildlife Reserve, Zimbabwe, and some numerical results for the optimal control problem are presented.