A model for ovine brucellosis incorporating direct and indirect transmission

In this work, we construct and analyse an ovine brucellosis mathematical model. In this model, the population is divided into susceptible and infected subclasses. Susceptible individuals can contract the disease in two ways: (i) direct mode – caused by contact with infected individuals; (ii) indirect mode – related to the presence of virulent organisms in the environment. We derive a net reproductive number and analyse the global asymptotic behaviour of the model. We also perform some numerical simulations, and investigate the effect of a slaughtering policy.