Avian malaria is a mosquito-borne parasitic disease of birds caused by protists of the genera Plasmodium, most notably Plasmodium relictum. This disease has been identified as a primary cause of the drastic decline and extinctions of birds, in particular Hawaiian honeycreepers (Drepanidinae), where rates of mortality may exceed 90%. We formulate an epizootiological model of the transmission dynamics of avian malaria between populations of bird hosts and mosquito vectors using a system of compartmental ordinary differential equations. We derive the basic reproduction number as well as criteria for the existence and local stability of disease-free and enzootic equilibria. These results provide useful information for evaluating management strategies. A local sensitivity analysis of certain model invariants to uncertain parameter values is performed to ascertain which biological factors have the largest impact on ecological outcomes and, in particular, long-term bird population densities. We discuss and compare the effectiveness of two disease control and conservation strategies: captive propagation of honeycreepers and larval mosquito habitat reduction. We provide examples of combinations of these strategies that either are predicted to eliminate enzootic avian malaria or to increase predicted bird density above a given ecologically meaningful threshold.