Dog Overpopulation Research

After readings several articles and journals supported by years of research and well-respected scientists. I see only a few opinions available to reduce the population of stray cats and dog. There is opinion of doing absolutely nothing. By doing nothing, the population of stray dog and cats would be reduced, the potential epidemics will not be stopped or prevented. This would continue to effect the general human population through the epidemics not only would the general human population effected but the animal population would as be effected and hopefully reduce the stray population as well. There is no denying that we also suffer from an overpopulation of humans. Is ethical to allow the humans to be subject to these epidemics such as rabies?