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Over the past decades, there has been tremendous progress towards eliminating canine rabies in Latin America. Major components of rabies prevention programs in Latin America leading to these successes have been constant and intense surveillance for rabid dogs and uninterrupted yearly mass dog vaccination campaigns. However, vital measures to control COVID-19 in Latin America have had the negative trade-off of jeopardizing these rabies elimination and prevention activities. In this paper, we aimed to assess the effect of interrupting canine rabies surveillance and mass dog vaccination campaigns on rabies trends. We built a deterministic compartment model of dog rabies dynamics parameterized for conditions found in Arequipa, Peru, where there is an ongoing dog rabies epidemic. Our model suggests that a decrease in canine vaccination coverage as well as decreased surveillance leading to an increased length of survival of infected dogs could lead to a sharp rise in canine rabies and, subsequently, human rabies risk. We examined our results over the best estimate of the basic reproductive number in Arequipa (R₀ = 1.44) and a range of plausible values for R₀ (1.36 - 2). The rising trend was consistent. It is very possible that COVID-19 will continue to challenge our public health departments in the short- and medium-term. Innovative strategies to conduct dog vaccination and rabies surveillance during these trying times should be considered to safeguard the achievements made in Latin America towards the elimination of dog-mediated human rabies.