In this paper we propose a method for sparse dynamic allocation of resources to bound the risk of spreading processes, such as epidemics and wildfires, using convex optimization and dynamic programming techniques. Here, risk is defined as the risk of an undetected outbreak, i.e. the product of the probability of an outbreak occurring and the future impact of that outbreak, and we can allocate budgeted resources each time step to bound and minimize the risk. Our method in particular provides sparsity of resources, which is important due to the large network structures involved with spreading processes and has advantages when resources can not be distributed widely.