—We study in this paper a generalization of the basic strictly periodic scheduling problem where two positive integer constants, associated to each task, are introduced such that to replace the usual strict period. This problem is motivated by the combat of the dengue which is one of the major tropical disease. We discuss general properties and propose two integer mathematical models of the problem considered which are compared theoretically. We also suggest a lower bound which is derived from the structure of the problem. It appears to be quickly obtained and of good quality. Three greedy algorithms are proposed to provide feasible solutions which are compared with the optimum (when it can be obtained by the use of ILOG-Cplex10.0). It is shown that for special instances greedy algorithms are optimal.