A vector valued optimization approach to the study of a class of epidemics
The authors present a polyoptimization problem for a reaction-diffusion system which models the spread of an epidemic of oro-fecal origin. A solution of the system is unique for all control functions representing a sanitation program in the city placed on the coast of the sea and on the coast itself. The specific initial and boundary conditions have a mixed character. The uncontrolled system is described by a linear parabolic model while the control part is given by bilinear continuous operators. The objectives for the optimization represent the cost of the sanitation activities, the cost of the epidemic itself and the economic (psychological) effects of the duration of the epidemic. The authors discuss an existence result for Pareto optimal solutions and give necessary conditions for solutions which follow from the generalized Pontryagin maximum principle.
existence result for Pareto optimal solutions
generalized Pontryagin maximum principle
scientific article; zbMATH DE number 4202096
scientific article