For a stochastic differential equation SVIR epidemic model with vaccination, we prove almost sure exponential stability of the disease-free equilibrium for ℛ(0) < 1, where ℛ(0) denotes the basic reproduction number of the underlying deterministic model. We study an optimal control problem for the stochastic model as well as for the underlying deterministic model. In order to solve the stochasti...

This article is about numerical control of HIV propagation. The contribution of the article is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the developed model to compute optimal control profiles; finally, the computed results are applied to the real problem yielding important and practically relev...

In this paper we develop and illustrate methods for estimating the degree of suboptimality of receding horizon schemes with respect to infinite horizon optimal control. The proposed a posteriori and a priori methods yield estimates which are evaluated online along the computed closed–loop trajectories and only use numerical information which is readily available in the scheme.

This paper serves as an introduction to the theory of optimal control applied to systems of discrete time models with an emphasis on disease models. We outline the steps in solving such optimal control problems and discuss the necessary conditions. A simple disease example provides detailed methodology in charactering the optimal control through the use of Pontryagin’s Maximum Principle. Numeri...

In this paper we investigate POD discretizations of abstract linearquadratic optimal control problems with control constraints. We apply the discrete technique developed in [12] and prove error estimates for the corresponding discrete controls, where we combine error estimates for the state and the adjoint system from [17, 18]. Finally, we present numerical examples that illustrate the theoreti...

There is a growing consensus that a portfolio of customers with different demand lead times can lead to higher, more regular revenues and better capacity utilization. Customers with positive demand lead times place orders in advance of their needs, resulting in advance demand information. This gives rise to the problem of finding effective inventory control policies under advance demand informa...