Abstract
In this paper, we study the necessary conditions as well as sufficient conditions for optimality of stochastic SEIR model. The most distinguishing feature, compared with the well-studied SEIR model, is that the model system follows stochastic differential equations (SDEs) driven by Brownian motions. Hamiltonian function is introduced to derive the necessary conditions. Using the explicit formulation of adjoint variables, desired necessary conditions for optimal control results are obtained. We also establish a sufficient condition which is called verification theorem for the stochastic SEIR model.
Highlights
New corona viruses are very harmful to people
Motivated by the actual situation in reality and the lack of theory, this paper studies the optimal control of stochastic SEIR model
Maria do Rosario de et al [10] considered an optimal control problem with mixed control-state constraint for a SEIR epidemic model of human infectious diseases. Motivated by their pioneering work and the lack of theory, this paper is concerned with the necessary conditions for optimality of the stochastic SEIR model. e model system follows SDEs driven by Brownian motions and with the corresponding cost
Summary
New corona viruses are very harmful to people. Especially, COVID-19 is currently being spread around the world. Our main objective is to derive necessary conditions for optimality of the stochastic SEIR model by using the stochastic maximum principle (SMP). Stochastic optimal control problems have received considerable research attention in recent years due to wide applicability in a number of different fields such as physics, biology, economics, and management science. As it is well known, dynamic programming principle (DPP) and SMP are two main tools to study stochastic control problems. Let (x∗, u∗) be the optimal pair of Problem P. e standard Hamiltonian function is given by. Let (x∗, u∗) be the optimal pair of Problem P with x∗ : (S∗, E∗, I∗, R∗)τ. en, u∗(.) fulfills (12), where (pS(.), pR(.)) admits (10)
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