title: Vaccination Control in a Stochastic SVIR Epidemic Model.
abstract: 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 stochastic problem numerically, we use an approximation based on the solution of the deterministic model.
authors.affiliation: University of the Western Cape, Private Bag X17, Bellville 7535, South Africa.
authors.forename: Peter J
authors.initials: PJ
authors.lastname: Witbooi
authors.affiliation: University of the Western Cape, Private Bag X17, Bellville 7535, South Africa.
authors.forename: Grant E
authors.initials: GE
authors.lastname: Muller
authors.affiliation: University of the Western Cape, Private Bag X17, Bellville 7535, South Africa.
authors.forename: Garth J
authors.initials: GJ
authors.lastname: Van Schalkwyk
mesh_terms: D050936:Basic Reproduction Number; D019295:Computational Biology; D003198:Computer Simulation; D058872:Epidemics / Q000517:prevention & control* / Q000706:statistics & numerical data; D006801:Humans; D017053:Infection Control / Q000379:methods / Q000706:statistics & numerical data; D008954:Models, Biological; D015233:Models, Statistical; D013269:Stochastic Processes; D014611:Vaccination / Q000379:methods* / Q000706:statistics & numerical data