Vaccination Control in a Stochastic SVIR Epidemic Model

Peter J Witbooi; Grant E Muller; Garth J Van Schalkwyk

doi:10.1155/2015/271654

Vaccination Control in a Stochastic SVIR Epidemic Model

Comput Math Methods Med. 2015:2015:271654. doi: 10.1155/2015/271654. Epub 2015 May 24.

Authors

Peter J Witbooi¹, Grant E Muller¹, Garth J Van Schalkwyk¹

Affiliation

¹ University of the Western Cape, Private Bag X17, Bellville 7535, South Africa.

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.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Basic Reproduction Number
Computational Biology
Computer Simulation
Epidemics / prevention & control*
Epidemics / statistics & numerical data
Humans
Infection Control / methods
Infection Control / statistics & numerical data
Models, Biological*
Models, Statistical
Stochastic Processes
Vaccination / methods*
Vaccination / statistics & numerical data