OPTIMAL CONTROL APPLIED TO RIFT VALLEY FEVER

Authors


K. Renee Fister, Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, e-mail: kfister@murraystate.edu

Abstract

Abstract Rift Valley Fever (RVF) virus is a mosquito-born pathogen that infects livestock but it also has the capability to infect humans through direct or indirect contact with blood or organs of infected animals and by bites from infected mosquitos. The economic and social cost of the disease to rural populations can lead to a cascade of negative effects on the sustainability of animal and human populations. Vaccines exist to protect against this disease. Through a compartment model depicting the interactions leading to the spread of RVF in Aedes and Culex mosquitos and a livestock population, an optimal control problem is developed to minimize the number of vaccinated livestock at the final time while minimizing the negative effects of the infected Aedes and Culex mosquitos and the cost of the vaccination process. The unique optimal vaccination strategy is produced for given high transmission parameters and numerical results portray that vaccination depends on the level of effectiveness of the protocol.

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