bakare-nwozo
TRANSCRIPT
OPTIMAL CONTROL ANALYSIS OF THE IMPACT OF VACCINATION
IN MALARIA DISEASE EPIDEMIC MODEL
Bakare E.A 1,2 and Nwozo C.R 1
1. Department of Mathematics, University of Ibadan, Ibadan, Nigeria
2. Department of Mathematics, Federal University Oye Ekiti, Ekiti State, Nigeria.
1,[email protected], 1 [email protected]
ABSTRACT
We formulate and analyzed a compartmental deterministic model for the transmission of malaria disease. The model contain the systems of continuous time ordinary differential equations in compartments involving human and vector(mosquito) population. We imposed a control parameter(vaccination) in order to prevent the disease occurrence in human. Our model has a disease-free equilibrium that is globally asymptotically stable if the basic reproduction number is less than unity, while the endemic equilibrium exists and it is globally asymptotically stable whenever the basic reproduction number is greater than unity. We further use the optimal control theory , by deriving its necessary conditions for optimal control of the malaria disease using the Pontryagin’s Maximum Principle (PMP).We finally discussed results from our numerical simulation to illustrate our analytical results.
Keywords: vaccination, Global stability, Basic reproduction number, Pontryagin’s Maximum Principle, Optimal system, Optimal control, Hamiltonian, Simulation.