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Mathematical Analysis of Transfusion – Transmitted Malaria Model with Optimal Control
Michael Olaniyi Adeniyi
Version 1
: Received: 10 September 2018 / Approved: 12 September 2018 / Online: 12 September 2018 (06:14:00 CEST)
Version 2 : Received: 8 January 2019 / Approved: 10 January 2019 / Online: 10 January 2019 (04:56:22 CET)
Version 2 : Received: 8 January 2019 / Approved: 10 January 2019 / Online: 10 January 2019 (04:56:22 CET)
How to cite: Adeniyi, M.O.; Aderele, O.R. Mathematical Analysis of Transfusion – Transmitted Malaria Model with Optimal Control. Preprints 2018, 2018090214 (doi: 10.20944/preprints201809.0214.v1). Adeniyi, M.O.; Aderele, O.R. Mathematical Analysis of Transfusion – Transmitted Malaria Model with Optimal Control. Preprints 2018, 2018090214 (doi: 10.20944/preprints201809.0214.v1).
Abstract
An SIR (Susceptible – Infected – Removed) mathematical model for the transmission dynamics of the Transfusion –Transmitted Malaria (TTM) model with optimal control pair and was developed and studied in this research work. The model Transfusion –Transmitted Malaria disease – free equilibrium and endemic equilibriums points were determined. The model exhibited two equilibriums; disease-free and endemic equilibrium. It was shown that the disease – free equilibrium was locally asymptotically stable if the associated basic reproduction numbers is less than unity while the disease persists if is greater than unity. The global stability of the Transfusion –Transmitted Malaria model at the disease – free equilibrium was established using the comparison method. The optimality system was derived and an optimal control model of blood screening and drug treatment for the Transfusion –Transmitted Malaria model was investigated. Conditions for the optimal control were considered using Pontryagin’s Maximum Principle and solved numerically using the Forward and Backward Finite Difference Method (FBDM). Numerical results obtained are in perfect agreement with our analytical results.
Subject Areas
malaria; transfusion-transmitted; basic reproduction number; stability; equilibrium; optimal control
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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