Comparative studies for the fractional optimal control in transmission dynamics of west nile virus. (English) Zbl 1377.37119
Summary: In this paper, optimal control for a novel West Nile virus (WNV) model of fractional order derivative is presented. The proposed model is governed by a system of fractional differential equations (FDEs), where the fractional derivative is defined in the Caputo sense. An optimal control problem is formulated and studied theoretically using the Pontryagin maximum principle. Two numerical methods are used to study the fractional-order optimal control problem. The methods are, the iterative optimal control method (OCM) and the generalized Euler method (GEM). Positivity, boundedness and convergence of the IOCM are studied. Comparative studies between the proposed methods are implemented, it is found that the IOCM is better than the GEM.
MSC:
| 37N25 | Dynamical systems in biology |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
| 92D30 | Epidemiology |
Keywords:
fractional optimal control; generalized Euler method; Caputo’s fractional derivative; Pontryagin’s maximum principleReferences:
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