IJPAM: Volume 77, No. 4 (2012)

OPTIMAL CONTROL PROBLEM FOR
A HOST-PARASITOID MODEL

K.W. Blayneh$^1$, Pierre Ngnepieba$^2$
$^1$Department of Mathematics
Florida A&M University
Tallahassee, FL 32307, USA


Abstract. An optimal control model for a host-parasitoid interaction is considered. The host-parasitoid interaction is described by a coupled pair of partial differential equation (with initial and boundary values) for the host; and a delay ordinary differential equation (with initial value) for the parasitoid. The parasitoid population is assumed to be a biological control agent against the host which is assumed to be a pest population. A time dependent control measure is practiced to make sure that the parasitoid is effective in diminishing the host population. An objective function is defined to study the possibility of minimizing the cost of control measures while maximizing the effectiveness of the parasitiod. Existence of a unique solution is proved to the resulting host-parasitoid state equations. Other results include establishing a unique optimal solution of the optimal control model.

Received: March 6, 2012

AMS Subject Classification: 92D25, 49K20

Key Words and Phrases: host-parasitoid, biological control, optimal solution

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 4