Modelling and Optimal Control of Insect Transmitted Plant Disease
Alex Xavery Matofali, Department of Mathematics, Informatics and Computational Sciences, Sokoine University of Agriculture (SUA), Morogoro, Tanzania.
Insect-vectored diseases pose one of the greatest threats to plants on a global scale. At present, few effective control strategies have been developed to prevent the transmission of insect-transmitted diseases. These strategies largely rely on the use of chemical insecticides which have negative impacts on the environments and human health. In this study, a mathematical model is formulated and analysed to study the optimal control of the insects transmitted plants diseases. The model is sub-divided into two sub-populations namely the plant population and the insect population. The plant population is divided into two classes, namely; susceptible plants and infected plants and vector (insect) population comprises susceptible vector and infected vector. The optimal control model is formulated and analysed to minimize the transmission of disease from an infected vector (insect) to susceptible plant. Optimal control method using Pontryagin’s Maximum Principle was applied to determine the necessary conditions for the optimal control of the impact of plant inoculation. It is concluded that, if the plants are controlled then more plants will be produced compared with plants without control.
Modelling, Optimal, Insects, Transmission, Disease
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