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Impact of roguing and insecticide spraying on mosaic disease in Jatropha curcas

Al-Basir F., Roy P. K., Ray S.

Control and Cybernetics

2017

Vol. 46, no. 4

325--344

Jatropha curcas plant is greatly impaired by mosaic disease, caused by the viruses (Begomovirus), transmitted by whiteﬂies, which act as the vector. Roguing (i.e. removal of infected plant) and spraying of insecticides are common methods, employed in order to get rid of the disease. In this article, a mathematical model has been developed to study the mosaic disease dynamics while considering preventive measures of roguing and insecticide spraying. Suﬃcient conditions for the stability of equilibrium points of the system are among the results obtained through qualitative analysis. We obtain the basic reproduction number R0 and show that the disease free system is stable for R0 < 1 and unstable for R0 > 1. The region of stability of equilibrium points in diﬀerent parameter spaces have also been analysed. Hopf bifurcation at the endemic steady state has been studied subsequently, as well. Finally, by formulating an optimal control problem, optimal application of roguing and spraying techniques has been determined, keeping in mind the cost eﬀective control of the mosaic disease. Pontryagin minimum principle has been utilized to solve the optimal control problem. Numerical simulations illustrate the validity of the analytical outcomes.

Optimal control of a fractional-order enzyme kinetic model

Al-Basir F., Elaiw A. M., Kesh D., Roy P. K.

Control and Cybernetics

2015

Vol. 44, no. 4

443--461

Enzymes play a signiﬁcant role in controlling the characteristics of various chemical and biochemical reactions. They act as catalysts that increase the rate of reaction without undergoing any change in quantity. Enzymatic reactions occur through the active sites, which combine with the substrates to form intermediate complexes, subsequently leading to products. An enzyme having two active sites can show cooperative phenomena. Against this background, an enzyme-kinetic mathematical model is formulated using fractional order derivatives. Optimal control mechanism has been incorporated into the fractional-order model system to maximize the product output. Euler-Lagrange optimality conditions are derived for the FOCP (fractional order control problem) using maximum principle. Numerical iterative schemes have been developed to solve the fractional order optimal control problem through Matlab.