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Eco-epidemiological Model and Optimal Control Analysis of Tomato Yellow Leaf Curl Virus Disease in Tomato Plant
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The purpose of this study is to analyze the impact of control strategies
namely insecticide spray, roguing of a diseased tomato plant, protective
netting to protect tomato plant from TYLCVD. Thus, a mathematical model
for the transmission dynamics of TYLCVD that includes these control
strategies is formulated and analyzed. In the case of constant control,
the basic reproduction number is calculated and the existence and
stability of equilibria are investigated. Besides, an optimal control
model with constraints is formulated and investigated. In the
non-constant control case, Pontryagin's Maximum Principle is used to
deduce necessary conditions for the optimal control of the disease. It
is shown that all the combined efforts of two of three strategies can
significantly reduce the disease except the combination of the use of
insecticide spray and rouging infected tomato plants. Relatively the
other, the use of roguing diseased tomato plants and protective netting,
and the use of insecticides spray, roguing diseased plants and
protective netting are better decreased the disease. Moreover, the use
of roguing diseased plants and protective netting has a similar effect
as the use of insecticides spray, roguing diseased tomato plants, and
protective netting. As resources are scarce, we recommend that
policy-makers should adopt the combination of the use of roguing
diseased tomato plants and protective netting as a strategy.
Title: Eco-epidemiological Model and Optimal Control Analysis of Tomato Yellow Leaf Curl Virus Disease in Tomato Plant
Description:
The purpose of this study is to analyze the impact of control strategies
namely insecticide spray, roguing of a diseased tomato plant, protective
netting to protect tomato plant from TYLCVD.
Thus, a mathematical model
for the transmission dynamics of TYLCVD that includes these control
strategies is formulated and analyzed.
In the case of constant control,
the basic reproduction number is calculated and the existence and
stability of equilibria are investigated.
Besides, an optimal control
model with constraints is formulated and investigated.
In the
non-constant control case, Pontryagin's Maximum Principle is used to
deduce necessary conditions for the optimal control of the disease.
It
is shown that all the combined efforts of two of three strategies can
significantly reduce the disease except the combination of the use of
insecticide spray and rouging infected tomato plants.
Relatively the
other, the use of roguing diseased tomato plants and protective netting,
and the use of insecticides spray, roguing diseased plants and
protective netting are better decreased the disease.
Moreover, the use
of roguing diseased plants and protective netting has a similar effect
as the use of insecticides spray, roguing diseased tomato plants, and
protective netting.
As resources are scarce, we recommend that
policy-makers should adopt the combination of the use of roguing
diseased tomato plants and protective netting as a strategy.
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