| Citation: |
Yuwei Xiao, Fumin Zhang, Xinyan Guo, Ruoshi Tang, Yang Liu, Yunzhu Zhou. OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS OF AN INTEGRATED INTERVENTION MODEL INCORPORATING VECTOR PREFERENCE FOR MOSO BAMBOO SOOTY MOLD DISEASE[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 1064-1100. doi: 10.11948/20260219
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OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS OF AN INTEGRATED INTERVENTION MODEL INCORPORATING VECTOR PREFERENCE FOR MOSO BAMBOO SOOTY MOLD DISEASE
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Abstract
Understanding the transmission mechanisms of Moso bamboo sooty mold disease and the vector preference behavior of its vector insect (bamboo aphid) is of great significance for developing cost-effective integrated pest management strategies. This study constructs a compartmental model that incorporates vector preference to describe the transmission dynamics of the disease between bamboo plants and bamboo aphids. Through rigorous mathematical derivation, an explicit expression for the basic reproduction number $\mathcal{R}_0$ of the disease is obtained. Global sensitivity analysis identified the key parameters that most significantly influence the dynamics of disease transmission. Theoretical and numerical findings indicate: (ⅰ) When $\mathcal{R}_0 <1$, the disease-free equilibrium of model (2.1) is globally asymptotically stable (GAS); when $\mathcal{R}_0 > 1$, the system is uniformly persistent and possesses a unique positive equilibrium, which is GAS. (ⅱ) Under identical state variables and parameter values in this model, compared to the model ignoring vector preference $(\phi=1)$, the model incorporating vector preference $(\phi>1)$ overestimates the disease’s potential transmission capacity while simultaneously underestimating the actual infection scale. (ⅲ) Spraying insecticides and injecting nutrient solutions are long-term control measures that should be implemented throughout the entire disease management process. In contrast, using yellow adhesive traps to capture pests and removing bamboo plants exhibiting symptoms of sooty mold are short-term control strategies suitable for use during the early stages of an outbreak. Considering the cost-effectiveness of labor and materials, these measures can be discontinued in later stages. (ⅳ) According to the optimal control model for the disease and related numerical simulation results, the integrated control measure combining insecticide spraying with nutrient solution injection is found to be the most cost-effective among all strategies. This study provides a theoretical basis and decision-making support for the prevention and control of the disease.
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References
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Yuwei Xiao, Fumin Zhang, Xinyan Guo, Ruoshi Tang, Yang Liu, Yunzhu Zhou. OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS OF AN INTEGRATED INTERVENTION MODEL INCORPORATING VECTOR PREFERENCE FOR MOSO BAMBOO SOOTY MOLD DISEASE[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 1064-1100. doi: 10.11948/20260219
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Figure 1.
A schematic of system (2.1) showing transitions between different classes for Moso bamboo and bamboo aphids.
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Figure 2.
The weighted digraph
$ (\mathcal{G},A) $ -
Figure 3.
The long-term behavior of
$ E_h(t) $ $ I_h(t) $ $ E_v(t) $ $ I_v(t) $ $ \mathcal{R}_0= 0.0079< 1 $ $E^0$ -
Figure 4.
The long-term behavior of
$ S_h(t) $ $ E_h(t) $ $ I_h(t) $ $ S_v(t) $ $ E_v(t) $ $ I_v(t) $ $ \mathcal{R}_0 = 1.3869 > 1 $ $ E^* $ -
Figure 5.
Global sensitivity analysis of
$\mathcal{R}_0$ -
Figure 6.
Effect of vector preference
$\phi$ -
Figure 7.
Effect of
$\phi$ $\mathcal{R}_0$ $I_{h\infty}$ -
Figure 8.
Simulation results of the Moso bamboo sooty mold model (2.1) as a function of time without control and with optimal control for: (a) Total number of
$ E_h $ $ I_{h} $ $ E_v $ $ I_v $ $ \rho_1 = 0.5 $ $ \rho_2 = 0.5 $ $ \rho_3 = 0.6 $ $ \rho_4 = 0.5 $ $ T_f = 50 $ -
Figure 9.
The optimal controls of the Moso bamboo sooty mold model (2.1) for: (a) Insecticide treatment
$(u_1)$ $(u_2)$ $(u_3)$ $(u_4)$ $ \rho_1 = 0.5 $ $ \rho_2 = 0.5 $ $ \rho_3 = 0.6 $ $ \rho_4 = 0.5 $ $ T_f = 50 $ -
Figure 10.
Numerical simulation of the Moso bamboo sooty mold model (2.1) over time, employing plans A, B, C, D, E, and F for: (a) Total number of
$ E_h $ $ I_{h} $ $ E_v $ $ I_v $ -
Figure 11.
The optimal control measures for the Moso bamboo sooty mold model (2.1) employing strategies A, B, C, D, E, and F for: (a) Pesticide application; (b) nutrient solution application; (c) removal of Moso bamboo with sooty mold symptoms; (d) yellow adhesive trap management.
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Figure 12.
Numerical simulation of the Moso bamboo sooty mold model (2.1) over time employing plans G, H, I, and J for: (a) Total number of
$ E_h $ $ I_{h} $ $ E_v $ $ I_v $ -
Figure 13.
The optimal control measures for the Moso bamboo sooty mold model (2.1) employing plans G, H, I, and J for: (a) Pesticide application; (b) nutrient solution application; (c) removal of Moso bamboo with sooty mold symptoms; (d) yellow adhesive trap management.
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Figure 14.
Numerical simulation of the Moso bamboo sooty mold model (2.1) over time, employing plans A, H, and K for: (a) Total number of
$ E_{h} $ $ I_{h} $ $ E_{v} $ $ I_v $ -
Figure 15.
The optimal control measures for the Moso bamboo sooty mold model (2.1) employing plans A, H, and K for: (a) Pesticide application; (b) nutrient solution application; (c) removal of Moso bamboo with sooty mold symptoms; (d) yellow adhesive trap management.