Mathematical modeling and analysis of the effect of the rugose spiraling whitefly on coconut trees

Suganya Govindaraj; Senthamarai Rathinam; Suganya Govindaraj; Senthamarai Rathinam

doi:10.3934/math.2022722

AIMS Mathematics

2022, Volume 7, Issue 7: 13053-13073. doi: 10.3934/math.2022722

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Research article

Mathematical modeling and analysis of the effect of the rugose spiraling whitefly on coconut trees

Suganya Govindaraj ,
Senthamarai Rathinam ^,

Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur-603203, Tamilnadu, India

Received: 21 February 2022 Revised: 13 April 2022 Accepted: 19 April 2022 Published: 09 May 2022
MSC : 34D20, 37N25, 92-10, 92D25, 92D45

Coconut trees are severely affected by the rugose spiraling whitefly (Aleurodicus rugioperculatus Martin), which is an exotic pest. The dynamics of the disease caused by this pest are analyzed using a mathematical model. The equilibrium points are proved to be locally and globally asymptotically stable under some conditions. Our study, with sensitivity analysis, reveals that the contact rate plays a crucial role in the system that has a direct impact on disease spread. Further, with optimal control, we evoke the optimum level of spraying insecticide, which results in better control over disease with minimum cost of spraying. Additionally, an approximate analytical solution has been derived using a homotopy analysis method. The $ \hbar $-curves are provided to validate the region of convergence. The analytical results are compared with the results of numerical simulation and they are found to be in good agreement. Our goal is to keep the spread under control so that yield is unaffected. Controlling the contact rate with control measures can reduce the risk of healthy trees becoming infected and the intensity of infection.
- mathematical model,
- coconut trees,
- rugose spiraling whitefly,
- stability,
- analytical approximation,
- sensitivity analysis,
- optimal control
Citation: Suganya Govindaraj, Senthamarai Rathinam. Mathematical modeling and analysis of the effect of the rugose spiraling whitefly on coconut trees[J]. AIMS Mathematics, 2022, 7(7): 13053-13073. doi: 10.3934/math.2022722

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Abstract

Coconut trees are severely affected by the rugose spiraling whitefly (Aleurodicus rugioperculatus Martin), which is an exotic pest. The dynamics of the disease caused by this pest are analyzed using a mathematical model. The equilibrium points are proved to be locally and globally asymptotically stable under some conditions. Our study, with sensitivity analysis, reveals that the contact rate plays a crucial role in the system that has a direct impact on disease spread. Further, with optimal control, we evoke the optimum level of spraying insecticide, which results in better control over disease with minimum cost of spraying. Additionally, an approximate analytical solution has been derived using a homotopy analysis method. The $ \hbar $-curves are provided to validate the region of convergence. The analytical results are compared with the results of numerical simulation and they are found to be in good agreement. Our goal is to keep the spread under control so that yield is unaffected. Controlling the contact rate with control measures can reduce the risk of healthy trees becoming infected and the intensity of infection.

References

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