Modeling and numerical simulation of Lumpy skin disease: Optimal control dynamics approach

Awatif J. Alqarni; Awatif J. Alqarni

doi:10.3934/math.2025465

AIMS Mathematics

2025, Volume 10, Issue 4: 10204-10227. doi: 10.3934/math.2025465

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Modeling and numerical simulation of Lumpy skin disease: Optimal control dynamics approach

Awatif J. Alqarni ^,

Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha, 61922, Saudi Arabia

Received: 25 February 2025 Revised: 15 April 2025 Accepted: 22 April 2025 Published: 29 April 2025
MSC : 93C10, 92B05, 90C31, 34D20

In this research, I aimed to develop a mathematical system that simulates the mechanics of lumpy skin disease (LSD) transmission in cattle. The approach of optimal control was used, and the samples were divided into six categories: Infected, recovered, susceptible, vaccinated, susceptible vector insects, and infected vector insects. The Runge-Kutta technique from the fourth order was used to solve the numerical system, and the effects of various preventative actions like treatment, vaccination, and pesticide spraying on the dissemination of the disease were studied. The stability of the mathematical model was investigated, and it was determined that the disease-free equilibrium point is stable when the infection fails to spread within the population. A sensitivity analysis was performed, and the results showed that the exceedingly sensitive parameters are the natural mortality rate of vector insects and the vaccination rate. The hypothesis of optimal control was used to identify the optimal strategies to reduce the disease's proliferation, and it was found that the combination of all measures significantly reduces the number of infected cases and is a reason for increasing the number of recovered cattle, emphasizing the significance of other measures like early vaccination and isolation of infected cattle.
- Lumpy skin disease model,
- optimal control problem,
- stability analysis,
- sensitivity analysis,
- numerical simulation
Citation: Awatif J. Alqarni. Modeling and numerical simulation of Lumpy skin disease: Optimal control dynamics approach[J]. AIMS Mathematics, 2025, 10(4): 10204-10227. doi: 10.3934/math.2025465

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Abstract

In this research, I aimed to develop a mathematical system that simulates the mechanics of lumpy skin disease (LSD) transmission in cattle. The approach of optimal control was used, and the samples were divided into six categories: Infected, recovered, susceptible, vaccinated, susceptible vector insects, and infected vector insects. The Runge-Kutta technique from the fourth order was used to solve the numerical system, and the effects of various preventative actions like treatment, vaccination, and pesticide spraying on the dissemination of the disease were studied. The stability of the mathematical model was investigated, and it was determined that the disease-free equilibrium point is stable when the infection fails to spread within the population. A sensitivity analysis was performed, and the results showed that the exceedingly sensitive parameters are the natural mortality rate of vector insects and the vaccination rate. The hypothesis of optimal control was used to identify the optimal strategies to reduce the disease's proliferation, and it was found that the combination of all measures significantly reduces the number of infected cases and is a reason for increasing the number of recovered cattle, emphasizing the significance of other measures like early vaccination and isolation of infected cattle.

References

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