Sensitivity analysis of fractional order SVEIR Lumpy Skin Disease model

Abstract

Lumpy skin disease (LSD) is a highly contagious and often fatal infection in cattle, primarily characterized by the formation of skin lumps. It leads to severe economic losses due to reduced milk production, weight loss, infertility, and hide damage. This study aims to comprehensively analyze the dynamics of LSD and devise effective mitigation strategies through mathematical modeling. A fractional SVEIR model is proposed to predict the transmission dynamics within affected cattle populations. The model’s feasibility is verified using the Laplace transformation, demonstrating both local stability, using the Matignon criterion, and global stability, employing Lyapunov functions and LaSalle’s invariance principle. The basic reproduction number ($R_{LSD}$) is calculated using the next-generation matrix method. Sensitivity analysis, based on the normalized forward sensitivity index, identifies key parameters influencing $R_{LSD}$: A 30% decrease in the average number of bites ($\beta$) reduces the infected cattle population by 16.58%. A 30% increase in the recovery rate ($\rho$) leads to a 29.35% reduction in infections. Increasing the vaccination rate ($\gamma$) by 79% lowers the number of sick cattle by 20%. Numerical simulations explore LSD transmission across five cattle populations under different scenarios of disease persistence and elimination. The findings are supported by theoretical analysis and visually represented through graphical illustrations, offering valuable insights into LSD control and prevention strategies.