Fractional order mathematical modeling of lumpy skin disease

Abstract

In this article, we study the fractional-order SEIR mathematical model of Lumpy Skin Disease (LSD) in the sense of Caputo. The existence, uniqueness, non-negativity and boundedness of the solutions are established using fixed point theory. Using a next-generation matrix, the reproduction number $R_{0}$ is determined for the disease’s prognosis and durability. Using the fractional Routh-Hurwitz stability criterion, the evolving behaviour of the equilibria is investigated. Generalized Adams–Bashforth–Moulton approach is applied to arrive at the solution of the proposed model. Furthermore, to visualise the efficiency of our theoretical conclusions and to track the impact of arbitrary-order derivative, numerical simulations of the model and their graphical presentations are carried out using MATLAB(R2021a).

Keywords

• Lumpy skin disease
• SEIR mathematical model
• fractional derivative
• fixed point theory
• Adams-Bashforth-Moulton method

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