Analysis of Lumpy Skin Disease Transmission via Optimal Control and Numerical Verification by Neural Network

Abstract

Lumpy skin disease (LSD) mainly targets cattle, particularly buffalo and cows and it is characterised by the development of lumps or nodules on the skin and other parts throughout the body. This disease leads to significant losses in dairy production and cattle populations, making it
crucial to address this issue through a mathematical modelling approach. In this work, we formulate a mathematical model to understand the spread of LSD considering all potential routes through which the disease may propagate within a community. We investigate basic results in the model and determine its equilibrium points. The model undergoes sensitivity analysis as well as local stability and global stability analysis assuming the basic reproductive number is less than one. We explore the uniqueness, existence, boundedness and feasibility of the model’s solutions. To prevent the spread of the disease and we introduce a new vaccination class into the model and the model is extended to include optimal control to a mathematical model strategies focusing on vaccination and treatment to evaluate their effectiveness to minimize infection and costs. The results demonstrate that a combination of targeted vaccination and timely treatment can significantly reduce the spread of LSD supporting the implementation of cost-effective control measures. This modelling approach
provides valuable insights for policymakers and veterinary health authorities in designing effective disease management strategies. The model is then solved by using Euler’s method and the results are graphically displayed using MATLAB. An Artificial Neural Network (ANN) is also employed to approximate solution and analyze system dynamics. This approach provides effective strategies and accurate predictions for managing complex processes.