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The LSD mainly affects the cattle population and other animals, especially buffalo and cows. Due to the significant loss of dairy products and cattle population, it is necessary to highlight this issue by means of a mathematical modeling approach. We formulate a mathematical model for understanding LSD by taking all the possible routes that cause the disease to spread in the community. We study the basic results for the model and then obtain their possible equilibria. The model’s local and global asymptotical stability analysis is shown for the basic reproduction number less than unity. We further find a list of suitable parameter values for the model parameters and present the graphical results of the model. A new approach to solve fractional order system has been given, and applied to the proposed model. For the model’s sensitive parameters, we give a numerical simulation and show their impact on disease transmission.