Outbreaks of African swine fever can result in substantial financial repercussions for pig industries in affected areas thereby stemming from the significant mortality rates among pigs and disruptions in the market. In this work, the behavior of an African swine fever virus model with a Caputo fractional derivative is analyzed. The existence and uniqueness results for the proposed fractional order model of African swine fever virus are investigated. The stability of the proposed model is examined within the framework of Ulam-Hyers and generalized Ulam-Hyers. The fractional Adams-Bashforth-Moulton predictor–corrector method is applied to simulate the model, which is compared with the fractional Euler method to validate its efficiency.

This present study analyzes COVID-19 transmission using a nonlinear mathematical model with a Caputo fractional derivative. By using fixed point theory, the existence and uniqueness of the solution are examined. We compute the basic reproduction number and investigate the stability analysis of the model. Approximate solutions are obtained using fractional Adam–Bashforth–Moulton method. A comprehensive exploration of optimal control is performed, utilizing one control parameter to investigate the fluctuations in the infected people under some conditions. The simulation results demonstrate the potential of fractional order derivatives with control parameter for a pandemic situation.