Efficiency of Control Strategies for TYLCV Disease Using a Fractional‐Order Model

Abstract

ABSTRACT This study aims to analyze the spread dynamics of tomato yellow leaf curl virus (TYLCV) within a caputo fractional order model (FOM) that takes into account the interactions between tomato plants (TPs) and the virus‐transmitting whitefly. The FOM was developed to include five classes: susceptible TPs, latently TPs, infected TPs, susceptible whiteflies, and infected whiteflies. We investigate the theoretical aspects of the proposed FOM, such as the existence, uniqueness, positivity, and boundedness of its solutions. Equilibrium points (EPs), including the disease‐free equilibrium (DFE) point and the endemic equilibrium point (EEP), were calculated and their local and global stability was studied, along with the control reproduction number (CRN), derived through the next‐generation matrix (NGM) method. Sensitivity analysis identifies the most effective parameters on the CRN. Implementing Pontryagin's maximum principle (PMP), optimal control strategies (OCSs) were designed, including , , , which are the use of virus‐resistant plant varieties, removal of infected TPs, and spraying of pesticides, respectively. The fractional optimal control problem (FOCP) was solved using the Adams‐type predictor‐corrector method (PCM). The results revealed that Strategy IV (combining all controls , , and ) was the most effective in reducing and while achieving the lowest cost ( at ). The proposed FOM also showed a higher control efficiency than the classical model (), achieving better results with lower values of (0.98, 0.95), providing an advanced mathematical framework to understand the dynamics of TYLCV propagation.