Fractional optimal control problem modeling bovine tuberculosis and rabies co-infection

Abstract

Bovine tuberculosis (bTB) and rabies are eminent zoonotic afflictions that significantly impact global economic stability and public health, with pronounced effects in developing nations. These diseases continuously pressure public health systems and obstruct efforts to improve livestock productivity and export capabilities. Studying the joint dynamics of bTB and rabies involves notable mathematical complexities due to the differences in their transmission mechanisms. Moreover, while there is some overlap among animal populations at risk for bTB and rabies, the exact proportion of animals susceptible to both diseases remains unspecified. In this work, we provide a simplified fractional-order optimal control model that integrates the dynamics of bTB and rabies co-infection. We determine the basic reproduction numbers for bovine tuberculosis $\left(R_0^T\right)$ and rabies $\left(R_0^R\right)$, as well as the overall reproduction number for the model $R=max\{R_0^T,R_0^R\}$. The qualitative analysis reveals that when $R<1$, the disease-free equilibrium is locally asymptotically stable. We implement optimal control analysis to identify the best strategies for preventing each disease separately and their co-infection. The optimal control problem is solved numerically utilizing a forward–backward predict-evaluate correct-evaluate (PECE) algorithm implemented in Matlab software. The simulation results show that strategy E ($i.e.$, implementation of all optimal controls) is significantly more effective in managing bovine tuberculosis but less effective in controlling rabies and co-infection. Conversely, strategy B ($i.e.$, applying vaccination and removal of optimal controls for animals affected by rabies) provides satisfactory optimal control results across the three infection scenarios.