Nonlinear Dynamics of a Zoonotic Disease with Control Interventions through Fractional Derivative

The zoonotic infection campylobacteriosis poses a significant public health burden, contributing to widespread morbidity and, in severe cases, mortality, particularly among vulnerable populations such as children, the elderly, and immunocompromised individuals. The economic impact is considerable, with costs arising from medical care, hospitalization, lost productivity, and the need for stringent food safety measures. In this paper, we model the dynamics of campylobacteriosis with drug resistance in humans and animals using fractional derivatives. The fundamental concepts of fractional derivatives are presented to analyze the disease dynamics. Our work focuses on both the quantitative and qualitative analysis of the proposed model. The fixed-point theorem is applied to investigate the existence and uniqueness of solutions. We also examine the stability of the system through analytical techniques. To further explore the system, a numerical scheme is introduced to visualize the solution pathways and assess the influence of various factors. We demonstrate the dynamics of campylobacteriosis with drug resistance, highlighting the effects of different factors on infection levels. Furthermore, our results identify the key factors crucial for effective disease control and management.