Analyzing the Role of Media Awareness in the Spread of Cat Scratch Disease Using a Fuzzy Fractional-Order Epidemic Model

Abstract

Cat Scratch Disease (CSD) is an emerging yet underreported zoonotic infection 
primarily caused by Bartonella henselae. Although it poses significant public health 
risks, particularly among immunocompromised individuals, it has received limited 
attention within the field of mathematical epidemiology. This study introduces a novel 
fuzzy fractional-order epidemic model to explore the impact of media awareness on 
mitigating the spread of CSD. The model employs Caputo-type fractional derivatives 
to capture memory-dependent transmission dynamics and incorporates fuzzy set 
theory to account for uncertainties in critical epidemiological parameters. A 
dedicated media awareness compartment is integrated into the framework, 
dynamically reducing the effective contact rate through behavioral change. The basic 
reproduction number R0R_0R0 is analytically derived using the next-generation 
matrix approach, and rigorous qualitative analysis establishes the existence, 
uniqueness, and stability of the system’s equilibria. Numerical experiments are 
conducted via the fuzzy Grünwald–Letnikov scheme with α-cut decomposition, 
providing robust approximations of system behavior. Simulation results reveal that 
sustained media interventions markedly reduce infection prevalence, flatten 
epidemic peaks, and delay outbreak progression. Overall, the findings highlight the 
crucial role of hygiene education and targeted communication strategies in managing 
zoonotic diseases. The proposed framework not only offers a more realistic and 
flexible tool for policy simulation but also holds promise for extension to other 
media-sensitive zoonoses, thereby contributing to improved epidemic preparedness 
and control.