Enhanced Modelling of Listeriosis Disease Transmission Using Fractal-Fractional Differential Equations with Fuzzy Logic

Listeriosis, caused by Listeria monocytogenes, presents significant public health risks, especially to vulnerable groups such as the elderly, immunocompromised individuals, and pregnant women. Despite advancements in food safety measures, the bacteria’s resilience across various environments makes their complete eradication challenging. This study addresses this challenge by incorporating uncertainty and memory effects into the disease modelling process. This study offers an advanced mathematical framework to analyse listeriosis dynamics using fractal-fractional differential equations and a fuzzy fractal-fractional approach. The integration of fractal calculus allows for a detailed examination of complex, multi-scale behaviours of real-world disease spread, while the incorporation of fuzzy logic accounts for inherent uncertainties in initial conditions and parameter values. Ensuring the mathematical validity of the proposed models, the research explores key properties such as existence, uniqueness, and Ulam-Hyers stability, which confirm the robustness and reliability of the solutions. A computational approach is utilized to solve the model, revealing the dynamics of susceptible, infected, and recovered populations, as well as the bacterial class and the progression of spoiled and unspoiled food packages over time. The importance of fractal dimensions in the Listeriosis model is emphasized by variation maps that depict changes over time. The extension of the model to include fuzzy initial conditions enhances predictive capabilities and supports decision-making by accommodating uncertainty. The findings underscore the importance of applying sophisticated mathematical tools, such as fractal-fractional and fuzzy differential equations, to improve the understanding and management of listeriosis and similar public health challenges, enabling more effective prevention and control strategies.