Forward-backward transcritical bifurcation: control and optimisation in a novel fuzzy SIR model

Understanding the dynamics of infectious disease spread is critical for effective public health interventions. Traditional epidemic models, such as SIR and SEIR, use deterministic parameters that often fail to account for real world uncertainty caused by incomplete data, behavioural variability, and evolving pathogens. Fuzzy logic provides a powerful alternative by treating parameters like transmission and recovery rates as fuzzy variables, enabling models to incorporate imprecision and better reflect reality. Originating in control theory, fuzzy logic has found applications in engineering, space science and uncertainty modelling. This study develops a fuzzy epidemic model using a utility-based framework, deriving a fuzzy disease-free equilibrium and a generalised basic reproduction number. Critical bifurcation points and sensitivity analyses highlights key transitions and intervention strategies. This approach enhances epidemic forecasting and decision making under uncertainty, offering a robust tool for managing complex health crises.