A comparative analysis of autonomous and fuzzy non-autonomous SIQR models for infectious disease dynamics

This study presents a comparative analysis of the classical autonomous SIQR model and a fuzzy non-autonomous SIQR model to simulate infectious disease dynamics under uncertainty. The autonomous model uses fixed parameters, while the fuzzy model incorporates time varying and fuzzy logic-based parameters to capture real world variability. The basic reproduction number is derived for both models; however, the fuzzy model yields the range of values using membership function for transmission and recovery rates. Sensitivity analysis reveals the fuzzy model is more responsive to uncertainty, with up to 35% fluctuations in outcomes compared to less than 10% in the autonomous model. Incorporating fuzzy viral load results in more nuanced bifurcation patterns and adaptive control strategies. A collocation method is used for numerical simulation over 30 days, showing rapid convergence to disease free state. These findings highlight the fuzzy model potential for informing public strategies, especially during emerging outbreaks with uncertain data.