An Interval-Valued Caputo Fractional Derivative Dynamics Model for Infectious Diseases

Abstract

Mathematical modelling on interval valued plays a crucial role in understanding the transmission dynamics and control strategies of infectious diseases. This study presents a comprehensive interval-based mathematical model for an infectious disease, aimed at capturing the uncertainties and variability’s inherent in epidemiological data. Unlike traditional models that use fixed parameters, the proposed model incorporates interval-valued parameters to account for data imprecision and variability in transmission rates, contact rates, and recovery rates. By employing interval analysis, the model provides a range of possible outcomes, offering a healthier framework for predicting disease spread and assessing the impact of various intervention strategies. Simulations are conducted to explore different outbreak scenarios, examining the effects of varying parameter intervals on disease dynamics. The results demonstrate the model's ability to provide more flexible and realistic predictions, which are crucial for decision-making in public health policy. This interval-based approach offers a novel perspective on infectious disease modelling, highlighting the importance of accounting for uncertainty in epidemiological predictions and contributing to more effective disease control strategies.