Fractional-order modelling of pneumonia dynamics: a novel approach to disease impact analysis

Fractional calculus has emerged as a powerful tool for understanding the complex dynamics of infectious diseases. Despite advances in medical treatment, pneumonia remains a significant health challenge, particularly in vulnerable populations such as children and the elderly. This study introduces a fractional-order SVEIR (Susceptible, Vaccinated, Exposed, Infected, and Recovered) model using the Modified Atangana-Baleanu fractional derivative (MABC) to capture the non-local and memory effects inherent in pneumonia transmission. The existence and uniqueness of the model's solutions are explored through fixed-point theory, and numerical simulations are conducted using python. Comparative analysis demonstrates that the proposed fractional model provides a more accurate representation of pneumonia dynamics than other fractional and classical integer-order models. Sensitivity analysis highlights the critical role of vaccination and exposure rates in disease control. The findings suggest that enhanced vaccination strategies and treatment interventions can significantly reduce the spread of pneumonia, underscoring the importance of fractional modelling in epidemiological research.