A Comparative Analysis of Harmonic Mean, Holling Type II, Beddington–DeAngelis, and Crowley–Martin Incidence Rates of a Piecewise Dengue Fever Dynamics Model

Dengue fever remains a major global health threat, and mathematical models are crucial for predicting its spread and evaluating control strategies. This study introduces a highly flexible dengue transmission model using a novel piecewise fractional derivative framework, which can capture abrupt changes in epidemic dynamics, such as those caused by public health interventions or seasonal shifts. We conduct a rigorous comparative analysis of four widely used but distinct mechanisms of disease transmission (incidence rates): Harmonic Mean, Holling Type II, Beddington–DeAngelis, and Crowley–Martin. The model’s well-posedness is established, and the basic reproduction number (ℜ0) is derived for each incidence function. Our central finding is that the choice of this mathematical mechanism critically alters predictions. For example, models that account for behavioral changes (Beddington–DeAngelis, Crowley–Martin) identify different key drivers of transmission compared to simpler models. Sensitivity analysis reveals that vector mortality is the most influential control parameter in these more realistic models. These results underscore that accurately representing transmission behavior is essential for reliable epidemic forecasting and for designing effective, targeted intervention strategies.