Comprehensive analysis of disease dynamics using nonlinear fractional order SEIRS model with Crowley–Martin functional response and saturated treatment

Abstract

This paper presents a comprehensive study of disease spreading dynamics through the application of a nonlinear fractional order epidemic SEIRS model. By incorporating the Crowley–Martin type functional response and a saturated treatment function, the model effectively captures the intricacies of real-world epidemics. Our research establishes the existence, uniqueness, non-negativity and boundedness of the solution, while also investigating the model’s fundamental reproduction number. Additionally, we conduct a thorough analysis of the specific conditions governing the local and global stability of the model’s equilibriums. A notable observation is the variation of the reproduction number with the fractional-order $\alpha$, which represents a memory effect on individuals’ dynamic behavior and reveals the influence of interactions between compartments. To validate these theoretical findings, we employ numerical simulations using Matlab, demonstrating that inhibition measures for susceptibles and the saturated treatment parameters play a pivotal role in determining the disease state. Specifically, we observe that as these parameter values increase, the transition from endemic equilibrium to disease-free equilibrium occurs.