Reproduction Number and Stability of a Caputo Fractional Derivative Immuno-Metabolic Infection Model for Cats with Obesity and T2DM Effects
DOI:
https://doi.org/10.48165/jmmfc.2026.3104Keywords:
Fractional order(Caputo Fractional Derivative), T2DM Effects, Stability analysis, Reproduction Number.Abstract
We have study chronic inflammation, obesity and type 2 diabetes mellitus (T2DM) [33] are increas ingly recognized as key immuno-metabolic determinants of host susceptibility, infection progression, and recov ery in companion animals. Motivated by these mechanisms, we formulate a fractional-order immuno-metabolic epidemic model for infection transmission in cats stratified by metabolic health status. The model employs Ca puto derivatives of order 0 < ξ < 1 to capture memory-dependent immunological and inflammatory dynamics, including adipokine-driven chronic inflammation, obesity-induced metabolic impairment, and T2DM-associated immune dysfunction. The feline population is divided into metabolically healthy and metabolically impaired groups, each with susceptible, infected, and recovered classes, together with an additional variable describing systemic inflammation. Using the next-generation matrix method, we derive the basic reproduction number R0, explicitly decomposing contributions from healthy and metabolically impaired hosts. Analytical results show that metabolic impairment and inflammation enhance transmission through increased susceptibility and infec tiousness. Within a fractional Lyapunov framework, the disease-free equilibrium is locally and globally asymp totically stable when R0 < 1 and unstable when R0 > 1. The proposed model provides a rigorous mathematical framework for quantifying how chronic inflammation and metabolic disorders modulate infection dynamics in feline populations, underscoring the importance of incorporating immuno-metabolic factors into epidemic mod els to improve disease burden prediction and design targeted interventions for cats with obesity and T2DM. And plot the figure by the help of python.
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