Numerical and transcritical bifurcation analysis of Chikungunya dynamics within a fractional-fractal framework
Mehmet Kocabıyık · 2026
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Description
Kocabıyık, in a single-author 2026 study, builds a mathematical model of chikungunya, the mosquito-spread virus that causes fever and long-lasting joint pain. Standard epidemic models treat time as uniform and forget the past, but real outbreaks show memory, where earlier conditions shape later spread, and bursts at many timescales. The new model combines fractional derivatives, a calculus that weights history, with fractal time, which stretches and compresses the clock.
The author proves the model's solutions stay positive and bounded, works out its resting states, and computes the basic reproduction number, the threshold deciding whether an outbreak grows or fades. Analysis shows the system switches stability exactly at that threshold, as theory expects. Simulations then show the memory and fractal settings bending the epidemic curves away from classical predictions, lingering longer in some regimes. The author argues such models fit real outbreak shapes better.
Catalog record
| CREATOR | Mehmet Kocabıyık |
|---|---|
| YEAR | 2026 |
| COLLECTION | PAPERS |
| FORMAT | TXT |
| FILE SIZE | 159 KB |
| VERSION | 1.0 |
| LICENSE | CC BY 4.0 |
| RIGHTS | CC BY |
| SOURCE | Europe PMC |