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Qualitative behavior of a fractional order tuberculosis epidemic model with drug-resistant infectious and exogenous re-infection | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 مرداد 1405 | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2026.32127.1870 | ||
| نویسندگان | ||
| Azizeh Jabbari* ؛ Fatemeh Iranzad؛ Hossein kheiri | ||
| Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran | ||
| تاریخ دریافت: 26 خرداد 1405، تاریخ بازنگری: 19 تیر 1405، تاریخ پذیرش: 22 تیر 1405 | ||
| چکیده | ||
| This paper develops a fractional-order tuberculosis model incorporating incomplete treatment, drug-resistant infection, and exogenous reinfection. The system is analyzed mathematically and epidemiologically. Positivity and boundedness are established to ensure biological well-posedness. The disease-free equilibrium and the basic reproduction number are obtained using the next-generation matrix method. Local stability of the disease-free state is studied via linearization theory for fractional-order systems. Endemic equilibria are characterized by reducing the steady-state problem to a quadratic equation in the force of infection. The analysis shows that reinfection together with incomplete treatment can induce backward bifurcation, so a stable disease-free equilibrium and a stable endemic equilibrium may coexist even when the reproduction number is below one. Without reinfection, the disease-free equilibrium is globally asymptotically stable for a reproduction number less than one. {\color{revblue}Sensitivity analysis identifies the effective contact rate as the main driver of disease spread and the infectious treatment rate as the strongest suppressive parameter. Consistent numerical simulations confirm the theoretical results and show that the fractional order changes the transient dynamics of drug-sensitive and drug-resistant infections.} The results highlight treatment completion and reinfection reduction as key tuberculosis control targets. | ||
| کلیدواژهها | ||
| Fractional-order derivative؛ basic reproduction number؛ stability؛ tuberculosis؛ backward bifurcation | ||
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آمار تعداد مشاهده مقاله: 9 |
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