Open Access

ARTICLE

Modeling the Dynamics of Tuberculosis with Vaccination, Treatment, and Environmental Impact: Fractional Order Modeling

Muhammad Altaf Khan^1,*, Mahmoud H. DarAssi², Irfan Ahmad³, Noha Mohammad Seyam⁴, Ebraheem Alzahrani⁵

1 Faculty of Natural and Agricultural Sciences, University of the Free State, Bleomfontein, 9300, South Africa
2 Department of Basic Sciences, Princess Sumaya University for Technology, Amman, 11941, Jordan
3 Department of Clinical Laboratory Sciences, College of Applied Medical Science, King Khalid University, Abha, 62529, Saudi Arabia
4 Mathematical Sciences Department, College of Applied Sciences, Umm Al-Qura University, Makkah, 24381, Saudi Arabia
5 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

* Corresponding Author: Muhammad Altaf Khan. Email: