@article{Rao2026, 
author = {Mallela Ankamma Rao and Emad K Jaradat and Medisetty Padma Devi and Prasantha Bharathi Dhandapani and Carlos Martin-Barreiro and Mohannad Al-Hmoud},
title = {Mathematical modeling of COVID-19 and chronic kidney disease co-infection with vaccination and optimal control: a bifurcation and sensitivity analysis approach},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {17239-17292},
keywords = {COVID-19, chronic kidney disease (CKD), co-infection model, basic reproduction number, stability analysis, bifurcation analysis, sensitivity analysis, optimal control theory},
url = {https://www.sciopen.com/article/10.3934/math.2026707},
doi = {10.3934/math.2026707},
abstract = {Chronic kidney disease (CKD), affecting approximately 843 million individuals globally, substantially increases susceptibility to severe COVID-19 outcomes, while SARS-CoV-2 infection independently accelerates renal deterioration through cytokine storms and microvascular injury. Despite this clinically significant bidirectional interaction, rigorous mathematical characterization of their co-dynamics within a unified framework integrating stability theory, bifurcation analysis, and optimal control remains limited. We formulated a seven-compartment deterministic model incorporating CKD'S irreversibility, the enhanced blue susceptibility of CKD patients, and vaccine imperfection, calibrated against Indian epidemiological data. The basic reproduction number              R        0   was derived using the next-generation matrix method, and stability and bifurcation analysis were performed. Sensitivity analysis identified transmission and immunity waning as dominant drivers, while optimal control strategies significantly reduced co-infections and hospitalizations, demonstrating the effectiveness of coordinated intervention policies.}
}