Mathematical modeling of COVID-19 and chronic kidney disease co-infection with vaccination and optimal control: a bifurcation and sensitivity analysis approach

Mallela Ankamma Rao; Emad K Jaradat; Medisetty Padma Devi; Prasantha Bharathi Dhandapani; Carlos Martin-Barreiro; Mohannad Al-Hmoud; Mallela Ankamma Rao; Emad K Jaradat; Medisetty Padma Devi; Prasantha Bharathi Dhandapani; Carlos Martin-Barreiro; Mohannad Al-Hmoud

doi:10.3934/math.2026707

AIMS Mathematics

2026, Volume 11, Issue 6: 17239-17292. doi: 10.3934/math.2026707

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Mathematical modeling of COVID-19 and chronic kidney disease co-infection with vaccination and optimal control: a bifurcation and sensitivity analysis approach

1.
Department of Mathematics & Statistics, Vignan's Foundation for Science, Technology & Research (Deemed to be University), Yadadri Bhuvanagiri 508284, Telangana, India
2.
Department of Physics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia
3.
Department of Mathematics & Statistics, Vignan's Foundation for Science, Technology & Research (Deemed to be University), Vadlamudi, Guntur 522213, Andhra Pradesh, India
4.
Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore 641202, Tamil Nadu, India
5.
Facultad de Ingeniería, Universidad Espíritu Santo, Samborondón 0901952, Ecuador

Received: 26 March 2026 Revised: 02 May 2026 Accepted: 19 May 2026 Published: 15 June 2026
MSC : 92D30, 34D20, 37N25, 49J15, 93A30

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 $ \mathcal{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.
- COVID-19,
- chronic kidney disease (CKD),
- co-infection model,
- basic reproduction number,
- stability analysis,
- bifurcation analysis,
- sensitivity analysis,
- optimal control theory
Citation: Mallela Ankamma Rao, Emad K Jaradat, Medisetty Padma Devi, Prasantha Bharathi Dhandapani, Carlos Martin-Barreiro, Mohannad Al-Hmoud. Mathematical modeling of COVID-19 and chronic kidney disease co-infection with vaccination and optimal control: a bifurcation and sensitivity analysis approach[J]. AIMS Mathematics, 2026, 11(6): 17239-17292. doi: 10.3934/math.2026707

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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 $ \mathcal{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.

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