Parameter analysis of an extended immuno-epidemiological model using sensitivity and elasticity methods

Sarbaz H. A. Khoshnaw; Sarbaz H. A. Khoshnaw

doi:10.3934/bioeng.2026017

AIMS Bioengineering

2026, Volume 13, Issue 3: 347-365. doi: 10.3934/bioeng.2026017

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Research article

Parameter analysis of an extended immuno-epidemiological model using sensitivity and elasticity methods

Sarbaz H. A. Khoshnaw ^{1,2
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1.
Department of Mathematics, College of Basic Education, University of Raparin, Ranya, Sulaimani, Iraq
2.
Department of Artificial Intelligence, Faculty of Applied Sciences, Tishk International University, Erbil, Iraq

Received: 29 June 2026 Revised: 30 July 2026 Accepted: 19 August 2026 Published: 24 August 2026

Immuno-epidemiological modeling has been widely studied for understanding disease spread and supporting global control efforts. Mathematical and computational methods are important tools to study interactions between the immune system and infectious diseases. This work presented an extended immuno-epidemiological model that describes the dynamics of the model transmission rates. This study includes some key outputs. First, we calculated the basic reproduction number, R₀, which is used to assess disease transmissibility, design control strategies, and evaluate intervention effectiveness. Second, the local sensitivity analysis was numerically evaluated using non-normalization, half normalization, and full normalization techniques between the model states and parameters; it provides an important step forward in identifying the model critical parameters in the spreading of disease. Another model output was calculating the elasticity index between R₀ and the model parameters to identify the most critical parameters. Interestingly, numerical results showed the impact of the virus transmission rate, virus clearance rate, killing rate of infected cells, interferon degradation rate, and antibody production rate and discussed some model compartments for different parameter values. The findings help the local and international efforts in suggesting control strategies, optimizing interventions, and guiding public health decisions.
- Immuno–epidemiological model,
- mathematical modeling,
- sensitivity analysis,
- basic reproduction number
Citation: Sarbaz H. A. Khoshnaw. Parameter analysis of an extended immuno-epidemiological model using sensitivity and elasticity methods[J]. AIMS Bioengineering, 2026, 13(3): 347-365. doi: 10.3934/bioeng.2026017

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Abstract

Immuno-epidemiological modeling has been widely studied for understanding disease spread and supporting global control efforts. Mathematical and computational methods are important tools to study interactions between the immune system and infectious diseases. This work presented an extended immuno-epidemiological model that describes the dynamics of the model transmission rates. This study includes some key outputs. First, we calculated the basic reproduction number, R₀, which is used to assess disease transmissibility, design control strategies, and evaluate intervention effectiveness. Second, the local sensitivity analysis was numerically evaluated using non-normalization, half normalization, and full normalization techniques between the model states and parameters; it provides an important step forward in identifying the model critical parameters in the spreading of disease. Another model output was calculating the elasticity index between R₀ and the model parameters to identify the most critical parameters. Interestingly, numerical results showed the impact of the virus transmission rate, virus clearance rate, killing rate of infected cells, interferon degradation rate, and antibody production rate and discussed some model compartments for different parameter values. The findings help the local and international efforts in suggesting control strategies, optimizing interventions, and guiding public health decisions.

Acknowledgments

This research was partially supported by the University of Raparin. The author is thankful to the University for providing wonderful facilities. This support is greatly appreciated.

Conflict of interest

The author declares no conflicts of interest in this paper.

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