Mathematical modeling of the immune response mediated by human T-helper lymphocytes in viral diseases

Ledyz Cuesta-Herrera; Luis Pastenes; Fernando Córdova-Lepe; Ariel D. Arencibia; Ledyz Cuesta-Herrera; Luis Pastenes; Fernando Córdova-Lepe; Ariel D. Arencibia

doi:10.3934/mbe.2025103

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 11: 2807-2825. doi: 10.3934/mbe.2025103

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Mathematical modeling of the immune response mediated by human T-helper lymphocytes in viral diseases

1.
Departamento de Matemática, Física y Estadística, Universidad Católica del Maule, Talca 3480112, Chile
2.
Departamento de Biología y Química, Universidad Católica del Maule, Talca 3480112, Chile
3.
Centro de Biotecnología de los Recursos Naturales (CENBio), Universidad Católica del Maule, Talca 3480112, Chile

Received: 26 June 2025 Revised: 31 July 2025 Accepted: 07 August 2025 Published: 12 September 2025

Adaptive immunity, performed by T and B lymphocytes, seeks total virus elimination through specific recognition of viral antigens. It has been shown that innate or adaptive immune response regulation variations are associated with an excessive immune response, leading to tissue damage with an increased risk of complications and death. This article is a novel contribution focused on models that represent pathogenic interactions with humans. In our case, the objective was to build and analyze a mathematical model for SARS-CoV-2 infection in the human host, including elements of respiratory cell dynamics, viral particles, and immune-responding cells. The methodology developed considered modeling by means of ordinary differential equations, validation by comparing referenced studies, and sensitivity analysis with respect to the variables considered. Finally, a comparison of simulation models was performed, verifying that an increase in viral particles increases the response of some adaptive immune system cells in the human host.
- T Helper cells,
- coronavirus,
- immune system,
- mathematical model
Citation: Ledyz Cuesta-Herrera, Luis Pastenes, Fernando Córdova-Lepe, Ariel D. Arencibia. Mathematical modeling of the immune response mediated by human T-helper lymphocytes in viral diseases[J]. Mathematical Biosciences and Engineering, 2025, 22(11): 2807-2825. doi: 10.3934/mbe.2025103

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Abstract

Adaptive immunity, performed by T and B lymphocytes, seeks total virus elimination through specific recognition of viral antigens. It has been shown that innate or adaptive immune response regulation variations are associated with an excessive immune response, leading to tissue damage with an increased risk of complications and death. This article is a novel contribution focused on models that represent pathogenic interactions with humans. In our case, the objective was to build and analyze a mathematical model for SARS-CoV-2 infection in the human host, including elements of respiratory cell dynamics, viral particles, and immune-responding cells. The methodology developed considered modeling by means of ordinary differential equations, validation by comparing referenced studies, and sensitivity analysis with respect to the variables considered. Finally, a comparison of simulation models was performed, verifying that an increase in viral particles increases the response of some adaptive immune system cells in the human host.

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