Mathematical Model of SAR-CoV-2 and Influenza A Virus Coinfection within Host with CTL-Mediated Immunity

Mia Siti Khumaeroh, Najmudin Nuwari, Elvi Syukrina Erianto, Nela Rizka

Abstract


Coinfection of SARS-CoV-2 and Influenza A virus within a host poses a unique challenge in understanding immunological dynamics, especially the role of cytotoxic T lymphocytes (CTL) in mediating the immune response. This work present a mathematical model to examine the dynamics of coinfection within a host, highlighting CTL-mediated immunity. Generally, this model encompasses several compartments, including epithelial cells, free viruses, and CTLs specific of both SARS-CoV-2 and Influenza A. The basic properties of the model, equilibrum state analysis, stability using the Lyapunov function, and numerical simulations are examined to investigate the dynamics behavior of the model. Eight equilibrium states are identified: the virus-free equilibrium (E0), single SARS-CoV-2 infection without CTLs (E1), single Influenza A virus infection without CTLs (E2), single SARS-CoV-2 infection with SARS-CoV-2-specific CTLs (E3), single Influenza A virus infection with Influenza A virus-specific CTLs (E4), SARS-CoV-2 and Influenza A virus coinfection with SARS-CoV-2-specific CTLs (E5), SARS-CoV-2 and Influenza A virus coinfection with Influenza A virus-specific CTLs (E6), and SARS-CoV-2 and Influenza A virus coinfection with both SARS-CoV-2-specific and Influenza A virus-specific CTLs (E7). The existence and stability regions for each equilibrium state are determined and represented in the R1-R2 plane as threshold functions within the model. Numerical simulations confirm the results of the qualitative analysis, demonstrating that CTLs specific to SARS-CoV-2 and Influenza A virus can be activated, reducing the number of infected epithelial cells as well as inhibiting virus transmission within epithelial cells. Furthermore, analysis of parameter changes shows that increasing the proliferation rate of epithelial cells and CTLs, while lowering the virus formation rate, can shift the system's stability threshold and stabilize it at the virus-free equilibrium.

Keywords


SARS-CoV-2; Influenza A virus; Coinfection; CTL; Lyapunov

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References


BS. Mohan and N. Vinod, “Covid-19: an insight into sars-cov-2 pandemic originated at wuhan city in hubei province of china,†Journal of Infectious Diseases and Epidemiology, vol. 6, no. 4, p. 146, 2020. DOI:10.23937/2474-3658/1510146

D. Wu et al., “The sars-cov-2 outbreak: what we know,†International journal of infectious diseases, vol. 94, pp. 44–48, 2020. DOI:10.1016/j.ijid.2020.03.004

WHO, “WHO coronavirus (COVID-19),†2024, https://covid19.who.int/, Accesed on 13 March 2024.

A. Havasi et al., “Influenza a, influenza b, and sars-cov-2 similarities and differences–a focus on diagnosis,†Frontiers in Microbiology, vol. 13, p. 908525, 2022. DOI:10.3389/fmicb.2022.908525

M. Moghadami, “A narrative review of influenza: a seasonal and pandemic disease,†Iranian journal of medical sciences, vol. 42, no. 1, p. 2, 2017. DOI:10.30476/ijms.2016.40409

R. Scendoni et al., “Leading pathogens involved in co-infection and super-infection with covid-19: forensic medicine considerations after a systematic review and meta-analysis,†Pathogens, vol. 12, no. 5, p. 646, 2023. DOI:10.3390/pathogens12050646

N. Kumar et al., “Virological and immunological outcomes of coinfections,†Clinical microbiology reviews, vol. 31, no. 4, 2018. DOI:10.1128/CMR.00111-17

N. Teluguakula et al., “Sars-cov-2 and influenza co-infection: Fair competition or sinister combination?†Viruses, vol. 16, no. 5, p. 793, 2024. DOI:10.3390/v16050793

B. E. Dixon et al., “Symptoms and symptom clusters associated with sars-cov-2 infection in community-based populations: Results from a statewide epidemiological study,†PLoS One, vol. 16, no. 3, p. e0241875, 2021. DOI:10.1371/journal.pone.0241875

H. Yue et al., “The epidemiology and clinical characteristics of co-infection of SARS-CoV-2 and influenza viruses in patients during COVID-19 outbreak,†Journal of medical virology, vol. 92, no. 11, pp. 2870–2873, 2020. DOI:10.1002/jmv.26163

J.-H. Hwang et al., “Influenza viral infection is a risk factor for severe illness in covid-19 patients: a nationwide population-based cohort study,†Emerging microbes & infections, vol. 12, no. 1, 2023. DOI:10.1080/22221751.2022.2164215

D. Kim et al., “Rates of co-infection between sars-cov-2 and other respiratory pathogens,†JAMA, vol. 323, no. 20, p. 2085, 2020. DOI:10.1001/jama.2020.6266

J. Ca, “The immune system in health and disease,†2001, http://www. garlandscience. com.

A. K. Abbas, A. H. Lichtman, and S. Pillai, Cellular and Molecular Immunology E-Book: Cellular and Molecular Immunology E-Book. Elsevier Health Sciences, 2014.

A. Grifoni et al., “Targets of t cell responses to sars-cov-2 coronavirus in humans with covid-19 disease and unexposed individuals,†Cell, vol 181, no. 7, pp. 1489–1501, 2020. DOI:10.1016/j.cell.2020.05.015

N. L. La Gruta et al., “Understanding the drivers of MHC restriction of T cell receptors,†Nature Reviews Immunology, vol. 18, no. 7, pp. 467–478, 2018. DOI:10.1038/s41577-018-0007-5

C. Quirouette et al., “A mathematical model describing the localization and spread of influenza a virus infection within the human respiratory tract,†PLOS Computational Biology, vol. 16, no. 4, p. e1007705, 2020. DOI:10.1371/journal.pcbi.1007705

B. O. Emerenini et al., “Mathematical Modeling and Analysis of Influenza In-Host Infection Dynamics,†Letters in Biomathematics, vol. 8, no. 1, pp. 229–253, 2021. DOI:10.30707/lib8.1.1647878866.124006

P. Krishnapriya, M. Pitchaimani, and T. M. Witten, “Mathematical analysis of an influenza a epidemic model with discrete delay,†Journal of Computational and Applied Mathematics, vol. 324, pp. 155–172, 2017. DOI:10.1016/j.cam.2017.04.030

M. Erdem, M. Safan, and C. Castillo-Chavez, “Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine,†Bulletin of Mathematical Biology, vol. 79, no. 7, pp. 1612–1636, 2017. DOI:10.1007/s11538-017-0301-6

S. Liu, S. Ruan, and X. Zhang, “Nonlinear dynamics of avian influenza epidemic models,†Mathematical Biosciences, vol. 283, pp. 118–135, 2017. DOI:10.1016/j.mbs.2016.11.014

K. Koelle et al., “The changing epidemiology of SARS-CoV-2,†Science, vol. 375, no. 6585, pp. 1116–1121, 2022. DOI:10.1126/science.abm4915

K. T. Kubra et al., “Analysis and comparative study of a deterministic mathematical model of SARS-COV-2 with fractal-fractional operators: a case study,†Scientific Reports, vol. 14, no. 1, p. 6431, 2024. DOI:10.1038/s41598-024-56557-6

A. Weiss, M. Jellingsø, and M. O. A. Sommer, “Spatial and temporal dynamics of SARS-CoV-2 in COVID-19 patients: A systematic review and meta-analysis,†EBioMedicine, vol. 58, p. 102916, 2020. DOI:10.1016/j.ebiom.2020.102916

P. Baccam et al., “Kinetics of Influenza A Virus Infection in Humans,†Journal of Virology, vol. 80, no. 15, pp. 7590–7599, 2006. DOI:10.1128/JVI.01623-05

R. Syafitri, Trisilowati, and W. M. Kusumawinahyu, “Dynamics of Covid-19 model with public awareness, quarantine, and isolation,†Jambura Journal of Biomathematics (JJBM), vol. 4, no. 1, pp. 63–68, 2023. DOI:10.34312/jjbm.v4i1.19832

N. Q. Putri, P. Sianturi, and H. Sumarno, “Sensitivity Analyses of The Dynamics of Covid-19 Transmission in Response to Reinfection,†Jambura Journal of Biomathematics (JJBM), vol. 4, no. 1, pp. 15–22, 2023. DOI:10.34312/jjbm.v4i1.18394

H. Nasution et al., “Exploring of Homotopy Perturbation Method (HPM) for Solving Spread of COVID-19,†Jambura Journal of Biomathematics (JJBM), vol. 4, no. 2, pp. 138–145, 2023. DOI:10.37905/jjbm.v4i2.21560

F. Firmansyah and Y. M. Rangkuti, “Sensitivity Analysis and Optimal Control of Covid 19 Model,†Jambura Journal of Biomathematics (JJBM), vol. 4, no. 1, pp. 95–102, 2023. DOI:10.34312/jjbm.v4i1.19025

S. Chowdhury et al., “Mathematical modelling of COVID-19 disease dynamics: Interaction between immune system and SARS-CoV-2 within host,†AIMS Mathematics, vol. 7, no. 2, pp. 2618–2633, 2022. DOI:10.3934/math.2022147

M. M. Ojo et al., “Nonlinear optimal control strategies for a mathematical model of COVID-19 and influenza co-infection,†Physica A: Statistical Mechanics and its Applications, vol. 607, p. 128173, 2022. DOI:10.1016/j.physa.2022.128173

A. Elaiw, R. S. Alsulami, and A. Hobiny, “Global dynamics of IAV/SARS-CoV-2 coinfection model with eclipse phase and antibody immunity,†Math. Biosci. Eng, vol. 20, no. 2, pp. 3873–3917, 2023. DOI:10.3934/mbe.2023182

S. Halle et al., “In Vivo Killing Capacity of Cytotoxic T Cells Is Limited and Involves Dynamic Interactions and T Cell Cooperativity,†Immunity, vol. 44, no. 2, pp. 233–245, 2016. DOI:10.1016/j.immuni.2016.01.010

C. D. Murin, I. A. Wilson, and A. B. Ward, “Antibody responses to viral infections: a structural perspective across three different enveloped viruses,†Nature Microbiology, vol. 4, no. 5, pp. 734–747, 2019. DOI:10.1038/s41564-019-0392-y

K. Alligood, T. Sauer, and J. Yorke, Chaos: An Introduction to Dynamical Systems. Springer, 2000.

M. Hajja, “104.17 More proofs of the AM-GM inequality,†The Mathematical Gazette, vol. 104, no. 560, pp. 318–326, 2020. DOI:10.1017/mag.2020.59

J. P. Hespanha, “Uniform Stability of Switched Linear Systems: Extensions of LaSalle’s Invariance Principle,†IEEE Transactions on Automatic Control, vol. 49, no. 4, pp. 470–482, 2004. DOI:10.1109/TAC.2004.825641

T. Carter and M. Iqbal, “The Influenza A Virus Replication Cycle: A Comprehensive Review,†Viruses, vol. 16, no. 2, p. 316, 2024. DOI:10.3390/v16020316

B. Abdullah Marzoog, “Cytokines and Regulating Epithelial Cell Division,†Current Drug Targets, vol. 25, no. 3, pp. 190–200, 2024. DOI:10.2174/0113894501279979240101051345

J. A. Dudakov, A. M. Hanash, and M. R. van den Brink, “Interleukin-22: Immunobiology and Pathology,†Annual Review of Immunology, vol. 33, no. 1, pp. 747–785, 2015. DOI:10.1146/annurev-immunol-032414-112123

S. Peng et al., “CTLs heterogeneity and plasticity: implications for cancer immunotherapy,†Molecular Cancer, vol. 23, no. 1, p. 58, 2024. DOI:10.1186/s12943-024-01972-6

C. Janeway et al., Immunobiology: the immune system in health and disease. Garland Pub. New York, 2001, vol. 2.

S. SH and G. Don, “Viral Latency and Its Regulation: Lessons from the γ-Herpesviruses,†Cell Host Microbe., vol. 8, no. 1, pp. 100–105, 2010. DOI:10.1016/j.chom.2010.06.014




DOI: https://doi.org/10.37905/jjbm.v5i2.27782

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