Research ArticleNo Access

A model for the transmission dynamics of pneumococcal pneumonia and influenza co-infection

Mohsin Ali

https://orcid.org/0000-0001-6526-331X

Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan

E-mail Address: mohsin_ali@lums.edu.pk

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Adnan Khan

https://orcid.org/0000-0002-1394-9309

Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan

E-mail Address: adnan.khan@lums.edu.pk

Corresponding author.

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Shaper Mirza

https://orcid.org/0000-0002-6651-6101

Department of Life Sciences, Lahore University of Management Sciences, Lahore, Pakistan

E-mail Address: shaper.mirza@lums.edu.pk

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, and

Mudassar Imran

https://orcid.org/0000-0002-6506-8730

Department of Mathematics and Sciences, Ajman University, Ajman, UAE

E-mail Address: mudassar.imran@ajman.ac.ae

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https://doi.org/10.1142/S1793524523500869Cited by:1 (Source: Crossref)

Abstract

Synergistic interaction between influenza and pneumonia is well established in the literature. In this study, we present a model for the transmission dynamics of co-infection with influenza and pneumococcal pneumonia, with the goal of assessing the effects of influenza co-infection on the transmission of pneumonia. We derive an expression for the basic reproductive number $ℛ_{0} = max (ℛ_{f}, ℛ_{p})$ where $ℛ_{f}$ and $ℛ_{p}$ are, respectively, the reproductive numbers for flu and pneumonia. We show that in the case $ℛ_{f} \leq 1 \leq ℛ_{p}$ , infection with influenza is driven to extinction while pneumonia is endemic, with the endemic state being globally asymptotically stable. The converse result holds in the case where $ℛ_{p} \leq 1 \leq ℛ_{f}$ . We also show the existence of the co-infection equilibrium. In this case, we show that the presence of co-infection results in a possible backward bifurcation in the system at $ℛ_{0} = 1$ ; epidemiologically, this means that the spread of the infection will be harder to control. Numerical simulations are presented to verify the analytic results and gain further insights.

Keywords:

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References

1. H. Arduin, M. Domenech de Cellès, D. Guillemot, L. Watier and L. Opatowski , An agent-based model simulation of influenza interactions at the host level: Insight into the influenza-related burden of pneumococcal infections, BMC Infect. Dis. 17 (2017) 1–12. Crossref, Web of Science, Google Scholar
2. D. Bogaert, R. de Groot and P. Hermans , Streptococcus pneumoniae colonisation: The key to pneumococcal disease, Lancet Infect. Dis. 4(3) (2004) 144–154. Crossref, Web of Science, Google Scholar
3. C. Castillo-Chavez and B. Song , Dynamical models of tuberculosis and their applications, Math. Biosci. Eng. 1(2) (2004) 361. Crossref, Web of Science, Google Scholar
4. CDC.gov, Pneumococcal disease (2022), https://www.cdc.gov/pneumococcal/index.html. Google Scholar
5. D. S. Chertow and M. J. Memoli , Bacterial coinfection in influenza: A grand rounds review, JAMA 309(3) (2013) 275–282. Crossref, Web of Science, Google Scholar
6. S. E. Eikenberry, M. Mancuso, E. Iboi, T. Phan, K. Eikenberry, Y. Kuang, E. Kostelich and A. B. Gumel , To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic, Infect. Dis. Model. 5 (2020) 293–308. Web of Science, Google Scholar
7. Health.ny.gov, Pneumococcal disease (includes pneumococcal pneumonia, pneumococcal meningitis and pneumococcal bacteremia) (2014), https://www.health.ny.gov/diseases/communicable/pneumococcal/docs/fact_sheet.pdf. Google Scholar
8. W. Huang, K. L. Cooke and C. Castillo-Chavez , Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission, SIAM J. Appl. Math. 52(3) (1992) 835–854. Crossref, Web of Science, Google Scholar
9. M. Imran, M. T. Malik and S. M. Garba , Deterministic model for the role of antivirals in controlling the spread of the H1N1 influenza pandemic, Electron. J. Differ. Equ. 2011 (2011). Google Scholar
10. C. W. Kanyiri et al., Application of optimal control to influenza pneumonia coinfection with antiviral resistance, Comput. Math. Methods Med. 2020 (2020) 5984095. Crossref, Web of Science, Google Scholar
11. M. Kizito and J. Tumwiine , A mathematical model of treatment and vaccination interventions of pneumococcal pneumonia infection dynamics, J. Appl. Math. 2018 (2018) 2539465. Crossref, Google Scholar
12. J. LaSalle , The Stability of Dynamical Systems, CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM, Philadelphia, 1976); Khalid Hattaf Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, PO Box 7955 (2012). Crossref, Google Scholar
13. M. Nuño, Z. Feng, M. Martcheva and C. Castillo-Chavez , Dynamics of two-strain influenza with isolation and partial cross-immunity, SIAM J. Appl. Math. 65(3) (2005) 964–982. Crossref, Web of Science, Google Scholar
14. G. Palacios et al., Streptococcus pneumoniae coinfection is correlated with the severity of H1N1 pandemic influenza, PLoS One 4(12) (2009) e8540. Crossref, Web of Science, Google Scholar
15. M. A. Safi and A. B. Gumel , Mathematical analysis of a disease transmission model with quarantine, isolation and an imperfect vaccine, Comput. Math. Appl. 61(10) (2011) 3044–3070. Crossref, Web of Science, Google Scholar
16. S. Shrestha, B. Foxman, D. M. Weinberger, C. Steiner, C. Viboud and P. Rohani , Identifying the interaction between influenza and pneumococcal pneumonia using incidence data, Sci. Transl. Med. 5(191) (2013) 191ra84. Crossref, Web of Science, Google Scholar
17. A. M. Smith, F. R. Adler, R. M. Ribeiro, R. N. Gutenkunst, J. L. McAuley, J. A. McCullers and A. S. Perelson , Kinetics of coinfection with influenza a virus and Streptococcus pneumoniae, PLoS Pathog. 9(3) (2013) e1003238. Crossref, Web of Science, Google Scholar
18. T. Sura, V. Gering, C. Cammann, S. Hammerschmidt, S. Maaß, U. Seifert and D. Becher , Streptococcus pneumoniae and influenza A virus co-infection induces altered polyubiquitination in A549 cells, Front. Cell. Infect. Microbiol. 12 (2022) 118. Crossref, Web of Science, Google Scholar
19. M. C. Swai, N. Shaban and T. Marijani , Optimal control in two strain pneumonia transmission dynamics, J. Appl. Math. 2021 (2021) 8835918. Crossref, Google Scholar
20. H. R. Thieme , Mathematics in Population Biology (Princeton University Press, 2018). Crossref, Google Scholar
21. P. Van den Driessche and J. Watmough , Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180(1–2) (2002) 29–48. Crossref, Web of Science, Google Scholar
22. H. Wang, Y. Wang, P. Walker, C. Walters, P. Winskill, C. Whittaker, C. Donnelly, S. Riley and A. Ghani, Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand (2020). Google Scholar