Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

Overview

Journal Comput Math Methods Med

Publisher Hindawi

Specialty Medical Informatics

Date 2018 Sep 25

PMID 30245737

Citations 8

Authors

Caroline W Kanyiri

Kimathi Mark

Livingstone Luboobi

Affiliations

Soon will be listed here.

Abstract

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number, . The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lower to a critical value for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

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References

van der Vries E, Schutten M, Fraaij P, Boucher C, Osterhaus A . Influenza virus resistance to antiviral therapy. Adv Pharmacol. 2013; 67:217-46. DOI: 10.1016/B978-0-12-405880-4.00006-8. View

Mazel-Sanchez B, Boal-Carvalho I, Silva F, Dijkman R, Schmolke M . H5N1 Influenza A Virus PB1-F2 Relieves HAX-1-Mediated Restriction of Avian Virus Polymerase PA in Human Lung Cells. J Virol. 2018; 92(11). PMC: 5952157. DOI: 10.1128/JVI.00425-18. View

Saunders-Hastings P, Krewski D . Reviewing the History of Pandemic Influenza: Understanding Patterns of Emergence and Transmission. Pathogens. 2016; 5(4). PMC: 5198166. DOI: 10.3390/pathogens5040066. View

Lee S, Chowell G, Castillo-Chavez C . Optimal control for pandemic influenza: the role of limited antiviral treatment and isolation. J Theor Biol. 2010; 265(2):136-50. DOI: 10.1016/j.jtbi.2010.04.003. View

Li T, Chan M, Lee N . Clinical Implications of Antiviral Resistance in Influenza. Viruses. 2015; 7(9):4929-44. PMC: 4584294. DOI: 10.3390/v7092850. View

Ku A, Chan L . The first case of H5N1 avian influenza infection in a human with complications of adult respiratory distress syndrome and Reye's syndrome. J Paediatr Child Health. 1999; 35(2):207-9. DOI: 10.1046/j.1440-1754.1999.t01-1-00329.x. View

van den Driessche P, Watmough J . Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci. 2002; 180:29-48. DOI: 10.1016/s0025-5564(02)00108-6. View

Woolhouse M, Farrar J . Policy: An intergovernmental panel on antimicrobial resistance. Nature. 2014; 509(7502):555-7. DOI: 10.1038/509555a. View

Yuan J, Zhang L, Kan X, Jiang L, Yang J, Guo Z . Origin and molecular characteristics of a novel 2013 avian influenza A(H6N1) virus causing human infection in Taiwan. Clin Infect Dis. 2013; 57(9):1367-8. DOI: 10.1093/cid/cit479. View

10.

Smith G, Vijaykrishna D, Bahl J, Lycett S, Worobey M, Pybus O . Origins and evolutionary genomics of the 2009 swine-origin H1N1 influenza A epidemic. Nature. 2009; 459(7250):1122-5. DOI: 10.1038/nature08182. View

11.

Gao R, Cao B, Hu Y, Feng Z, Wang D, Hu W . Human infection with a novel avian-origin influenza A (H7N9) virus. N Engl J Med. 2013; 368(20):1888-97. DOI: 10.1056/NEJMoa1304459. View

12.

Taubenberger J, Morens D . Influenza viruses: breaking all the rules. mBio. 2013; 4(4). PMC: 3735197. DOI: 10.1128/mBio.00365-13. View

13.

Imran M, Malik T, R Ansari A, Khan A . Mathematical analysis of swine influenza epidemic model with optimal control. Jpn J Ind Appl Math. 2020; 33(1):269-296. PMC: 7097131. DOI: 10.1007/s13160-016-0210-3. View

14.

Hope-Simpson R . The role of season in the epidemiology of influenza. J Hyg (Lond). 1981; 86(1):35-47. PMC: 2134066. DOI: 10.1017/s0022172400068728. View

15.

White M, Lowen A . Implications of segment mismatch for influenza A virus evolution. J Gen Virol. 2017; 99(1):3-16. PMC: 5882089. DOI: 10.1099/jgv.0.000989. View

16.

Moscona A . Neuraminidase inhibitors for influenza. N Engl J Med. 2005; 353(13):1363-73. DOI: 10.1056/NEJMra050740. View

17.

Hayes J, Wolf C . Molecular mechanisms of drug resistance. Biochem J. 1990; 272(2):281-95. PMC: 1149697. DOI: 10.1042/bj2720281. View

18.

Blower S, Volberding P . What can modeling tell us about the threat of antiviral drug resistance?. Curr Opin Infect Dis. 2003; 15(6):609-14. DOI: 10.1097/00001432-200212000-00009. View

19.

Matheka D, Mokaya J, Maritim M . Overview of influenza virus infections in Kenya: past, present and future. Pan Afr Med J. 2013; 14:138. PMC: 3683518. DOI: 10.11604/pamj.2013.14.138.2612. View

20.

Cheng K, Leung P . What happened in China during the 1918 influenza pandemic?. Int J Infect Dis. 2007; 11(4):360-4. DOI: 10.1016/j.ijid.2006.07.009. View