×

Mathematical analysis of influenza A dynamics in the emergence of drug resistance. (English) Zbl 1431.92137

Summary: 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, \(R_{\text{c}}\). The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lower \(R_{\text{c}}\) to a critical value \(R_{\text{c}}^\ast\) 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.

MSC:

92D30 Epidemiology
34C60 Qualitative investigation and simulation of ordinary differential equation models
92C60 Medical epidemiology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] White, M. C.; Lowen, A. C., Implications of segment mismatch for influenza a virus evolution, Journal of General Virology, 99, 1, 3-16, (2017) · doi:10.1099/jgv.0.000989
[2] Taubenberger, J. K.; Morens, D. M., Influenza viruses: breaking all the rules, mBio, 4, 4, (2013) · doi:10.1128/mbio.00365-13
[3] CDC, How the Flu Virus Can Change: Drift and Shift, (2017), Atlanta, GA, USA: CDC, Atlanta, GA, USA
[4] Smith, G. J.; Vijaykrishna, D.; Bahl, J., Origins and evolutionary genomics of the 2009 swine-origin H1N1 influenza a epidemic, Nature, 459, 7250, 1122, (2009) · doi:10.1038/nature08182
[5] WHO, WHO/Europe—Influenza-Data and Statistics, (2017), Geneva, Switzerland: WHO, Geneva, Switzerland
[6] CDC, Clinical Signs and Symptoms of Influenza: Health Professionals–CDC, (2017), Atlanta, GA, USA: CDC, Atlanta, GA, USA
[7] Moscona, A., Neuraminidase inhibitors for influenza, New England Journal of Medicine, 353, 13, 1363-1373, (2005) · doi:10.1056/nejmra050740
[8] CDC, Preventing the Flu: Good Health Habits Can Help Stop Germs–CDC, (2017), Atlanta, GA, USA: CDC, Atlanta, GA, USA
[9] Matheka, D. M.; Mokaya, J.; Maritim, M., Overview of influenza virus infections in Kenya: past, present and future, Pan African medical journal, 14, (2013) · doi:10.11604/pamj.2013.14.138.2612
[10] Cheng, K.; Leung, P., What happened in china during the 1918 influenza pandemic?, International Journal of Infectious Diseases, 11, 4, 360-364, (2007) · doi:10.1016/j.ijid.2006.07.009
[11] Goeyvaerts, N.; Willem, L.; Van Kerckhove, K., Estimating dynamic transmission model parameters for seasonal influenza by fitting to age and season-specific influenza-like illness incidence, Epidemics, 13, 1-9, (2015) · doi:10.1016/j.epidem.2015.04.002
[12] Saunders-Hastings, P. R.; Krewski, D., Reviewing the history of pandemic influenza: understanding patterns of emergence and transmission, Pathogens, 5, 4, 66, (2016) · doi:10.3390/pathogens5040066
[13] CDC, Past Pandemics, (2017), Atlanta, GA, USA: CDC, Atlanta, GA, USA
[14] WHO, WHO—Influenza, (2017), Geneva, Switzerland: WHO, Geneva, Switzerland
[15] CDC, Seasonal Flu Death Estimate Increases Worldwide, (2017), Atlanta, GA, USA: CDC, Atlanta, GA, USA
[16] Hope-Simpson, R., The role of season in the epidemiology of influenza, Epidemiology & Infection, 86, 1, 35-47, (1981) · doi:10.1017/s0022172400068728
[17] Finkelman, B. S.; Viboud, C.; Koelle, K.; Ferrari, M. J.; Bharti, N.; Grenfell, B. T., Global patterns in seasonal activity of influenza A/H3N2, A/H1N1, and B from 1997 to 2005: viral coexistence and latitudinal gradients, PLoS One, 2, 12, (2007) · doi:10.1371/journal.pone.0001296
[18] Shek, L. P.-C.; Lee, B.-W., Epidemiology and seasonality of respiratory tract virus infections in the tropics, Paediatric Respiratory Reviews, 4, 2, 105-111, (2003) · doi:10.1016/s1526-0542(03)00024-1
[19] Katz, M. A.; Schoub, B. D.; Heraud, J. M.; Breiman, R. F.; Njenga, M. K.; Widdowson, M.-A., Influenza in Africa: uncovering the epidemiology of a long-overlooked disease, Journal of Infectious Diseases, 206, 1, S1-S4, (2012) · doi:10.1093/infdis/jis548
[20] WHO, Influenza, (2017), Geneva, Switzerland: WHO, Geneva, Switzerland
[21] WHO, Influenza, (2018), Geneva, Switzerland: WHO, Geneva, Switzerland
[22] RGA, Seasonal Influenza and Mortality, (2018), St. Louis, MO, USA: RGA, St. Louis, MO, USA
[23] 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, Journal of Paediatrics and Child Health, 35, 2, 207-209, (1999) · doi:10.1046/j.1440-1754.1999.t01-1-00329.x
[24] Hien, T. T.; Liem, N. T.; Dung, N. T., Avian influenza a (H5N1) in 10 patients in Vietnam, New England Journal of Medicine, 350, 12, 1179-1188, (2004) · doi:10.1056/nejmoa040419
[25] Gao, R.; Cao, B.; Hu, Y., Human infection with a novel avian-origin influenza a (H7N9) virus, New England Journal of Medicine, 368, 20, 1888-1897, (2013) · doi:10.1056/nejmoa1304459
[26] 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, Journal of Virology, 92, 11, e00425–18, (2018) · doi:10.1128/jvi.00425-18
[27] Hurtado, T. R., Human influenza a (H5N1): a brief review and recommendations for travelers, Wilderness & Environmental Medicine, 17, 4, 276-281, (2006) · doi:10.1580/06-weme-ra-007r.1
[28] Li, F.; Choi, B.; Sly, T.; Pak, A., Finding the real case-fatality rate of H5N1 avian influenza, Journal of Epidemiology & Community Health, 62, 6, 555-559, (2008) · doi:10.1136/jech.2007.064030
[29] WHO, Influenza at the Human-Animal Interface, (2018), Geneva, Switzerland: WHO, Geneva, Switzerland
[30] Chen, H.; Yuan, H.; Gao, R., Clinical and epidemiological characteristics of a fatal case of avian influenza a h10n8 virus infection: a descriptive study, The Lancet, 383, 9918, 714-721, (2014) · doi:10.1016/s0140-6736(14)60111-2
[31] Zhang, Z.; Li, R.; Jiang, L., The complexity of human infected AIV H5N6 isolated from china, BMC Infectious Diseases, 16, 1, 600, (2016) · doi:10.1186/s12879-016-1932-1
[32] Huang, Y.; Li, X.; Zhang, H., Human infection with an avian influenza a (H9N2) virus in the middle region of china, Journal of Medical Virology, 87, 10, 1641-1648, (2015) · doi:10.1002/jmv.24231
[33] Yuan, J.; Zhang, L.; Kan, X., Origin and molecular characteristics of a novel 2013 avian influenza a (H6N1) virus causing human infection in Taiwan, Clinical Infectious Diseases, 57, 9, 1367-1368, (2013) · doi:10.1093/cid/cit479
[34] Alexander, M. E.; Bowman, C.; Moghadas, S. M.; Summers, R.; Gumel, A. B.; Sahai, B. M., A vaccination model for transmission dynamics of influenza, SIAM Journal on Applied Dynamical Systems, 3, 4, 503-524, (2004) · Zbl 1067.92051 · doi:10.1137/030600370
[35] Guo, D.; Li, K. C.; Peters, T. R.; Snively, B. M.; Poehling, K. A.; Zhou, X., Multi-scale modeling for the transmission of influenza and the evaluation of interventions toward it, Scientific Reports, 5, 1, (2015) · doi:10.1038/srep08980
[36] Srivastav, A. K.; Ghosh, M., Analysis of a simple influenza a (H1N1) model with optimal control, World Journal of Modelling and Simulation, 12, 4, 307-319, (2016)
[37] Mikolajczyk, R.; Krumkamp, R.; Bornemann, R.; Ahmad, A.; Schwehm, M.; Duerr, H., Influenza–insights from mathematical modelling, Deutsches Arzteblatt International, 106, 47, 777-782, (2009)
[38] Larson, E. W.; Dominik, J. W.; Rowberg, A. H.; Higbee, G. A., Influenza virus population dynamics in the respiratory tract of experimentally infected mice, Infection and Immunity, 13, 2, 438-447, (1976)
[39] Imran, M.; Malik, T.; Ansari, A. R.; Khan, A., Mathematical analysis of swine influenza epidemic model with optimal control, Japan Journal of Industrial and Applied Mathematics, 33, 1, 269-296, (2016) · Zbl 1333.92058 · doi:10.1007/s13160-016-0210-3
[40] Lee, S.; Chowell, G.; Castillo-Chávez, C., Optimal control for pandemic influenza: the role of limited antiviral treatment and isolation, Journal of Theoretical Biology, 265, 2, 136-150, (2010) · doi:10.1016/j.jtbi.2010.04.003
[41] Prosper, O.; Saucedo, O.; Thompson, D.; Torres-Garcia, G.; Wang, X.; Castillo-Chavez, C., Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza, Mathematical Biosciences and Engineering, 8, 1, 141-170, (2011) · Zbl 1260.92070
[42] Woolhouse, M.; Farrar, J., Policy: an intergovernmental panel on antimicrobial resistance, Nature, 509, 7502, 555-557, (2014) · doi:10.1038/509555a
[43] van der Vries, E.; Schutten, M.; Fraaij, P.; Boucher, C.; Osterhaus, A., Influenza virus resistance to antiviral therapy, Advances in Pharmacology, 67, 217-246, (2013) · doi:10.1016/B978-0-12-405880-4.00006-8
[44] Li, T.; Chan, M. C.; Lee, N., Clinical implications of antiviral resistance in influenza, Viruses, 7, 9, 4929-4944, (2015) · doi:10.3390/v7092850
[45] CDC, About Antimicrobial Resistance—Antibiotic/Antimicrobial Resistance, (2017), Atlanta, GA, USA: CDC, Atlanta, GA, USA
[46] Hayes, J. D.; Wolf, C. R., Molecular mechanisms of drug resistance, Biochemical Journal, 272, 2, 281, (1990) · doi:10.1042/bj2720281
[47] Blower, S.; Aschenbach, A.; Gershengorn, H.; Kahn, J., Predicting the unpredictable: transmission of drug-resistant HIV, Nature Medicine, 7, 9, 1016-1020, (2001) · doi:10.1038/nm0901-1016
[48] Blower, S.; Volberding, P., What can modeling tell us about the threat of antiviral drug resistance?, Current Opinion in Infectious Diseases, 15, 6, 609-614, (2002) · doi:10.1097/00001432-200212000-00009
[49] Ison, M. G.; Gubareva, L. V.; Atmar, R. L.; Treanor, J.; Hayden, F. G., Recovery of drug-resistant influenza virus from immunocompromised patients: a case series, Journal of Infectious Diseases, 193, 6, 760-764, (2006) · doi:10.1086/500465
[50] Kamali, A.; Holodniy, M., Influenza treatment and prophylaxis with neuraminidase inhibitors: a review, Infection and Drug Resistance, 6, 187, (2013)
[51] CDC, Influenza Antiviral Drug Resistance, (2017), Atlanta, GA, USA: CDC, Atlanta, GA, USA
[52] Hayden, F. G.; de Jong, M. D., Emerging influenza antiviral resistance threats, Journal of Infectious Diseases, 203, 1, 6-10, (2011) · doi:10.1093/infdis/jiq012
[53] Lipsitch, M.; Cohen, T.; Murray, M.; Levin, B. R., Antiviral resistance and the control of pandemic influenza, PLoS Medicine, 4, 1, e15, (2007) · doi:10.1371/journal.pmed.0040015
[54] Jnawali, K.; Morsky, B.; Poore, K.; Bauch, C. T., Emergence and spread of drug resistant influenza: a two-population game theoretical model, Infectious Disease Modelling, 1, 1, 40-51, (2016) · doi:10.1016/j.idm.2016.07.003
[55] McCaw, J. M.; Wood, J. G.; McCaw, C. T.; McVernon, J., Impact of emerging antiviral drug resistance on influenza containment and spread: influence of subclinical infection and strategic use of a stockpile containing one or two drugs, PLoS One, 3, 6, (2008) · doi:10.1371/journal.pone.0002362
[56] Ferguson, N. M.; Mallett, S.; Jackson, H.; Roberts, N.; Ward, P., A population-dynamic model for evaluating the potential spread of drug-resistant influenza virus infections during community-based use of antivirals, Journal of Antimicrobial Chemotherapy, 51, 4, 977-990, (2003) · doi:10.1093/jac/dkg136
[57] Stilianakis, N. I.; Perelson, A. S.; Hayden, F. G., Emergence of drug resistance during an influenza epidemic: insights from a mathematical model, Journal of Infectious Diseases, 177, 4, 863-873, (1998) · doi:10.1086/515246
[58] ISG, Vaccine Efficacy and Effectiveness, (2017), Melbourne, VIC, Australia: Influenza Specialist Group, Melbourne, VIC, Australia
[59] CDC, Flu Vaccine Coverage Remains Low This Year, (2017), Atlanta, GA, USA: Centers for Disease Control and Prevention, Atlanta, GA, USA
[60] Van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180, 1, 29-48, (2002) · Zbl 1015.92036 · doi:10.1016/s0025-5564(02)00108-6
[61] Nishiura, H.; Chowell, G., The effective reproduction number as a prelude to statistical estimation of time-dependent epidemic trends, Mathematical and Statistical Estimation Approaches in Epidemiology, 103-121, (2009), Berlin, Germany: Springer, Berlin, Germany · Zbl 1345.92151
[62] Rodrigues, H. S.; Monteiro, M. T. T.; Torres, D. F. M., Sensitivity analysis in a dengue epidemiological model, Conference Papers in Science, 2013, (2013) · doi:10.1155/2013/721406
[63] Chitnis, N.; Hyman, J. M.; Manore, C. A., Modelling vertical transmission in vector-borne diseases with applications to rift valley fever, Journal of Biological Dynamics, 7, 1, 11-40, (2013) · doi:10.1080/17513758.2012.733427
[64] Hategekimana, F.; Saha, S.; Chaturvedi, A., Dynamics of amoebiasis transmission: stability and sensitivity analysis, Mathematics, 5, 4, 58, (2017) · Zbl 1394.92123 · doi:10.3390/math5040058
[65] Chowell, G.; Hyman, J. M., Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases, (2016), Berlin, Germany: Springer, Berlin, Germany · Zbl 1351.92004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.