Research article

Mathematical analysis of an SIR respiratory infection model with sex and gender disparity: special reference to influenza A

  • Received: 11 November 2017 Accepted: 01 December 2018 Published: 26 March 2019
  • The aim of this work is to study the impact of sex and gender disparity on the overall dynamics of influenza A virus infection and to explore the direct and indirect effect of influenza A mass vaccination. To this end, a deterministic SIR model has been formulated and throughly analysed, where the equilibrium and stability analyses have been explored. The impact of sex disparity (i.e., disparity in susceptibility and in recovery rate between females and males) on the disease outcome (i.e., the basic reproduction number $R_0$ and the endemic prevalence of influenza in females and males) has been investigated. Mathematical and numerical analyses show that sex and gender disparities affect on the severity as well as the endemic prevalence of infection in both sexes. The analysis shows further that the efficacy of the vaccine for both sexes ($e_1 \& e_2$) and the response of the gender to mass-vaccination campaigns $\psi$ play a crucial role in influenza A containment and elimination process, where they impact significantly on the protection ratio as well as on the direct, indirect and total effect of vaccination on the burden of infection.

    Citation: Muntaser Safan. Mathematical analysis of an SIR respiratory infection model with sex and gender disparity: special reference to influenza A[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2613-2649. doi: 10.3934/mbe.2019131

    Related Papers:

  • The aim of this work is to study the impact of sex and gender disparity on the overall dynamics of influenza A virus infection and to explore the direct and indirect effect of influenza A mass vaccination. To this end, a deterministic SIR model has been formulated and throughly analysed, where the equilibrium and stability analyses have been explored. The impact of sex disparity (i.e., disparity in susceptibility and in recovery rate between females and males) on the disease outcome (i.e., the basic reproduction number $R_0$ and the endemic prevalence of influenza in females and males) has been investigated. Mathematical and numerical analyses show that sex and gender disparities affect on the severity as well as the endemic prevalence of infection in both sexes. The analysis shows further that the efficacy of the vaccine for both sexes ($e_1 \& e_2$) and the response of the gender to mass-vaccination campaigns $\psi$ play a crucial role in influenza A containment and elimination process, where they impact significantly on the protection ratio as well as on the direct, indirect and total effect of vaccination on the burden of infection.


    加载中


    [1] B. Hancioglu, D. Swigon and G. Clermont, A dynamical model of human immune response to influenza A virus infection, J. Theor. Biol., 246 (2007), 70–86.
    [2] L. Mohler, D. Flockerzi, H. Sann, et al., Mathematical model of influenza A virus production in large-scale microcarrier culture, Biotechnol. Bioeng., 90 (2005), 46–58.
    [3] C. J. Luke and K. Subbarao, Vaccines for pandemic influenza, Emerg. Infect. Dis., 12 (2006), 66–72.
    [4] M. Erdem, M. Safan, C. Castillo-Chavez, Mathematical Analysis of an SIQR Influenza model with Imperfect quarantine, B. Math. Biol., 79 (2017), 1612–1636.
    [5] A. Flahault, E. Vergu, L. Coudeville, et al., Strategies for containing a global influenza pandemic, Vaccine, 24 (2006), 6751–6755.
    [6] B. J. Coburn, B. G.Wagner and S. Blower, Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1), BMC Med., 7 (2009), 30–37.
    [7] P. Y. Boelle, P. Bermillon, J. C. Desenclos, A preliminary estimation of the reproduction ratio for new influenza A(H1N1) from the outbreak in Mexico, March-April 2009, Eurosurveillance, 14 (2009), pii=19205.
    [8] H. Nishiura, C. Castillo-Chavez, M. Safan, et al., Transmission potential of the new influenza A (H1N1) virus and its age-specificity in Japan, Eurosurveillance, 14 (2009), pii=19227.
    [9] H. Nishiura H, G. Chowell, M. Safan, et al., Pros and cons of estimating the reproduction number from early epidemic growth rate of influenza A (H1N1) 2009, Theor. Biol. Med. Model., 7 (2010), 1–9.
    [10] M. Nuno, Z. Feng, M. Martcheva, et al., Dynamics of two-strain influenza with isolation and partial cross-immunity, SIAM J. Appl. Math., 65 (2005), 964–982.
    [11] A. L. Vivas-Barber, C. Castillo-Chavez and E. Barany, Dynamics of an "SAIQR" Influenza Model, Biomath., 3 (2014), 1–13.
    [12] H. Hethcote, M. Zhien and L. Shengbing, Effects of quarantine in six endemic models for infectious diseases, Math. Biosci., 180 (2002), 141–160.
    [13] A. Ruggieri, W. Malorni and W. Ricciardi, Gender disparity in response to anti-viral vaccines: new clues toward personalized vaccinology, Ital. J. Gender-Specific Med., 2 (2016), 93–98.
    [14] S. L. Klein, A. Pekosz, C. Passaretti, et al., Sex, Gender and Influenza, World Health Organization, Geneva, (2010), 1–58.
    [15] S. L. Klein and K. L. Flanagan, Sex differences in immune responses, Nat. Rev. Immunol., 16 (2016), 626–638.
    [16] D. Furman, B. P. Hejblum, N. Simon, et al., Systems analysis of sex differences reveals an immunosuppressive role for testosterone in the response to influenza vaccination, P. Natl. Acad. Sci. USA, 111 (2014), 869–874.
    [17] S. L. Klein, A. Hodgson and D. P. Robinson, Mechanisms of sex disparities in influenza pathogenesis, J. Leukoc. Biol., 92 (2012), 67–73.
    [18] S. L. Klein, I. Marriott and E. N. Fish, Sex-based differences in immune function and responses to vaccination, Trans. R. Soc. Trop. Med. Hyg., 109 (2015), 9–15.
    [19] A. Ruggieri, S. Anticoli, A. D'Ambrosio, et al., The influence of sex and gender on immunity, infection and vaccination, Ann. Ist. Super Sanità, 52 (2016), 198–204.
    [20] A. L. Fink and S. Klein, Sex and Gender Impact Immune Responses to Vaccines Among the Elderly, Physiology, 30 (2015), 408–416.
    [21] J. Fisher, N. Jung, N. Robinson, et al., Sex differences in immune responses to infectious diseases, Infection, 43 (2015), 399–403.
    [22] S. L. Klein, Sex influences immune responses to viruses, and efficacy of prophylaxis and therapeutic treatments for viral diseases, Bioessays, 34 (2012), 1050–1059.
    [23] J. V. Lunzen and M. Altfeld, Sex Differences in Infectious Diseases? Common but Neglected, J. Infect. Dis., 209(S3) (2014), S79–80.
    [24] X. Tan, L. Yuan, J. Zhou, et al., Modelling the initial transmission dynamics of influenza A H1N1 in Guangdong Province, China, Int. J. Infect. Dis., 17 (2017), e479–e484.
    [25] N. S. Cardell and D. E. Kanouse, Modeling heterogeneity in susceptibility and infectivity for HIV infection, in Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture notes in biomathematics, 88 (eds. C. Castillo-Chavez), Springer-Verlag, Berlin Heidelberg New York London Paris Tokyo Hong Kong, (1989), 138–156.
    [26] M. Safan and K. Dietz, On the eradicability of infections with partially protective vaccination in models with backward bifurcation, Math. Biosci. Eng., 6 (2009), 395–407.
    [27] M. Safan, M Kretzschmar and K. P. Hadeler, Vaccination based control of infections in SIRS models with reinfection: special reference to pertussis, J. Math. Biol., 67 (2013), 1083–1110.
    [28] O. Neyrolles and L. Quintana-Murci, Sexual Inequality in Tuberculosis, PLoS Med., 6 (2009), e1000199. https://doi.org/10.1371/journal.pmed.1000199.
    [29] World Health Organization, Global tuberculosis control 2009: epidemiology, strategy, financing, Geneva: WHO, 2009. Available from: http://www.who.int/tb/country/en/index.html.
    [30] European Centre for Disease Prevention and Control, Pertussis. In: ECDC. Annual epidemiological report for 2015. Stockholm: ECDC; 2017.
    [31] World Health Organization (2018), Global Health Observatory (GHO) data: Number of women living with HIV, accessed 29 November 2018, http://www.who.int/gho/hiv/epidemic$_ $status/cases$_$adults$_$women$_$children$_$text/en/.
    [32] U.S. Department of Health & Human Services, Office on Women's Health (last updated 21 November 2018), Women and HIV, accessed 29 November 2018, https://www. womenshealth.gov/hiv-and-aids/women-and-hiv.
    [33] Avert (last updated 21 August 2018), Global information and education on HIV and AIDS: Women and girls (HIV and AIDS), accessed 29 November 2018, https://www.avert.org/ professionals/hiv-social-issues/key-affected-populations/women.
    [34] O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The Construction of next-Generation Matrices for Compartmental Epidemic Models, J. R. Soc. Interface, 47 (2010), 873–885.
    [35] H. Thieme, Mathematics in Population Biology, Princeton university press, Princeton, New Jersey, 2003.
    [36] C. Castillo-Chavez, Z. Feng and W. Huang, On the computation of R0 and its role on global stability, in Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction (eds. C. Castillo-Chavez, S. Blower, P. van den Driessche, D. Krirschner and A. A. Yakubu), The IMA Volumes in Mathematics and its Applications 125, Springer-Verlag, New York, (2002), 229–250.
    [37] O. Patterson-Lomba, M. Safan, S. Towers, et al., Modeling the Role of Healthcare Access Inequalities in Epidemic Outcomes, Math. Biosci. Eng., 13 (2016), 1011–1041.
    [38] United States Centers for Disease Control and Prevention (2011) A CDC framework for preventing infectious diseases: Sustaining the Essentials and Innovating for the Future, October 2011.
    [39] World Health Organization. Evaluation of influenza vaccine effectiveness: a guide to the design and interpretation of observational studies, Geneva: World Health Organization, 2017.
    [40] H. L. Smith and H. Thieme, Dynamical Systems and Population Persistence, AMS, 2011.
    [41] M. Eichner, M. Schwehm, L. Eichner, et al., Direct and indirect effects of influenza vaccination, BMC Infect. Dis., 17 (2017), 308–315.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4060) PDF downloads(683) Cited by(3)

Article outline

Figures and Tables

Figures(11)  /  Tables(2)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog