1
How to cite this paper
APA: Molavi-Arabshahi, M & Moradi, B. (2026). Using mathematical models to understand and control Influenza A (H1N1) outbreaks with quarantine and treatment. Journal of Future Sustainability, 6(3), 181-192.
Chicago/Turabian: Molavi-Arabshahi, M & Moradi, B. 2026. "Using mathematical models to understand and control Influenza A (H1N1) outbreaks with quarantine and treatment." Journal of Future Sustainability 6, no. 3 (2026): 181-192.
AMA: Molavi-Arabshahi, M & Moradi, B. Using mathematical models to understand and control Influenza A (H1N1) outbreaks with quarantine and treatment. Journal of Future Sustainability. 2026;6(3):181-192.
References
Arino, J., Brauer, F., van den Driessche, P., Watmough, J., & Wu, J. (2006). Simple models for containment of a pan-demic. Journal of the Royal Society Interface, 3(8), 453–457. https://doi.org/10.1098/rsif.2006.0112
Boëlle, P. Y., Bernillon, P., & Desenclos, J. C. (2009). A preliminary estimation of the reproduction ratio for the new in-fluenza A (H1N1) from the outbreak in Mexico, March–April 2009. Eurosurveillance, 14(19), Article 19205, 1–4. https://doi.org/10.2807/ese.14.19.19205-en
Brauer, F., & Castillo-Chavez, C. (2012). Mathematical models in population biology and epidemiology (2nd ed.). Springer.
Brauer, F., Castillo-Chavez, C., & Feng, Z. (2019). Mathematical models in epidemiology. Springer.
Cauchemez, S., Donnelly, C. A., Reed, C., Ghani, A. C., Fraser, C., Kent, C. K., Finelli, L., & Ferguson, N. M. (2009). Household transmission of 2009 pandemic influenza A (H1N1) virus in the United States. New England Journal of Medicine, 361(27), 2619–2627. https://doi.org/10.1056/NEJMoa0905498
Centers for Disease Control and Prevention. (2010). CDC estimates of 2009 H1N1 influenza cases, hospitalizations and deaths in the United States, April 2009 – January 16, 2010. https://www.cdc.gov/h1n1flu/estimates_2009_h1n1.htm
Coen, P. G., Cartwright, K., & Stuart, J. (2000). Mathematical modelling of infection and disease due to Neisseria men-ingitidis and Neisseria lactamica. International Journal of Epidemiology, 29(1), 180–188. https://doi.org/10.1093/ije/29.1.180
Daley, D. J., & Gani, J. (2005). Epidemic modelling: An introduction. Cambridge University Press.
Diekmann, O., Heesterbeek, J. A. P., & Roberts, M. G. (2010). The construction of next-generation matrices for com-partmental epidemic models. Journal of the Royal Society Interface, 7(47), 873–885. https://doi.org/10.1098/rsif.2009.0386
Flahault, A., Vergu, E., & Boëlle, P. Y. (2009). Potential for a global dynamic of influenza A (H1N1). BMC Infectious Diseases, 9, Article 129, 1–4. https://doi.org/10.1186/1471-2334-9-129
Fraser, C., Donnelly, C. A., Cauchemez, S., Hanage, W. P., Van Kerkhove, M. D., Hollingsworth, T. D., Griffin, J. T., Baggaley, R. F., Jenkins, H. E., Lyons, E. J., Jombart, T., Hinsley, W. R., Grassly, N. C., Balloux, F., Ghani, A. C., Ferguson, N. M., Rambaut, A., Pybus, O. G., Lopez-Gatell, H., … Riley, S. (2009). Pandemic potential of a strain of influenza A (H1N1): Early findings. Science, 324(5934), 1557–1561. https://doi.org/10.1126/science.1176062
Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemis-try, 81(25), 2340–2361. https://doi.org/10.1021/j100540a008
Hanselman, D., & Littlefield, B. (2005). Mastering MATLAB 7. Prentice Hall.
Harrison, L. H., Dwyer, D. M., Maples, C. T., & Billmann, L. (1999). Risk of meningococcal infection in college stu-dents. JAMA, 281(20), 1906–1910. https://doi.org/10.1001/jama.281.20.1906
Kenah, E., Lipsitch, M., & Robins, J. M. (2008). Generation interval contraction and epidemic data analy-sis. Mathematical Biosciences, 213(1), 71–79. https://doi.org/10.1016/j.mbs.2008.02.009
Longini, I. M., Jr., Halloran, M. E., Nizam, A., & Yang, Y. (2004). Containing pandemic influenza with antiviral agents. American Journal of Epidemiology, 159(7), 623–633. https://doi.org/10.1093/aje/kwh092
Longini, I. M., Jr., Nizam, A., Xu, S., Ungchusak, K., Hanshaoworakul, W., Cummings, D. A. T., & Halloran, M. E. (2005). Containing pandemic influenza at the source. Science, 309(5737), 1083–1087. https://doi.org/10.1126/science.1115717
Rhodes, C. J., & Anderson, R. M. (2008). Contact rate calculation for a basic epidemic model. Mathematical Bioscienc-es, 216(1), 56–62. https://doi.org/10.1016/j.mbs.2008.08.007
Trottier, H., & Philippe, P. (2001). Deterministic modeling of infectious diseases: Theory and methods. The Internet Journal of Infectious Diseases, 1(2). https://print.ispub.com/api/0/ispub-article/11215
Weinstein, M. C., O'Brien, B., Hornberger, J., Jackson, J., Johannesson, M., McCabe, C., & Luce, B. R. (2003). Princi-ples of good practice for decision analytic modeling in health-care evaluation: Report of the ISPOR Task Force on Good Research Practices—Modeling Studies. Value in Health, 6(1), 9–17. https://doi.org/10.1046/j.1524-4733.2003.00234.x
Boëlle, P. Y., Bernillon, P., & Desenclos, J. C. (2009). A preliminary estimation of the reproduction ratio for the new in-fluenza A (H1N1) from the outbreak in Mexico, March–April 2009. Eurosurveillance, 14(19), Article 19205, 1–4. https://doi.org/10.2807/ese.14.19.19205-en
Brauer, F., & Castillo-Chavez, C. (2012). Mathematical models in population biology and epidemiology (2nd ed.). Springer.
Brauer, F., Castillo-Chavez, C., & Feng, Z. (2019). Mathematical models in epidemiology. Springer.
Cauchemez, S., Donnelly, C. A., Reed, C., Ghani, A. C., Fraser, C., Kent, C. K., Finelli, L., & Ferguson, N. M. (2009). Household transmission of 2009 pandemic influenza A (H1N1) virus in the United States. New England Journal of Medicine, 361(27), 2619–2627. https://doi.org/10.1056/NEJMoa0905498
Centers for Disease Control and Prevention. (2010). CDC estimates of 2009 H1N1 influenza cases, hospitalizations and deaths in the United States, April 2009 – January 16, 2010. https://www.cdc.gov/h1n1flu/estimates_2009_h1n1.htm
Coen, P. G., Cartwright, K., & Stuart, J. (2000). Mathematical modelling of infection and disease due to Neisseria men-ingitidis and Neisseria lactamica. International Journal of Epidemiology, 29(1), 180–188. https://doi.org/10.1093/ije/29.1.180
Daley, D. J., & Gani, J. (2005). Epidemic modelling: An introduction. Cambridge University Press.
Diekmann, O., Heesterbeek, J. A. P., & Roberts, M. G. (2010). The construction of next-generation matrices for com-partmental epidemic models. Journal of the Royal Society Interface, 7(47), 873–885. https://doi.org/10.1098/rsif.2009.0386
Flahault, A., Vergu, E., & Boëlle, P. Y. (2009). Potential for a global dynamic of influenza A (H1N1). BMC Infectious Diseases, 9, Article 129, 1–4. https://doi.org/10.1186/1471-2334-9-129
Fraser, C., Donnelly, C. A., Cauchemez, S., Hanage, W. P., Van Kerkhove, M. D., Hollingsworth, T. D., Griffin, J. T., Baggaley, R. F., Jenkins, H. E., Lyons, E. J., Jombart, T., Hinsley, W. R., Grassly, N. C., Balloux, F., Ghani, A. C., Ferguson, N. M., Rambaut, A., Pybus, O. G., Lopez-Gatell, H., … Riley, S. (2009). Pandemic potential of a strain of influenza A (H1N1): Early findings. Science, 324(5934), 1557–1561. https://doi.org/10.1126/science.1176062
Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemis-try, 81(25), 2340–2361. https://doi.org/10.1021/j100540a008
Hanselman, D., & Littlefield, B. (2005). Mastering MATLAB 7. Prentice Hall.
Harrison, L. H., Dwyer, D. M., Maples, C. T., & Billmann, L. (1999). Risk of meningococcal infection in college stu-dents. JAMA, 281(20), 1906–1910. https://doi.org/10.1001/jama.281.20.1906
Kenah, E., Lipsitch, M., & Robins, J. M. (2008). Generation interval contraction and epidemic data analy-sis. Mathematical Biosciences, 213(1), 71–79. https://doi.org/10.1016/j.mbs.2008.02.009
Longini, I. M., Jr., Halloran, M. E., Nizam, A., & Yang, Y. (2004). Containing pandemic influenza with antiviral agents. American Journal of Epidemiology, 159(7), 623–633. https://doi.org/10.1093/aje/kwh092
Longini, I. M., Jr., Nizam, A., Xu, S., Ungchusak, K., Hanshaoworakul, W., Cummings, D. A. T., & Halloran, M. E. (2005). Containing pandemic influenza at the source. Science, 309(5737), 1083–1087. https://doi.org/10.1126/science.1115717
Rhodes, C. J., & Anderson, R. M. (2008). Contact rate calculation for a basic epidemic model. Mathematical Bioscienc-es, 216(1), 56–62. https://doi.org/10.1016/j.mbs.2008.08.007
Trottier, H., & Philippe, P. (2001). Deterministic modeling of infectious diseases: Theory and methods. The Internet Journal of Infectious Diseases, 1(2). https://print.ispub.com/api/0/ispub-article/11215
Weinstein, M. C., O'Brien, B., Hornberger, J., Jackson, J., Johannesson, M., McCabe, C., & Luce, B. R. (2003). Princi-ples of good practice for decision analytic modeling in health-care evaluation: Report of the ISPOR Task Force on Good Research Practices—Modeling Studies. Value in Health, 6(1), 9–17. https://doi.org/10.1046/j.1524-4733.2003.00234.x