Acta Scientific Microbiology (ASMI) (ISSN: 2581-3226)

Review Article Volume 3 Issue 4

Mathematical Modeling of the 2019 Measles Outbreak on US Population

Durgesh N Sinha1*, Nicholas Klahn2 and Samiye Pehlivan3*

1Adjunct Assistant Professor, Temple University, Philadelphia, Strayer University, Rowan College at Burlington County, Community College of Philadelphia, Mercer County Community College, New Jersey, USA
2Senior student of Medical track, Rowan College at Burlington County, New Jersey, USA
3Sophomore student of Medical track, Rowan College at Burlington County, New Jersey, USA

*Corresponding Author: Durgesh N Sinha, Adjunct Assistant Professor, Temple University, Philadelphia, Strayer University, Rowan College at Burlington County, Community College of Philadelphia, Mercer County Community College, New Jersey, USA.

Received: March 11, 2020; Published: March 31, 2020

×

Abstract

  This paper analyzes the 2019 measles epidemic in the United States through a developed mathematical model. We simulated our model in MATLAB using differential equations and found that in vaccinated populations, viral spread was severely hindered when compared to populations that were unvaccinated. The lack of viral prevalence was backed up by the basic reproduction number being less than one (R0 = 0.03976).

Keywords: Mathematical Modeling; Measles; MATLAB

×

References

  1. MacFadden DR and Gold WL. “Measles”. CMAJ: Canadian Medical Association Journal6 (2014): 450.
  2. White SJ., et al. “Measles, mumps, and rubella”. Clinical Obstetrics and Gynecology2 (2012): 550-559.
  3. La Torre G., et al. “The effectiveness of measles-mumps-rubella (MMR) vaccination in the prevention of pediatric hospitalizations for targeted and untargeted infections: A retrospective cohort study”. Human Vaccines and Immunotherapeutics8 (2017): 1879-1883.
  4. Griffin DE. “The Immune Response in Measles: Virus Control, Clearance and Protective Immunity”. Viruses10 (2016): 282.
  5. Patel M., et al. “National Update on Measles Cases and Outbreaks - United States, January 1-October 1, 2019”. Morbidity and Mortality Weekly Report 68 (2019): 893-896.
  6. Patel M., et al. “Increase in Measles Cases - United States, January 1-April 26, 2019”. Morbidity and Mortality Weekly Report 68 (2019): 402-404.
  7. Pickering L., et al. “Red Book: 2009 Report of the Committee on Infectious Diseases (28th edition)”. American Academy of Pediatrics (2009).
  8. CDC/National Center for Health Statistics. “Vaccination coverage for selected diseases among children aged 19-35 months, by race, Hispanic origin, poverty level, and location of residence in metropolitan statistical area: United States, selected years 1998-2017” (2017).
  9. CDC/National Center for Health Statistics. “Vaccination coverage for selected diseases among adolescents aged 13-17 years, by selected characteristics: United States, selected years 2008-2017” (2017).
  10. National Notifiable Diseases Surveillance System (NNDSS). “Measles Cases and Outbreaks” (2020).
  11. Central Intelligence Agency. “The World Factbook: United States” (2018).
  12. Kamgang JC and Sallet G. “Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE)”. Mathematical Biosciences1 (2008): 1-12.
  13. Shuai Z and van den Driessche P. “Global Stability of Infectious Disease Models Using Lyapunov Functions”. SIAM Journal on Applied Mathematics 73 (2013): 1513-1532.
  14. Safi MA and Garba SM. “Global Stability Analysis of SEIR Model with Holling Type II Incidence Function”. Computational and Mathematical Methods in Medicine (2012): 826052.
  15. Melesse DY and Gumel AB. “Global asymptotic properties of an SEIRS model with multiple infectious stages”. Journal of Mathematical Analysis and Applications1 (2010): 202-217.
  16. Li MY., et al. “Global Dynamics of an SEIR Epidemic Model with Vertical Transmission”. SIAM Journal on Applied Mathematics 1 (2001): 58-69.
×

Citation

Citation: Durgesh N Sinha.,et al. “Mathematical Modeling of the 2019 Measles Outbreak on US Population".Acta Scientific Microbiology 3.4 (2020): 209-214.



Indexed In






News and Events


  • Certification for Review
    Acta Scientific certifies the Editors/reviewers for their review done towards the assigned articles of the respective journals.
  • Submission Timeline for Upcoming Issue
    The last date for submission of articles for regular Issues is December 15, 2020.
  • Publication Certificate
    Authors will be issued a "Publication Certificate" as a mark of appreciation for publishing their work.
  • Best Article of the Issue
    The Editors will elect one Best Article after each issue release. The authors of this article will be provided with a certificate of “Best Article of the Issue”.
  • Welcoming Article Submission
    Acta Scientific delightfully welcomes active researchers for submission of articles towards the upcoming issue of respective journals.
  • Contact US