Research Article Open Access

Dynamical Analysis on the Transmission of Pertussis with Maternally Derived Immunity

Aisha Aliyu Yakubu1, Farah Aini Abdullah1, Ahmad Izani Md Ismail1 and Yazariah Mohd Yatim1
  • 1 Universiti Sains Malaysia, Malaysia
Journal of Mathematics and Statistics
Volume 16 No. 1, 2020, 104-112

DOI: https://doi.org/10.3844/jmssp.2020.104.112

Submitted On: 16 March 2020
Published On: 26 June 2020

How to Cite: Yakubu, A. A., Abdullah, F. A., Md Ismail, A. I. & Yatim, Y. M. (2020). Dynamical Analysis on the Transmission of Pertussis with Maternally Derived Immunity. Journal of Mathematics and Statistics, 16(1), 104-112. https://doi.org/10.3844/jmssp.2020.104.112

Abstract

A susceptible-infected-recovered compartmental model incorporating maternally derived immunity compartment is analyzed in this study. The stability of the pertussis-disease-free and endemic equilibrium is studied. The basic reproduction number is obtained and its behavior analyzed by varying parameters. Numerical simulations indicated that when the waning parameter is increased, the frequency at which the population attains stability varies. However, the infected population does not go extinct even at equilibrium.

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Keywords

  • Pertussis
  • Basic Reproduction Number
  • Stability Analysis
  • Numerical Simulations