Dynamical Analysis on the Transmission of Pertussis with Maternally Derived Immunity

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.