The effect of the incidence function on the existence of backward bifurcation

  • David J. Gerberry Department of Mathematics, Xavier University, Cincinnati, OH, USA
  • Andrew M. Philip Department of Biology, Xavier University, Cincinnati, OH, USA
Keywords: Backward bifurcation, incidence function, mass action, standard incidence

Abstract

In modelling, the dynamics of infectious disease, the choice of the specific mathematical formulation of disease transmission (i.e. the incidence function) is one of the initial assumptions to be made. While inconsequential in many situations, we show that the incidence function can have an effect on the existence of backward bifurcation (the phenomenon where a disease can persist even when the basic reproductive number is less than 1). More specifically, we compare mass action (MA) and standard incidence (SI) (the most common incidence functions) versions of two hallmark models in the backward bifurcation literature and an original combination model. Our findings indicate that the SI formation of disease transmission is more conducive to backward bifurcation than MA, a trend seen in all the models analysed.

Published
2016-12-01
How to Cite
Gerberry, David J., and Andrew M. Philip. 2016. “The Effect of the Incidence Function on the Existence of Backward Bifurcation”. Letters in Biomathematics 3 (1), 181–199. https://doi.org/10.1080/23737867.2016.1217757.
Section
Research