Open AccessBasic reinfection number and backward bifurcation
Author(s) -
Bingbing Song
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021400
Subject(s) - basic reproduction number , bifurcation , mathematics , measure (data warehouse) , phenomenon , reproduction , biology , computer science , medicine , physics , population , nonlinear system , genetics , quantum mechanics , database , environmental health
Some epidemiological models exhibit bi-stable dynamics even when the basic reproduction number $ {{{\cal R}_{0}}} $ is below $ 1 $, through a phenomenon known as a backward bifurcation. Causes for this phenomenon include exogenous reinfection, super-infection, relapse, vaccination exercises, heterogeneity among subpopulations, etc. To measure the reinfection forces, this paper defines a second threshold: the basic reinfection number. This number characterizes the type of bifurcation when the basic reproduction number is equal to one. If the basic reinfection number is greater than one, the bifurcation is backward. Otherwise it is forward. The basic reinfection number with the basic reproduction number together gives a complete measure for disease control whenever reinfections (or relapses) matter. We formulate the basic reinfection number for a variety of epidemiological models.