Backward Bifurcation as a Desirable Phenomenon: Increased Fecundity Through Infection

Area of Science:

• Epidemiology
• Mathematical Biology
• Population Dynamics

Background:

• Backward or subcritical bifurcation is typically undesirable in epidemiological models, necessitating R₀ below a significantly reduced threshold for control.
• However, certain characteristics passed across generations can make this bifurcation advantageous, enhancing host reproductive rates or population size.

Purpose of the Study:

• To investigate an epidemiological model with susceptible and infected classes, focusing on characteristics like increased fecundity passed via contact.
• To analyze the conditions leading to a backward or subcritical bifurcation and its implications for population dynamics and fitness.

Main Methods:

• Development of a mathematical model incorporating susceptible and infected individuals with differential reproductive rates.
• Analysis of bifurcation conditions, particularly focusing on the role of susceptible and infected birth rates.
• Examination of how increased fecundity or 'inoculation' impacts population size and equilibrium.

Main Results:

• The study identifies conditions where a backward or subcritical bifurcation leads to a larger total population size at equilibrium, suggesting increased host fitness.
• A key finding is that an increase in susceptible newborns, driven by higher reproduction rates in infected individuals, is the primary cause of this desirable bifurcation.
• The model demonstrates that facilitating 'inoculation' can unexpectedly increase population size due to the backward bifurcation.

Conclusions:

• Contrary to typical assumptions, backward or subcritical bifurcations can be ecologically advantageous, promoting species survival and expansion.
• The model highlights the critical role of differential birth rates between infected and susceptible individuals in generating beneficial bifurcations.
• Findings have implications for understanding host-pathogen dynamics, particularly in systems like insect-Wolbachia interactions and amphibian populations.