Emergence of: a reversed backward bifurcation , reversed hysteresis
effect and backward bifurcation phenomenon in a COVID-19 mathematical
model
Abstract
A Coronavirus Disease 2019 (COVID-19) epidemiological model
incorporating a boosted infection-acquired immunity and heterogeneity in
infection-acquired immunity among recovered individuals is designed. The
model is used to investigate whether incorporating these two processes
can induce new epidemiological insights. Analytical findings reveal
co-existence of multiple endemic equilibria on either regions divided by
the fundamental threshold (control reproduction number). Numerical
findings conducted to validate analytical results show that
heterogeneity in infection-acquired immunity among recovered individuals
can induce various bifurcation structures such as reversed
backward bifurcation, forward bifurcation, backward
bifurcation and reversed hysteresis effect. Moreover, numerical
results show that reversed backward bifurcation is annihilated or
switches to the usual forward bifurcation if infection-acquired
immunity among recovered individuals with strong immunity is assumed to
be everlasting. However, this is only possible if primary infection is
more likely than reinfection. In case reinfection is more likely to
occur than primary infection, reversed backward bifurcation
structure switches to a backward bifurcation phenomenon. Further,
longer duration of infection-acquired immunity does lead to COVID-19
decline over time but does not lead to flattening of the COVID-19 peak.