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 coexistence 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.