Modeling Monkeypox Epidemics: Thresholds, Temporal Dynamics, and Waning Immunity from Smallpox Vaccination

This study investigates the dynamics of Monkeypox virus (MPXV) through a novel theoretical framework that extends classical epidemic threshold theory. The dual threshold theory is introduced, highlighting the interplay between the time-dependent basic reproduction number and the susceptible population density. Epidemic initiation is shown to occur when the time dependent reproductive number is greater than the threshold value of one and the susceptible population density at any time is greater than the critical threshold density of susceptibles. The model incorporates waning immunity from prior smallpox vaccination and immunity loss from previous MPXV infections, revealing complex epidemic behaviors such as oscillatory waves, prolonged outbreaks, and extended inter-epidemic periods under high transmission scenarios. Sensitivity analyses identify key drivers of epidemic initiation and progression, emphasizing the critical influence of waning immunity and zoonotic reservoirs. Public health implications underline the importance of targeted vaccination campaigns, rodent control, and continuous surveillance to reduce epidemic risks and prevent resurgence. This study provides actionable insights for managing MPXV outbreaks, while the dual threshold framework offers a robust theoretical foundation for understanding the dynamics of waning of vaccine cross immunity and zoonotic diseases.